How do you solve (x-6/5)/x-(x-10 1/2)/(x-5)=(x+21)/(x^2-5x)?

1 Answer
Nov 5, 2017

x = 50/11

Explanation:

Rewriting the right side of the equation,
The common denominator is x^2 - 5x

((x-5)(x-6/5))/(x^2 - 5x) - (x(x-10.5))/(x^2 - 5x) = (x+21)/(x^2 - 5x)

Multiplying both sides of the equation by x^2 - 5x,

(x-5)(x-6/5) - x(x-10.5) = x+21

Simplifying further,
(x^2 - 31/5x + 6) - (x^2 - 10.5x) = x+21
x^2 - 31/5x - x^2 + 10.5x - x=21-6
-33/10x = 15
x = 50/11