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#