x/(x-5) -2/(x+5)=50/(x^2-25)

Question

solve for x

Answer 1

x²-25=(x+5)(x-5), so multiply through by x²-25:

x(x+5)-2(x-5)=50,

x²+5x-2x+10=50,

x²+3x-40=0=(x+8)(x-5), so x=-8 or 5. But if x=5 the original expression involves dividing by zero which is indeterminate.

Therefore the solution is x=-8.

CHECK

-8/(-13)-2/(-3)=8/13+2/3=(24+26)/39=50/39;

50/((-8)²-25)=50/(64-25)=50/39. So LHS=RHS, confirming that x=-8 is the solution.