Question 95844
Solve for y:
{{{1/(y+5) - 8/(y-5) = 11/(y^2-25)}}} Add the two fractions on the left side.  The LCD is {{{(y+5)(y-5) = y^2-25}}}
{{{((y-5)-8(y+5))/(y^2-25) = 11/(y^2-25)}}} Multiply both sides by{{{y^2-25}}} and simplify.
{{{y-5-8y-40 = 11}}}
{{{-7y-45 = 11}}} Add 45 to both sides.
{{{-7y = 56}}} Divide both sides by -7.
{{{y = -8}}}

Check:  Substitute y = -8 in original equation.
{{{1/(-8+5) - 8/(-8-5) = 11/((-8)^2-25)}}} Evaluate.
{{{1/(-3) - 8/(-13) = 11/(64-25)}}}
{{{13/(-39) - 24/(-39) = 11/39}}}
{{{(-13+24)/(39) = 11/39}}}
{{{11/39 = 11/39}}} OK!