How do you solve #x/(x+2) - 2/(x-2) = (x^2+4)/(x^2-4)#?
1 Answer
Multiply through by
Explanation:
Given:
#x/(x+2)-2/(x-2) = (x^2+4)/(x^2-4)#
Note that
Multiply both sides by
#x(x-2)-2(x+2) = x^2+4#
Note that this potentially (and does) introduces spurious solutions for
The left hand side simplifies as follows:
#x(x-2)-2(x+2) = x^2-2x-2x-4 = x^2-4x-4#
So the equation becomes:
#color(red)(cancel(color(black)(x^2)))-4x-4 = color(red)(cancel(color(black)(x^2)))+4#
Subtract
#-4x = 8#
Divide both sides by
#x=-2#
This is not a solution of the original equation, since if
So the original problem has no solutions.