How do you solve the rational equation #(2x) / (x+2) - 2 = (x-8) / (x-2)#?

1 Answer
Dec 24, 2016

Answer:

The solution for the above rational equation is #x=6,-4#

Explanation:

#(2x)/(x+2)-2=(x-8)/(x-2)#

or, #(2x-2(x+2))/(x+2)=(x-8)/(x-2)rarr#Take LCM on LHS.

or, #(2x-2x-4)/(x+2)=(x-8)/(x-2)rarr#Simplify LHS.

or, #(-4)/(x+2)=(x-8)/(x-2)#

or, #(-4)*(x-2)=(x+2)(x-8)rarr# Cross Multiply.

or, #-4x+8=x(x-8)+2(x-8)rarr#Simplify.

or, #-4x+8=x^2-8x+2x-16rarr#Simplify.

or, #-4x+8=x^2-6x-16rarr#Simplify

or, #-4x+4x+8-8=x^2-6x+4x-16-8rarr#Adding #4x#

and subtracting #8# from both sides.

or, #x^2-2x+24=0rarr#By simplifying RHS.

or, #x^2+4x-6x-24=0rarr#Factoring new LHS.

or, #x(x+4)-6(x+4)=0#

or, #(x-6)(x+4)=0rarr#Factored new LHS.

Either

#x-6=0#

or, #x=6#

Or,

#x+4=0#

or, #x=-4#

Hence, the solution for this equation is #x=6,-4#