SOLUTION: Find the solution sets for the following: 2/ x+1 + 6 = 3/x-1

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Question 92159: Find the solution sets for the following:
2/ x+1 + 6 = 3/x-1
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the solution sets for the following:
Assume you mean:
2%2F%28%28x%2B1%29%29 + 6 = 3%2F%28%28x-1%29%29
:
Multiply each term in the equation by (x+1)(x-1), results in:
2(x-1) + 6(x+1)(x-1) = 3(x+1)
:
2x - 2 + 6(x^2 - 1) = 3x + 3; FOILed (x+1)*(x-1)
2x - 2 + 6x^2 - 6 = 3x + 3
:
Arrange as a quadratic equation on the left:
6x^2 + 2x - 3x - 2 - 6 - 3 = 0
:
6x^2 - x - 11 = 0
:
Use the quadratic formula to find x: a=6; b=-1; c=-11
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
x+=+%28-%28-1%29+%2B-+sqrt%28-1%5E2+-+4+%2A+6+%2A+-11+%29%29%2F%282%2A6%29+
:
x+=+%28%2B1+%2B-+sqrt%28%2B1+-+%28-264%29+%29%29%2F%2812%29+; minus a minus is a plus
:
x+=+%28%2B1+%2B-+sqrt%28+265+%29%29%2F%2812%29+
:
Two solutions:
x+=+%28%2B1+%2B+16.2788%29%2F%2812%29+
x = %2B17.2788%2F12
x = +1.44
and
x+=+%28%2B1+-+16.2788%29%2F%2812%29+
x = -15.2788%2F12
x = -1.273
:
You should check these solutions in the original equation.