SOLUTION: I hope i picked the right section to put this problem in. alright here is the problem, i am totally lost on how to do this: (x/x+4) - (2/x-1) = (20/x^2+3x-4) HELP!

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: I hope i picked the right section to put this problem in. alright here is the problem, i am totally lost on how to do this: (x/x+4) - (2/x-1) = (20/x^2+3x-4) HELP!      Log On

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Question 195715: I hope i picked the right section to put this problem in.
alright here is the problem, i am totally lost on how to do this:
(x/x+4) - (2/x-1) = (20/x^2+3x-4)
HELP!
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x%2B4%29-2%2F%28x-1%29=20%2F%28x%5E2%2B3x-4%29 Start with the given equation.


x%2F%28x%2B4%29-2%2F%28x-1%29=20%2F%28%28x%2B4%29%28x-1%29%29 Factor. Take note that x%3C%3E-4 or x%3C%3E1 as these values cause a division by zero.


Multiply every term on both sides by the LCD %28x%2B4%29%28x-1%29. Doing this will eliminate all of the fractions.


%28x-1%29%28x%29-%28x%2B4%29%282%29=20 Cancel out and simplify


x%28x-1%29-2%28x%2B4%29=20 Rearrange the terms.


x%5E2-x-2x-8=20 Distribute.


x%5E2-x-2x-8-20=0 Subtract 20 from both sides.


x%5E2-3x-28=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-3, and c=-28


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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-3, and c=-28


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--112+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-28%29 to get -112


x+=+%283+%2B-+sqrt%28+9%2B112+%29%29%2F%282%281%29%29 Rewrite sqrt%289--112%29 as sqrt%289%2B112%29


x+=+%283+%2B-+sqrt%28+121+%29%29%2F%282%281%29%29 Add 9 to 112 to get 121


x+=+%283+%2B-+sqrt%28+121+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%283+%2B-+11%29%2F%282%29 Take the square root of 121 to get 11.


x+=+%283+%2B+11%29%2F%282%29 or x+=+%283+-+11%29%2F%282%29 Break up the expression.


x+=+%2814%29%2F%282%29 or x+=++%28-8%29%2F%282%29 Combine like terms.


x+=+7 or x+=+-4 Simplify.


So the possible answers are x+=+7 or x+=+-4


However, we stated earlier that x%3C%3E-4 or x%3C%3E1 (they cause a division by zero). So we must ignore the possible solution x+=+-4 (it is not in the domain)


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Answer:


So the only solution is x+=+7