`(6x)/(x+4)+4=(2x+2)/(x-1)`
LCD is `(x+4)(x-1)`
Multiply each term of the equation by LCD and simplify,
`(x+4)(x-1)((6x)/(x+4))+4(x+4)(x-1)=(x+4)(x-1)((2x+2)/(x-1))`
`6x(x-1)+4(x+4)(x-1)=(x+4)(2x+2)`
`6x^2-6x+4(x(x-1)+4(x-1))=x(2x+2)+4(2x+2)`
`6x^2-6x+4(x^2-x+4x-4)=2x^2+2x+8x+8`
`6x^2-6x+4(x^2+3x-4)=2x^2+10x+8`
`6x^2-6x+4x^2+12x-16=2x^2+10x+8`
`6x^2+4x^2-6x+12x-16=2x^2+10x+8`
`10x^2+6x-16=2x^2+10x+8`
Isolate the terms containing x,
`10x^2-2x^2+6x-10x=8+16`
`8x^2-4x=24`
`8x^2-4x-24=0`
Factorize ,
`4(2x^2-x-6)=0`
`4(2x^2-4x+3x-6)=0`
`4(2x(x-2)+3(x-2))=0`
`4(x-2)(2x+3)=0`
Use the zero product property,
`x-2=0` or `2x+3=0`
`x=2` or `2x=-3`
`x=2` or `x=-3/2` ``
Let's check the solutions by plugging them in the original equation,
For x=2,
`(6*2)/(2+4)+4=(2*2+2)/(2-1)`
`(12)/6+4=6/1`
`2+4=6`
`6=6`
It's true.
For x=`-3/2` ,
`(6(-3/2))/(-3/2+4)+4=(2(-3/2)+2)/(-3/2-1)`
`-9/(5/2)+4=(-1)/(-5/2)`
`-18/5+4=2/5`
`(-18+20)/5=2/5`
`2/5=2/5`
It's true,
So, Solutions of the equation are 2 and `-3/2`
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