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# Solve the equation by using LCD

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6x/x+4 + 4 = 2x-2/x-1

Guest May 14, 2017
#1
+93664
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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

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
edited by Melody  May 15, 2017