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

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Question 167696: x+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!
%28x%2B1%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%28x%2B1%29-35%281%2Bx%29=6%281%2Bx%29%283-x%29 Multiply and simplify


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


105%2B70x-35x%5E2-35-35x=18%2B12x-6x%5E2 Distribute


-35x%5E2%2B35x%2B70=-6x%5E2%2B12x%2B18 Combine like terms.


-35x%5E2%2B35x%2B70%2B6x%5E2-12x-18=0 Get all terms to the left side.


-29x%5E2%2B23x%2B52=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-29, b=23, 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-%2823%29+%2B-+sqrt%28+%2823%29%5E2-4%28-29%29%2852%29+%29%29%2F%282%28-29%29%29 Plug in a=-29, b=23, and c=52


x+=+%28-23+%2B-+sqrt%28+529-4%28-29%29%2852%29+%29%29%2F%282%28-29%29%29 Square 23 to get 529.


x+=+%28-23+%2B-+sqrt%28+529--6032+%29%29%2F%282%28-29%29%29 Multiply 4%28-29%29%2852%29 to get -6032


x+=+%28-23+%2B-+sqrt%28+529%2B6032+%29%29%2F%282%28-29%29%29 Rewrite sqrt%28529--6032%29 as sqrt%28529%2B6032%29


x+=+%28-23+%2B-+sqrt%28+6561+%29%29%2F%282%28-29%29%29 Add 529 to 6032 to get 6561


x+=+%28-23+%2B-+sqrt%28+6561+%29%29%2F%28-58%29 Multiply 2 and -29 to get -58.


x+=+%28-23+%2B-+81%29%2F%28-58%29 Take the square root of 6561 to get 81.


x+=+%28-23+%2B+81%29%2F%28-58%29 or x+=+%28-23+-+81%29%2F%28-58%29 Break up the expression.


x+=+%2858%29%2F%28-58%29 or x+=++%28-104%29%2F%28-58%29 Combine like terms.


x+=+-1 or x+=+52%2F29 Simplify.


So the possible answers are x+=+-1 or x+=+52%2F29

However, if you plug in x+=+-1, then you will get a division by zero. So the only answer is x+=+52%2F29



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Answer:


So the solution is x+=+52%2F29 which approximates to x=1.793