How do you solve #\frac { 4} { x - 1} + \frac { 4} { x + 1} = 3#?

1 Answer
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Sep 15, 2017

#x=3# and #x=(-1)/3#

Explanation:

First, we have to give the terms on the left a common denominator.
To do this, we will multiply #4/(x-1)# by #(x+1)/(x+1)# and #4/(x+1)# by #(x-1)/(x-1)#

Here is the result:

#(4x+4)/(xˆ2-1)+(4x-4)/(xˆ2-1)=3#

We will add the like terms together.

#(8x)/(xˆ2-1)=3#

Now, we multiply both sides by #xˆ2-1#

#8x=3xˆ2-3#

Since this is a quadratic, we'll set equal to zero and factor.

#3xˆ2-8x-3=0#

#(x-3)(3x+1)=0#

Setting each factor equal to 0, we get

#x=3# and #x=(-1)/3#

Neither solution is extraneous.

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