How do you solve x/(x+2) - 2/(x-2) = (x^2+4)/(x^2-4)?

1 Answer
Konstantinos Michailidis
Feb 27, 2016

There are no real solutions

Explanation:

First we must exclude the values that nullifies the denominators
which are x=2 and x=-2
It is

x/(x+2) - 2/(x-2) = (x^2+4)/(x^2-4)=> (x*(x-2)-2*(x+2))/(x^2-4)=(x^2+4)/(x^2-4)=> (x^2-4x-4)/(x^2-4)=(x^2+4)/(x^2-4)=> 1/(x^2-4)*[x^2-4x-4-x^2-4]=0=> 1/(x^2-4)*(-4x-8)=0=> -4*(x+2)/[(x-2)*(x+2)]=0=> -4/(x-2)=0

From the last equation is apparent that there no real solutions

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