solving rational equation

trying to figure out where i did wrong
x/x-4 -4/x-5 = 4/x^2-9x +20

x/x-4 -4/x-5= 4/(x-4)(x-5)
domain x not equal +- 4,5

x(x-4)(x-5)/x-4 - 4(x-4)(x-5)/x-5= 4(x-4)(x-5)/(x-4)(x-5)

x(x-5)-4(x-4)=4
x^2-5x-4x+16=4
x^2-9x+16=4
x^2-9x+16-4=4
x^2-9x+16-4=0
x^2-9x+12=0
(x-2)(x-6)

4 answers

x^2-9x+12=0***right so far
(x-2)(x-6) ***recheck this. What two numbers multiply to 12 and add to 9?
1 x 12
2 x 6
3 x 4
it would be none of these
The world is not made of whole numbers. Use the quadratic equation.

And, recheck the math. I checked it twice, and that was the only error I could find.
Y=7x-16, -7x+y=3 are the lines perpendicular, parallel or niether