How to add rational expressions.

Answers

Answer 1
First, some general rules to remember:

Rational expressions (fractions) can only be added or subtracted if they have a common denominator.
The numerator and denominator of a fraction may be multiplied by the same quantity. This will result in a fraction that is equivalent to the original fraction.
For a fractional answer to be in final form, the fraction must be reduced to lowest terms.
Adding or subtracting rational expressions is a four-step process:

Write all fractions as equivalent fractions with a common denominator.
Combine the fractions as a single fraction that has the common denominator.
Simplify the expression in the top of the fraction.
Reduce the fraction to lowest terms.
To see this process, we'll look at some examples.


Example 1

Step 1: To find a common denominator, start by factoring the denominators of both fractions.



The least common denominator of these two fractions is 2(x+6)(x-6).

Looking at the first fraction, we can see that the factor missing from its denominator is (x-6). In the next step, we'll multiply the top and bottom of the first fraction by (x-6).

Looking at the second fraction, we can see that the factor missing from its denominator is 2. In the next step, we'll multiply the top and bottom of the second fraction by 2.






Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:






Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.



Step 4: Now we'll reduce the fraction to lowest terms










Example 2



Step 1: To find a common denominator, start by factoring the denominators of both fractions.



The least common denominator of these two fractions is (x+4)(x+1)(x+3).

Looking at the first fraction, we can see that the factor missing from its denominator is (x+3). In the next step, we'll multiply the top and bottom of the first fraction by (x+3).

Looking at the first fraction, we can see that the factor missing from its denominator is (x+4). In the next step, we'll multiply the top and bottom of the first fraction by (x+4).






Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:






Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.










Step 4: Now we'll reduce the fraction to lowest terms


Related Questions

Please help I don’t understand

Answers

Write your questions

Answer:

The value of x so f (x) = 7 is 5.

Step-by-step explanation:

Who has the best conclusion?
A.Sheryl said the lowest grade was a 70 and the highest grade was a 92.
B.Shania said the highest grade was a 100.
C.Andrea said the lowest grade was a 68 and the highest grade was a 92.
D.Allen said the range of the scores was 32.​

Answers

Answer:

B. Shania's conclusion is the only accurate one.

Step-by-step explanation:

How to graph an equation.

Answers

Answer:

Below

Step-by-step explanation:

To graph an equation, we must have a y-intercept and a slope. Now, our equation is y = mx + b

We just replace the slope with 'm' and the y-intercept with 'b'. Let's say that our slope is 4 and y-intercept is 5. Then our equation will be y = 4x + 5.

Hoped this helped.

What is an equation of the line perpendicular to
y=1/5x+2 that contains (15,-4)

Answers

Answer:

y + 4 = -5(x - 15)

Step-by-step explanation:

The given line has a slope of 1/5.  Any new line perpendicular to this given line has a slope which is the negative reciprocal of 1/5:  -5.

Use the point-slope equation of a line:  y - k = m(x - h), where (h, k) is the point through which the new line passes.  Here h = 15 and k = -4, so we have:

y + 4 = -5(x - 15)

This line is perpendicular to the given line and also passes through (15, -4).

Find x if the line through the points (6, x) and (1,-5) has a slope of 2.

Answers

Answer:

Step-by-step explanation:

Use the slope formula

m = (y2 - y1)/(x2 - x1)

y2 = x

y1 = -5

x2 = 6

x1 = 1

m = 2

Solution

2 = (x - - 5)/(6 - 1)

2 = (x + 5)/ 5                   Multiply both sides of the equation by 5

5*2 = 5(x + 5)/5              Simplify

10 = x + 5                         Subtract 5 from both sides

10-5 = x

x = 5

what is the answer??????​

Answers

Answer:

1) B. 1 1/32

2) A. 1.8

Solution:

2 3/4 as an improper fraction is 11/4.

2 2/3 as an improper fraction is 8/3.

11/4 ÷ 8/3

11/4 ÷ 3/8 (reciprocal method)

11/4 × 3/8 (change the operation to multiplication)

11/4 × 3/8 = 33/32 (multiply)

33/32 ⇒ 1 1/32 (simplify)

1 4/5 as an improper fraction is 9/5.

9/5 ⇒ 1.8

The 66-mm-diameter solid shaft is made of 2014-t6 aluminum and is subjected to the distributed and concentrated torsional loadings shown where t=1. 7 kn⋅m.

Answers

Answer:

bbc

Step-by-step explanation:

Evaluate $\frac{20}{101}-\frac{20}{99}$. Express your answer in simplest form.

Answers

Detail: 37









Answer: 69


Gummi


Blick: 55

The times for running a 5K for a local charity event are Normally distributed with a mean time of 28 minutes and
standard deviation of 5.4 minutes. Which time represents the 60th percentile?
Find the z-table here.

A. 19.6 minutes
B. 26.6 minutes
C. 29.4 minutes
D. 36.4 minutes

Answers

Answer:

29.4 minutes represents the 60th percentile

Step-by-step explanation:

Given :  The times for running a 5K for a local charity event are Normally distributed, with a mean time of 28 minutes and standard deviation of 5.4 minutes.

To Find : Which time represents the 60th percentile?

 19.6 minutes

26.6 minutes

29.4 minutes

36.4 minutes

Solution:

time represents the 60th percentile

Means  60 % data = 0.6 below this

from z table ,  z score for this =  0.253

z score  = ( Value - Mean ) / SD

=> 0.253  = ( Value - 28 ) /5.4

=> 1.3662  =  Value - 28

=>  Value = 29.3662

=>  Value = 29.4

29.4 minutes represents the 60th percentile

: Mr. Burkett drove his car at an average speed of 70 miles per hour for 3.5 hours and then traveled at an

average speed of 65 miles per hour for 2.5 hours. What was the total distance in miles that he traveled during this time?

Answers

Answer:

Mr Burkett travelled 407.5 miles during his full trip.

Step-by-step explanation:

First, we must determine the distance he travelled in the first 3.5 hours. Luckily, we know his speed during that time so we can just multiply 70 miles per hour by 3.5 hours. That is 245 miles.

In the second step, we must determine the distance he travelled during the second part of his trip where he slowed down a bit. 65 miles per hour times 2.5 hours is 162.5 miles.

Finally, we can just add them! 245 + 162.5 = 407.5.

57 multiplied 2794?
IXL question

Answers

Ok the answer is 159,258

Here is an inequality -10+x÷4+5>7x-5÷3

Answers

Answer:

here is the answer x>1/2

A phone is regularly priced at $350. If you get it on sale for 15% off, how much do you pay?

Answers

52.5

Explanation:
x/18. 30/100 cross multiply 30*18=5250
5250 divided by 100= 52.5
The answer is 52.5 because once you divide 5250/100 then you get 52.5

(a + 2)/(a ^ 2 + a) - 3/(a - 2)​

Answers

Answer:

Step-by-step explanation:

(a + 2)/(a ^ 2 + a) - 3/(a - 2)​

The LCD is (a^2 + a)(a - 2) so we have

[(a + 2) - 3(a^2 + a)] /  (a^2 + a)(a - 2)

= (-3a^2 - 3a + a + 2) / (a^2 + a)(a - 2)

= -3a^2 - 2a + 2 / (a^2 + a)(a - 2)

What is the equation of this graphed line?



Enter your answer in slope-intercept form in the box.
__________

Answers

Answer:

y = 2x +2

Step-by-step explanation:

The general slope-intercept equation of a line is y=mx+b , where m is the slope and b is the y-intercept ( where the line intersects the y-axis)

From the graph we see that

m= difference in y/difference in x = (6 - -6)/ (2- -4) = 12/6 = 2

m=2 is the slope

b is where the line cuts the y-axis and is at 2

b=2 is the y-intercept

Substitute m and b in the general equation to find the equation of the graphed line.

y = 2x +2

HELPPPPPPP plssssssss

Answers

Answer:

The length of FB IS D) 7 units

A vertical parabola has its vertex in the second quadrant and y=ax2+bx is the equation of this parabola. Sketch the line that has equation y=ax+b.

Answers

The vertex of a parabola is the minimum or the maximum point of the parabola.

See attachment for the equation of [tex]\mathbf{y = 2x + 1}[/tex]

The equation of the parabola is given as:

[tex]\mathbf{y = ax^2 + bx}[/tex]

For the vertex of the parabola to be in the second quadrant, then the following must be true:

a > 0 and b > 0

Take for instance:

a = 2, and b = 1

So, we have:

[tex]\mathbf{y = 2x^2 + 1x}[/tex]

Rewrite as:

[tex]\mathbf{y = 2x^2 + x}[/tex]

Factor out x

[tex]\mathbf{y = x(2x + 1)}[/tex]

So, the line equation is:

[tex]\mathbf{y = 2x + 1}[/tex]

See attachment for the equation of [tex]\mathbf{y = 2x + 1}[/tex]

Read more about parabolas at:

https://brainly.com/question/20333425

You are choosing between two health clubs Club A offers membership for a fee of $21 plus a monthly fee of $20. Club B offers
membership for a fee of $35 plus a monthly fee of $13. After how many months will the total cost of each health club be the same?

Answers

Answer:

$$x=5$$, so after five months the costs would equal each other

Step-by-step explanation:

i think pls mark brainliest

10. Simplify each 12x°(x-4) x=6​

Answers

Answer: 144

Step-by-step explanation:

since x=6  and im assuming ° means multiplication

12(6) times (6-4)

72 times 2

144

Answer:

144

Step-by-step explanation:

(12)(6)(6−4)

=144

If x # y = 2x + y, then 1 # 2 =

Answers

Answer:

1 # 2 = 4

Step-by-step explanation:

1 # 2 = 2*1 + 2 = 2 + 2 = 4

to return a book to the library on time, Billy needs to read 40 pages every day. However, Billy reads 15 fewer pages than he should each day, and returns the book 6 days late. In how many days was he supposed to read the book?

Answers

Using proportions, it is found that he was supposed to read the book in 10 days.

This question can be solved by proportions, using a inverse rule of three, as when the number of pages read per day increases, the time to finish the book decreases.Reading 40 pages every day, he finishes the book in x days. He read 40 - 15 = 25 pages every day, and finished the book in x + 6 days, hence, the rule of three is:

40 pages - x days

25 pages - x + 6 days

Applying line multiplication, as it is an inverse rule of three:

[tex]40x = 25(x + 6)[/tex]

[tex]40x = 25x + 150[/tex]

[tex]15x = 150[/tex]

[tex]x = \frac{150}{15}[/tex]

[tex]x = 10[/tex]

He was supposed to read the book in 10 days.

A similar problem is given at https://brainly.com/question/24372153

Don’t understand please help

Answers

Answer:

Table I blank is 1

Table II blank is 1.398

6457/25 using partial products

Set up using the same way please.

Answers

Answer: 6457/25=258.28

Step-by-step explanation:

Answer:

258.28  Hope this helps! Please mark brainliest it means a lot to me

Step-by-step explanation:

Th=0

H=2

T=5

0=8

tenth=2

hundredth=8

You could get the answer by doing long division/standard algorithm

Solve for x

#6:

X=_

#7

X= _​

Answers

Step-by-step explanation:

for the first one let's write our equation

(13x+2)+(3x-4)+(5x-7)=180

Combine like terms

21x-9=180

Add 9 to both sides

21x=189

Divide both sides by 21

x=9

Now for the second one

Let's write our equation

(19x-18)+(7x+1)+(10x-9)=180

Combine like terms

36x-26=180

Add 26 to both sides

36x = 206

Divide both sides by 36

x = 5.72222...

Theo leased a corvette for his wedding. The total cost (C) was $777. Find out how many hours the corvette was leased using the equation: C = 10h + 75

I MIGHT GIVE BRAINLY PLS HELP 100 POINTS

Answers

Answer:

70.2

Step-by-step explanation:

777 = 10h + 75

=> 702 = 10h

=> h = 70.2

Therefore, it took 70.2 hours to lease the corvette.

Hoped this helped.

I NEED HELPP!!!
Penny attended a four year state college. She took out a student loan to pay for her tuition and room & board for the four years she was attending the college. Her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. Now that she has graduated, she will have to start paying back her loan. Fortunately, Penny has a grace period of one year before she has to start paying back the loan. Her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. During her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. Her goal is to be able to payoff the loan in 10 years.
_______________________________________________
Given all of this information, answer the following questions:

1. What is the original loan amount, i.e. how much were the total costs for tuition plus room & board for the four years that Penny attended the college?

2. What is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? This is the amount that she will be responsible for paying back. (Round your answer to the nearest whole dollar)

3. Given that she can pay back the loan in full after 10 years of payments, what is the total amount she will end up paying back (both principal and interest that has accrued over the 10 years)? And how much will her monthly payments on the loan be for those 10 years? (Round your answers to the nearest whole dollar)

I will mark most brainlest whoever gets it right for me :)))

Answers

Sorry I can't help you :(

Put 62%, 0.71, 0.8, 5/8 in ascending order

Answers

Answer:

0.62 < 5/8 < 0.71 < 0.8

That’s it in ascending order

0.8 > 0.71 > 5/8 > 0.62

That’s it in descending order

Step-by-step explanation:

Answer:

62%, 5/8, 0.71, 0.8

Step-by-step explanation:

62% in form of a decimal is 0.62 and 5/8 is 0.625 when u round off its 0.63 which is 0.01 more than 62%. then 0.71 is 0.1 less than 0.8

On a sunny day, Michelle and Nancy noticed that their shadows were different lengths. Nancy measured Michelle's shadow and found that it was 24.0 inches long. Michelle then measured Nancy's shadow and found that it was 13.5 inches long.

Answers

Answer: Whats the catch? Its just telling how long their shadows are. Are you missing a part of the problem? If yes, 24.0 (michelle) is 10.5 inches longer than nancy’s shadow (13.5) Or if you have to find the total, 24.0 + 13.5 = 37.5 inches.

If 6 numbers have a mean of 5, and five of the numbers are 3, 2, 1, 7, and 6, what is the sixth number?​

Answers

Answer:

see below

Step-by-step explanation:

the total value of the 6 numbers is 30 and the sum of the given 5 numbers is 19 therefore the 6th number is 11

Definition: An event that is made up of two or more outcomes is called
Example: Rolling a 5 on a die and flipping heads on a coin.

Answers

A compound event, I believe
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