SOLUTION: Solve for x: 5/(x+1) + 4/3 =(x+1)/(x-1)

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Question 177043: Solve for x: 5/(x+1) + 4/3 =(x+1)/(x-1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F%28x%2B1%29+%2B+4%2F3+=%28x%2B1%29%2F%28x-1%29 Start with the given equation.


5%283%28x-1%29%29+%2B+4%28%28x%2B1%29%28x-1%29%29+=3%28x%2B1%29%28x%2B1%29 Multiply EVERY term by the LCD 3%28x%2B1%29%28x-1%29 to clear the fractions.


15%28x-1%29+%2B+4%28%28x%2B1%29%28x-1%29%29+=3%28x%2B1%29%28x%2B1%29 Multiply


15%28x-1%29+%2B+4%28x%5E2-1%29+=3%28x%5E2%2B2x%2B1%29 FOIL


15x-15+%2B+4x%5E2-4+=3x%5E2%2B6x%2B3 Distribute


15x-19+%2B+4x%5E2+=3x%5E2%2B6x%2B3 Combine like terms.


15x-19%2B4x%5E2-3x%5E2-6x-3=0 Get all terms to the left side.


x%5E2%2B9x-22=0 Combine like terms.


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Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=9, and c=-22


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-%289%29+%2B-+sqrt%28+%289%29%5E2-4%281%29%28-22%29+%29%29%2F%282%281%29%29 Plug in a=1, b=9, and c=-22


x+=+%28-9+%2B-+sqrt%28+81-4%281%29%28-22%29+%29%29%2F%282%281%29%29 Square 9 to get 81.


x+=+%28-9+%2B-+sqrt%28+81--88+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-22%29 to get -88


x+=+%28-9+%2B-+sqrt%28+81%2B88+%29%29%2F%282%281%29%29 Rewrite sqrt%2881--88%29 as sqrt%2881%2B88%29


x+=+%28-9+%2B-+sqrt%28+169+%29%29%2F%282%281%29%29 Add 81 to 88 to get 169


x+=+%28-9+%2B-+sqrt%28+169+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-9+%2B-+13%29%2F%282%29 Take the square root of 169 to get 13.


x+=+%28-9+%2B+13%29%2F%282%29 or x+=+%28-9+-+13%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29 or x+=++%28-22%29%2F%282%29 Combine like terms.


x+=+2 or x+=+-11 Simplify.


So the answers are x+=+2 or x+=+-11