`(6x)/(x+4)+4=(2x+2)/(x-1)` Solve the equation by using the LCD. Check for extraneous solutions.

Expert Answers

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LCD is `(x+4)(x-1)`

Multiply each term of the equation by LCD and simplify,









Isolate the terms containing x,




Factorize ,





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,





It's true.

For x=`-3/2` ,






It's true,

So, Solutions of the equation are 2 and `-3/2`


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