Question

Solve for u:
u − 2/
u − 4
+ 6 = u +
u − 6/
4 − u

Answer 1

If you mean

(u-2)/(u-4) + 6 = u + (u-6)/(4-u)

multiply by u-4 to clear the fractions:

(u-2) + 6(u-4) = u(u-4) - (u-6)
u-2+6u-24 = u^2-4u-u+6
u^2 - 12u + 32 = 0
(u-4)(u-8) = 0

u = 4 or 8

But, u=4 is not allowed, because the original equation divided by (u-4). So, the only solution is u=8.