How do you solve (x-6/5)/x-(x-10 1/2)/(x-5)=(x+21)/(x^2-5x)x65xx1012x5=x+21x25x?

1 Answer
Nov 5, 2017

x = 50/11x=5011

Explanation:

Rewriting the right side of the equation,
The common denominator is x^2 - 5xx25x

((x-5)(x-6/5))/(x^2 - 5x) - (x(x-10.5))/(x^2 - 5x) = (x+21)/(x^2 - 5x)(x5)(x65)x25xx(x10.5)x25x=x+21x25x

Multiplying both sides of the equation by x^2 - 5xx25x,

(x-5)(x-6/5) - x(x-10.5) = x+21(x5)(x65)x(x10.5)=x+21

Simplifying further,
(x^2 - 31/5x + 6) - (x^2 - 10.5x) = x+21(x2315x+6)(x210.5x)=x+21
x^2 - 31/5x - x^2 + 10.5x - x=21-6x2315xx2+10.5xx=216
-33/10x = 153310x=15
x = 50/11x=5011