Question 62197
x/(x+2) - 3/(x-2) = (2x+12)/(x^2-4)

We know (x+2)(x-2) = (x^2-4)

Multiplying through out by the LCD = (x+2)(x-2)...

x(x-2) - 3(x+2) = 2x+12

==> x^2 - 2x - 3x - 6 = 2x + 12

==> x^2 - 5x - 6 = 2x + 12

==> x^2 - 5x - 6 - 2x - 12 = 0  [adding - 2x - 12 to both the sides]

==> x^2 - 7x - 18 = 0

==> x^2 - 9x + 2x - 18 = 0  [splitting the middle term]

==> x(x-9) + 2(x-9) = 0  [removing the common factor]

==> (x-9)(x+2) = 0

==> x-9 = 0   or  x+2 = 0

==> x = 9  or  x = -2

Good Luck!!!