SOLUTION: Please help me solve this equation: x+3/x-5=56-3x/x^2-13x+40

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Question 195572This question is from textbook McDougal Littell Algebra 1
: Please help me solve this equation: x+3/x-5=56-3x/x^2-13x+40 This question is from textbook McDougal Littell Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B3%29%2F%28x-5%29=%2856-3x%29%2F%28x%5E2-13x%2B40%29 Start with the given equation.


%28x%2B3%29%2F%28x-5%29=%2856-3x%29%2F%28%28x-5%29%28x-8%29%29 Factor


Multiply every term on both sides by the LCD %28x-5%29%28x-8%29. Doing this will eliminate all of the fractions.



%28x-8%29%28x%2B3%29=56-3x Cancel out and simplify.


x%5E2-5x-24=56-3x FOIL


x%5E2-5x-24-56%2B3x=0 Get all terms to the left side.


x%5E2-2x-80=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-2, and c=-80


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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-80%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-2, and c=-80


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-80%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%28-80%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--320+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-80%29 to get -320


x+=+%282+%2B-+sqrt%28+4%2B320+%29%29%2F%282%281%29%29 Rewrite sqrt%284--320%29 as sqrt%284%2B320%29


x+=+%282+%2B-+sqrt%28+324+%29%29%2F%282%281%29%29 Add 4 to 320 to get 324


x+=+%282+%2B-+sqrt%28+324+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+18%29%2F%282%29 Take the square root of 324 to get 18.


x+=+%282+%2B+18%29%2F%282%29 or x+=+%282+-+18%29%2F%282%29 Break up the expression.


x+=+%2820%29%2F%282%29 or x+=++%28-16%29%2F%282%29 Combine like terms.


x+=+10 or x+=+-8 Simplify.


So the answers are x+=+10 or x+=+-8