You can put this solution on YOUR website! We need to multiply everything by the lowest common denominator in order to clear away all of the fractions...this is the normal first step in problems like this...what are called rational equations...so from
(6)/(x + 2) + (2x)/(2 - x) = (-24)/(x^2 - 4)
we multiply everything by (x^2 - 4)...
(x^2 - 4)[(6)/(x + 2) + (2x)/(2 - x) = (-24)/(x^2 - 4)]
and get
6(x - 2) - 2x(x + 2) = -24 notice the sign change on the second term
Now expand, combine and solve
6x - 12 - 2x^2 - 4x = -24
-2x^2 + 2x + 12 = 0 divide by -2
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0
x = 3 or x = -2
But here you must check to see if your solutions are allowable...notice that x = -2 is not allowable in the original problem since the denominator goes to zero...thus the only answer is
x = 3
