simple algebra help...?

the least common denominator is (u+1)(u+6)(1) so multiply everything by that

(u + 5)/(u + 1) = (u + 6)/(u + 4) + 1
(u + 1)(u + 4)[(u + 5)/(u + 1)] = (u + 1)(u + 4)[(u + 6)/(u + 4) + 1]
(u + 4)(u + 5) = (u + 1)(u + 6) + (u + 1)(u + 4)
u(u) + u(5) + 4(u) + 4(5) = u(u) + u(6) + 1(u) + 1(6) + u(u) + u(4) + 1(u) + 1(4)
u^2 + 5u + 4u + 20 = u^2 + 6u + u + 6 + u^2 + 4u + u + 4
u^2 + 9u + 20 = u^2 + 7u + 6 + u^2 + 5u + 4
u^2 - u^2 - u^2 + 9u - 7u - 5u + 20 - 6 - 4 = 0
-u^2 - 3u + 10 = 0
u^2 + 3u - 10 = 0
u^2 + 5u - 2u - 10 = 0
(u^2 + 5u) - (2u + 10) = 0
u(u + 5) - 2(u + 5) = 0
(u + 5)(u - 2) = 0

u + 5 = 0
u = -5

u - 2 = 0
u = 2

∴ u = -5, 2

( u + 5 ) ( u + 4 ) = ( u + 6 ) ( u + 1 ) + ( u + 1 ) ( u + 4 )

u^2 + 9u + 20 = u^2 + 7u + 6 + u^2 + 5u + 4

u^2 + 9u + 20 = 2 u^2 + 12 u + 10

0 = u^2 + 3u - 10

( u + 5 ) ( u - 2 ) = 0

u = - 5 , u = 2

-6,-5

basically i found the "zeros" of the equation. Now multiply by the reciprocal (u+5)/(u+1) to both sides and you get:
0= ((u+6)(u+1)) / ((u+4)(u+5)) + (u+1) / (u+5)

combine everything by LCD: (u+4)

0= ((u+6)(u+1)) / ((u+4)(u+5)) +((u+1) (u+4)) / ((u+5)(u+4))



0= ((u+6)(u+1)(u+1)(u+4)) / ((u+4)(u+5))

and from here its easy by finding what makes u=0 by subbing in the opposite.

so we get: -6,-1,-4,-5

sub these back into the ORIGINAL equation and you fins you that -1 and -4 don't work ( zero at the bottom of the fractions )so toss them out the window. so that leaves you with: -6,-5

edit: spacing went stupid