# How do you solve #7/(x-4) = 1 + 9/(x+4)#?

##### 2 Answers

#### Explanation:

first, a common denominator for all the fractions needs to be found.

this is the lowest common multiple of

since

this gives

the denominator can then be taken away by multiplying everything by

then the brackets can be expanded:

(difference of two squares identity:

collect like terms:

then subtract

subtract

this forms a quadratic eqaution that can be factorised.

to do this, find two numbers that add to make

and multiply to make

for the number on the right-hand side to be

either

if

if

this means that the two possible values for

#### Explanation:

1) Give the addends on the right side a common denominator

2) Add the like fractions on the right by adding the numerators and keeping the common denominator

3) Combine like terms in the numerator on the right

4) Clear the first fraction by multiplying both sides by

5) Clear the second fraction by multiplying both sides by

6) Clear the parentheses by distributing the

7) Subtract

8) Set the equation to

9) Factor

10) Set the factors equal to

Answer:

**Check**

Sub in

Reduce the fraction to lowest terms