<PRE><B>Question 83579</B>
solve 6x divided by x+4 plus 4 equals 2x+2 divided by x-1
:
{{{(6x)/((x+4))}}}+ 4 = {{{((2x+2))/(( x-1))}}}
:
Multiply equation by the common denominator; (x+4)(x-1) and you have:
6x(x-1) + 4(x+4)(x-1) = (x+4)(2x+2)
:
6x^2 - 6x + 4(x^2 - x + 4x - 4) = 2x^2 + 2x + 8x + 8: FOILed
:
6x^2 - 6x + 4(x^2 + 3x - 4) = 2x^2 + 10x + 8: combined like terms
:
6x^2 - 6x + 4x^2 + 12x - 16  = 2x^2 + 10x + 8
:
6x^2 + 4x^2 - 2x^2 - 6x + 12x - 10x - 16 - 8 = 0; Group like terms on the left
:
8x^2 - 4x - 24 = 0
:
2x^2 - x - 6 = 0; simplified divided equation by 4
:
(2x + 3)(x - 2) = 0; factored
:
2x = -3
x = -3/2
and
x = +2
:
It would be good to check solutions by substitution in the original equation</PRE>