SOLUTION: Please help me solve this rational equation: {{{ 1/(2x+2) + 5/(x^2-1) = 1/(x-1)}}}

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Question 1072925: Please help me solve this rational equation:
+1%2F%282x%2B2%29+%2B+5%2F%28x%5E2-1%29+=+1%2F%28x-1%29

Found 4 solutions by Alan3354, josgarithmetic, ankor@dixie-net.com, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply by x^2-1 to eliminate fractions.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply left and right sides by 2%28x-1%29%28x%2B1%29 to eliminate the denominators.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
+1%2F%282x%2B2%29+%2B+5%2F%28x%5E2-1%29+=+1%2F%28x-1%29
Factor the denominators
+1%2F%282%28x%2B1%29%29+%2B+5%2F%28%28x-1%29%28x%2B1%29%29+=+1%2F%28x-1%29
Multiply by the common denominators 2(x+1)(x-1), cancel and we have
(x-1) + 2(5) = 2(x+1)
x - 1 + 10 = 2x + 2
9 - 2 = 2x - x
7 = x
:
:
Check in the original equation, replace x=7
+1%2F%2814%2B2%29+%2B+5%2F%2849-1%29+=+1%2F%287-1%29
1%2F16+%2B+5%2F48+=+1%2F6
3%2F48+%2B+5%2F48+=+8%2F48

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me solve this rational equation:
+1%2F%282x%2B2%29+%2B+5%2F%28x%5E2-1%29+=+1%2F%28x-1%29
2x + 2 = 2(x + 1)

x%5E2+-+1 = (x - 1)(x + 1)

LCD: 2(x + 1)(x - 1)

+1%2F%282x%2B2%29+%2B+5%2F%28x%5E2-1%29+=+1%2F%28x-1%29 

1(x - 1) + 5(2) = 1(2)(x + 1) ------ Multiplying by LCD, 2(x - 1)(x + 1)

x - 1 + 10 = 2x + 2

x + 9 = 2x + 2

x - 2x = 2 - 9

- x = - 7