How do you solve \frac { 7x } { x - 1} - \frac { 8x } { x - 9} = \frac { 4} { x ^ { 2} - 10x + 9}?

1 Answer
Jun 11, 2018

x=-15 and x=-9

Explanation:

Factoring: gives you
(x^2-10x+9)=(x-9)xx(x-1)

Therefore the original question:

(7x)/(x-1) - (8x)/(x-9) = 4/(x^2-10x+9)

can easily be solved by multiplying both sides with

(x-1)xx(x-9), and then solving for x: :

7x(x-9) - 8x(x-1) = 4

7x^2-36x-8x^2+8x-4=0

-(x^2+24x+4)=0

x^2+24x+4=0

again, factoring gives you the two solutions for x:

x=(-24+-sqrt(24^2-4xx4xx1))/(2xx1) = (-24+-6)/2 =

-> x=-15 and x=-9