SOLUTION: {{{3/(x-1)-6/(x^2-1)=1}}}

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Question 103008: 3%2F%28x-1%29-6%2F%28x%5E2-1%29=1
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F%28%28x-1%29%29 - 6%2F%28%28x%5E2-1%29%29 = 1
:
You can see that (x^2-1) is the difference of squares so factor that:
3%2F%28%28x-1%29%29 - 6%2F%28%28x-1%29%28x%2B1%29%29 = 1
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Common denominator would be (x-1)(x+1), multiply equation by that:
(x-1)(x+1)3%2F%28%28x-1%29%29 - (x-1)(x+1)6%2F%28%28x-1%29%28x%2B1%29%29 = 1(x-1)(x+1)
:
Cancel out the denominators and you have;
3(x+1) - 6 = (x-1)(x+1)
:
Multiply what's inside the brackets on the left, FOIL the right
3x + 3 - 6 = x^2 - 1
3x - 3 = x^2 - 1
:
Arrange as a quadratic equation:
x^2 - 3x - 1 + 3 = 0
x^2 - 3x + 2 = 0
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Factors to:
(x-2)(x-1) = 0
Two solutions:
x = +2
x = +1
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However x = 1, cannot be a solution. Note that if you substitute 1 for x,
both fractions have division by 0
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x = 2 is the only solution, check by subsitution
:
3%2F%28%282-1%29%29 - 6%2F%28%282%5E2-1%29%29 = 1
3 - 6%2F3 = 1
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