Question 62144
{{{x/(x+2) + 2/(x-2) = (-2x+19)/(x^2-4)}}} Factorise the expression on the bottom on the right as it is a difference of squares.
{{{x/(x+2) + 2/(x-2) = (-2x+19)/((x-2)(x+2))}}} Rewrite the problem over the LCD of (x-2)(x+2)
{{{x(x-2)/((x-2)(x+2)) + 2(x+2)/((x-2)(x+2)) = (-2x+19)/((x-2)(x+2))}}} Multiply both sides by the LCD of (x-2)(x+2) to eliminate the fraction part on the bottom.
{{{x(x-2) + 2(x+2) = -2x+19}}} Multiply out the terms on the left hand side.
{{{x^2-2x + 2x+4 = -2x+19}}}
{{{x^2-2x + 2x+4 = -2x+19}}} Get all terms on one side of the equation
{{{x^2+ 2x-15 = 0}}} Factorise
{{{(x+5)(x-3) = 0}}}

So the solutions are x=-5 or x=3