#1**+2 **

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 !!

Melody
May 15, 2017