How do you solve #\frac { 5} { x - 1} + \frac { 8} { x + 1} = \frac { 8} { x ^ { 2} - 1}#?

1 Answer
George C.
May 13, 2017

#x=11/13#

Explanation:

Given:

#5/(x-1)+8/(x+1) = 8/(x^2-1)#

Note that:

#x^2-1 = (x-1)(x+1)#

So let us multiply both left and right hand sides of the given equation to get:

#5(x+1)+8(x-1) = 8#

wich simplifies to:

#13x-3=8#

Add #3# to both sides to get:

#13x=11#

Divide both sides by #13# to get:

#x=11/13#

Note that this is neither #1# nor #-1#, so does not cause any of the denominators in the given equation to be zero. So it is a valid solution of the given equation.

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