2 - 12/(4 - x) = (2x + 4) / (x^2 - 16) we can rewrite this as
2 + 12/(x - 4) = 2(x + 2)/ [(x - 4) (x + 4) ] multiply through by [(x - 4) (x + 4) ]
2 [(x - 4) (x + 4) ] + 12(x + 4) = 2(x + 2) divide thrrough by 2
[(x - 4) (x + 4)] + 6(x + 4) = x + 2 simplify
x^2 - 16 + 6x + 24 = x + 2
x^2 + 6x + 8 = x + 2
x^2 + 5x + 6 = 0 factor
(x + 3) (x + 2) = 0 and setting each factor to 0 we have x = -2 or x = -3
{There are no extraneous solutions }
2 - 12/(4 - x) = (2x + 4) / (x^2 - 16) we can rewrite this as
2 + 12/(x - 4) = 2(x + 2)/ [(x - 4) (x + 4) ] multiply through by [(x - 4) (x + 4) ]
2 [(x - 4) (x + 4) ] + 12(x + 4) = 2(x + 2) divide thrrough by 2
[(x - 4) (x + 4)] + 6(x + 4) = x + 2 simplify
x^2 - 16 + 6x + 24 = x + 2
x^2 + 6x + 8 = x + 2
x^2 + 5x + 6 = 0 factor
(x + 3) (x + 2) = 0 and setting each factor to 0 we have x = -2 or x = -3
{There are no extraneous solutions }