How do you solve #(x-2)/(x+5) - 4/(x+1) = 1/(x+1)#?

1 Answer
Mar 17, 2018

Answer:

#x=9# or #x=-3#

Explanation:

First, lets rewrite the equation in the form

#(x-2)/(x+5) - 5/(x+1) = 0#

Then we multiply both sides of the equation by #(x+5)(x+1)# to get rid of the denominators.

This changes the equation to

#(x-2)(x+1)-5(x+5)=0 implies#
#(x^2-x-2)-(5x+25)=0 implies#
#x^2-6x-27=0 implies#
#x^2-9x+3x-27=0 implies#
#x(x-9)+3(x-9)=0 implies#
#(x-9)(x+3)=0#

Thus, either #x=9# or #x=-3#