SOLUTION: 1/x+2 +1/2=1/x-2 - 2x/x^2-4

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Question 151209: 1/x+2 +1/2=1/x-2 - 2x/x^2-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x%2B2%29+%2B1%2F2=1%2F%28x-2%29+-+%282x%29%2F%28x%5E2-4%29 Start with the given equation.


1%2F%28x%2B2%29+%2B1%2F2=1%2F%28x-2%29+-+%282x%29%2F%28%28x%2B2%29%28x-2%29%29 Factor x%5E2-4 to get %28x%2B2%29%28x-2%29



Multiply every term on both sides by the LCD 2%28x%2B2%29%28x-2%29. Doing this will eliminate all of the fractions.

2%28x-2%29%2B%28x%2B2%29%28x-2%29=2%28x%2B2%29%2B2%28-2x%29 Simplify


2%28x-2%29%2Bx%5E2-4=2%28x%2B2%29%2B2%28-2x%29 FOIL


2x-4%2Bx%5E2-4=2x%2B4-4x Distribute


2x-4%2Bx%5E2-4-2x-4%2B4x=0 Get all terms to the left side.


x%5E2%2B4x-12=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=4, and c=-12


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Plug in a=1, b=4, and c=-12


x+=+%28-4+%2B-+sqrt%28+16-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16--48+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-12%29 to get -48


x+=+%28-4+%2B-+sqrt%28+16%2B48+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--48%29 as sqrt%2816%2B48%29


x+=+%28-4+%2B-+sqrt%28+64+%29%29%2F%282%281%29%29 Add 16 to 48 to get 64


x+=+%28-4+%2B-+sqrt%28+64+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-4+%2B-+8%29%2F%282%29 Take the square root of 64 to get 8.


x+=+%28-4+%2B+8%29%2F%282%29 or x+=+%28-4+-+8%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29 or x+=++%28-12%29%2F%282%29 Combine like terms.


x+=+2 or x+=+-6 Simplify.


So the possible answers are x+=+2 or x+=+-6

However, if you plug in x+=+2, you'll get a denominator of 0. So the only answer is x+=+-6