xx22x24xx24Solutionxx22x24xx24 Subtract from both sides xx22
x/(x-2)-2/(x+2)=4x/(x^2-4)
Solution
x/(x-2)-2/(x+2)=4x/(x^2-4)
Subtract from both sides:
x/(x-2)-2/(x+2) - 4x/(x^2-4) =0
Taking (x-2)(x+2) as LCD :
{ x(x+2) -2(x-2) -4x }/(x^2-4) =0\\
{ x^2 +2x -2x+4 -4x }/(x^2 -4) =0
( x^2 -4x +4}/(x^2 -4) =0
Equating numerator to zero:
x^2 -4x+4=0
(x-2)^2 =0
x= 2, 2

