Question 18802
Here's one approach:

{{{1/(x+1) + a/(x-1) = (-2)/(x^2-1)}}} Add the fractions on the left side.
{{{((x-1)+a(x+1))/(x+1)(x-1) = (-2)/(x^2-1)}}} Simplify the left side.
{{{((x-1)+a(x+1))/(x^2-1) = (-2)/(x^2-1)}}} Multiply both sides by (x^2-1)
{{{(x-1)+a(x+1) = -2}}} Subtract (x-1) from both sides.
{{{a(x+1) = -2-(x-1)}}} Simplify the right side.
{{{a(x+1) = -(x+1)}}} Finally, divide both sides by (x+1)
{{{a = -1}}}

Answer: a must = -1

Check: Substitute a = -1

{{{1/(x+1) + (-1)/(x-1) = (-2)/(x^2-1)}}} Add the fractions on the left side.
{{{((x-1) - (x+1))/(x^2-1) = (-2)/(x^2-1)}}} Simplify the left side.
{{{(-2)/(x^2-1) = (-2)/(x^2-1)}}}