How do you evaluate \frac { 1} { x + 1} + \frac { 3} { 3x - 13} = \frac { 2} { x - 7}?

1 Answer
Jul 5, 2017

x=3

Explanation:

First, we will transfer all the terms to one side and then get one fraction:

1/(x+1)+3/(3x-13)-2/(x-7)=0

((3x-13)(x-7)+3(x+1)(x-7)-2(x+1)(3x-13))/((x+1)(3x-13)(x-7))=0

Then we will expand the numerator:

cancel(3x^2)-21x-13x+91cancel(+3x^2)-21x+3x-21cancel(-6x^2)+26x-6x+26=0

and state that

x!=-1 and x!=13/3 and x!=7

Let's sum like terms and get:

-32x+96=0

and the solution is:

x=96/32=3