Solve Rational Equation (three fractions)

Question

Solve for 'u' and show work:

(10/u^2-u-6) = (u/u+2) + (2/u-3)

Thank you!

Answer 1

assuming the usual carelessness with parentheses, I'll go with
10/(u^2-u-6) = u/(u+2) + 2/(u-3)
using a common denominator of (u+2)(u-3), that gives us
10 = u(u-3) + 2(u+2)
u^2 - u - 6 = 0
(u-3)(u+2) = 0
u = -2 or 3
But those values must be excluded from the original equation.
So, no solutions.