Question 5190
{{{x^2/(x^2-4) = x/(x+2) - 2x/(2-x)}}}

add polynomial fractions

{{{x^2/(x^2-4) = (x*(2-x)-2x*(x+2))/(x+2)/(x-2)}}}


{{{x^2/(x^2-4) = (x*(2-x)-2x*(x+2))/(x^2-4)}}}

Remove x^2-4 from both sides, being mindful that it cannot be zero, or that x cannot be +2 or - 2. 

{{{x^2 = x(2-x) - 2x(x+2)}}}
{{{x^2 = 2x-x^2 - 2x^2 - 4x}}}

{{{4x^2 +2x = 0}}}

{{{4x^2+x = 0}}}

*[invoke solve_quadratic_equation 4, 1, 0]

That's your answer. PLEASE double check my work.