SOLUTION: 1/1+x - 1/3-x = 6/35

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Question 167712: 1/1+x - 1/3-x = 6/35
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%29%2F%281%2Bx%29-%281%29%2F%283-x%29=%286%29%2F%2835%29 Start with the given equation.


Multiply EVERY term on both sides by the LCD 35%281%2Bx%29%283-x%29. Doing this will eliminate all of the fractions.


35%283-x%29-35%281%2Bx%29=6%281%2Bx%29%283-x%29 Multiply and simplify


35%283-x%29-35%281%2Bx%29=6%283%2B2x-x%5E2%29 FOIL


105-35x-35-35x=18%2B12x-6x%5E2 Distribute


-70x%2B70=-6x%5E2%2B12x%2B18 Combine like terms.


0=-6x%5E2%2B12x%2B18%2B70x-70 Get all terms to the right side.


0=-6x%5E2%2B82x-52 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-6, b=82, and c=-52


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-%2882%29+%2B-+sqrt%28+%2882%29%5E2-4%28-6%29%28-52%29+%29%29%2F%282%28-6%29%29 Plug in a=-6, b=82, and c=-52


x+=+%28-82+%2B-+sqrt%28+6724-4%28-6%29%28-52%29+%29%29%2F%282%28-6%29%29 Square 82 to get 6724.


x+=+%28-82+%2B-+sqrt%28+6724-1248+%29%29%2F%282%28-6%29%29 Multiply 4%28-6%29%28-52%29 to get 1248


x+=+%28-82+%2B-+sqrt%28+5476+%29%29%2F%282%28-6%29%29 Subtract 1248 from 6724 to get 5476


x+=+%28-82+%2B-+sqrt%28+5476+%29%29%2F%28-12%29 Multiply 2 and -6 to get -12.


x+=+%28-82+%2B-+74%29%2F%28-12%29 Take the square root of 5476 to get 74.


x+=+%28-82+%2B+74%29%2F%28-12%29 or x+=+%28-82+-+74%29%2F%28-12%29 Break up the expression.


x+=+%28-8%29%2F%28-12%29 or x+=++%28-156%29%2F%28-12%29 Combine like terms.


x+=+2%2F3 or x+=+13 Simplify.


So the answers are x+=+2%2F3 or x+=+13


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Answer:


So the solutions are x+=+2%2F3 or x+=+13