+118608
6x/x+4 + 4 = 2x-2/x-1
Do you mean
6x/(x+4) + 4 = (2x-2)/(x-1) ?
\(\frac{6x}{(x+4)} + 4 = \frac{(2x-2)}{(x-1)}\\ LCD=(x+4)(x-1)\\ (x+4)(x-1)[\frac{6x}{(x+4)} + 4 ]=(x+4)(x-1)[ \frac{(2x-2)}{(x-1)}]\\ \frac{6x(x+4)(x-1)}{(x+4)} + 4 (x+4)(x-1)= \frac{(2x-2)(x+4)(x-1)}{(x-1)}\\ 6x(x-1)+ 4 (x+4)(x-1)=(2x-2)(x+4)\\ 6x^2-6x+ 4 (x^2+3x-4)=2x^2+6x-8\\ 6x^2-6x+ 4x^2+12x-16=2x^2+6x-8\\ 8x^2-8=0\\ x^2-1=0\\ (x-1)(x+1)=0\\ x=\pm1 \)
Edit:
x cannot equal 1 becasue it would make the denominator in the question = 0
so the answer is
x = -1
Thanks for pointing this out to me CPhill 
I should have noted at the very beginning that x cannot equal 1 or -4 !!
Mistakes like this need to be carefully guarded against !!
