Solve the equation by factoring: x/(x-3)+7/(x+3)=18/(x^2-9)?

Question

precal problem

Answer 1

x / (x - 3) + 7 / (x + 3) = 18 / (x - 3) (x + 3)
x (x + 3) + 7 (x - 3) = 18
x ² + 3 x + 7 x - 21 = 18
x ² + 10 x - 39 = 0
(x + 13) (x - 3) = 0
x = - 13 , x = 3

Answer 2

Hi,

x = -13

First, your last denominator factors into (x-3)(x+3). To solve this problem, multiply each term by the common denominator of (x-3)(x+3). After cancelling out the denominators, this gives:

x(x+3) + 7(x-3) = 18

This simplifies and solves as follows:

x² + 3x + 7x - 21 = 18
x² + 10x - 39 = 0
(x + 13)(x - 3) = 0
x = -13 or x = 3

The answer x = 3 must be discarded because it makes the denominator equal to zero. So the only good answer is x = -13. (It checks too.)

I hope that helps!! :-)