# SOLUTION: I need to know how to start to solve this equation. 1/(x-1) + 1/2 = 2/(x^2-1)

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Question 638540: I need to know how to start to solve this equation.
1/(x-1) + 1/2 = 2/(x^2-1)

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Notice that:
(x^2-1)
is a "difference of squares"
(x^2-1^2)
we can factor as:
(x-1)(x+1)
.
So, we can rewrite your original equation:
1/(x-1) + 1/2 = 2/(x^2-1)
as:
1/(x-1) + 1/2 = 2/[(x-1)(x+1)]
multiply both sides by 2:
2/(x-1) + 1 = 4/[(x-1)(x+1)]
Now, we multiply both sides by (x-1)(x+1) to get:
2(x+1) + (x-1)(x+1) = 4
2x+2 + x^2-1 = 4
x^2+2x-1 = 4
x^2+2x-5 = 0