SOLUTION: 2/x+1 + 6 = 3/x-1

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Question 150890: 2/x+1 + 6 = 3/x-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%282%29%2F%28x%2B1%29%2B6=%283%29%2F%28x-1%29 Start with the given equation.


Multiply every term on both sides by the LCD %28x%2B1%29%28x-1%29. Doing this will eliminate all of the fractions.



2%28x-1%29%2B6%28x%2B1%29%28x-1%29=3%28x%2B1%29 Simplify.


2%28x-1%29%2B6%28x%5E2-1%29=3%28x%2B1%29 FOIL.


2x-2%2B6x%5E2-6=3x%2B3 Distribute.


2x-2%2B6x%5E2-6-3x-3=0 Subtract 3x from both sides. Subtract 3 from both sides.


6x%5E2-x-11=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=6, b=-1, and c=-11


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-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%286%29%28-11%29+%29%29%2F%282%286%29%29 Plug in a=6, b=-1, and c=-11


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%286%29%28-11%29+%29%29%2F%282%286%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%286%29%28-11%29+%29%29%2F%282%286%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--264+%29%29%2F%282%286%29%29 Multiply 4%286%29%28-11%29 to get -264


x+=+%281+%2B-+sqrt%28+1%2B264+%29%29%2F%282%286%29%29 Rewrite sqrt%281--264%29 as sqrt%281%2B264%29


x+=+%281+%2B-+sqrt%28+265+%29%29%2F%282%286%29%29 Add 1 to 264 to get 265


x+=+%281+%2B-+sqrt%28+265+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%281%2Bsqrt%28265%29%29%2F%2812%29 or x+=+%281-sqrt%28265%29%29%2F%2812%29 Break up the expression.


So our answers are x+=+%281%2Bsqrt%28265%29%29%2F%2812%29 or x+=+%281-sqrt%28265%29%29%2F%2812%29


which approximate to x=1.44 or x=-1.273