SOLUTION: x-3 over x-2 + x+1 over x+3 equals 2x squared +x+1 over x squared +x-6 for some reason my solution is x= -5 and in the andswer section of my book the solution is

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: x-3 over x-2 + x+1 over x+3 equals 2x squared +x+1 over x squared +x-6 for some reason my solution is x= -5 and in the andswer section of my book the solution is       Log On

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Question 14329: x-3 over x-2 + x+1 over x+3 equals 2x squared +x+1 over x squared +x-6
for some reason my solution is x= -5 and in the andswer section of my book the solution is x= 6. am I right or wrong?
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-3%29%2F%28x-2%29%29%2B%28%28x%2B1%29%2F%28x%2B3%29%29+=+%282x%5E2%2Bx%2B1%29%2F%28x%5E2%2Bx-6%29 Add the fractions on the left side.
%28%28x%2B3%29%28x-3%29%2B%28x%2B1%29%28x-2%29%29%2F%28x-2%29%28x%2B3%29+=+%282x%5E2%2Bx%2B1%29%2F%28x%5E2%2Bx-6%29 On the left side, multiply the factors in the numerator and multiply the factors in the denominator.
%28%28x%5E2-9%29%2B%28x%5E2-x-2%29%29%2F%28x%5E2%2Bx-6%29+=+%282x%5E2%2Bx%2B1%29%2F%28x%5E2%2Bx-6%29 Simplify.
2x%5E2-x-11+=+2x%5E2%2Bx%2B1 Subtract 2x%5E2 from both sides.
-x-11+=+x%2B1 Add x to both sides.
-11+=+2x%2B1 Subtract 1 from both sides.
-12+=+2x Divide both sides by 2.
-6+=+x
So, x = -6
Check:
%28%28-6-3%29%2F%28-6-2%29%29%2B%28%28-6%2B1%29%2F%28-6%2B3%29%29+=+%282%28-6%29%5E2+%2B%28-6%29%2B1%29%2F%28%28-6%29%5E2%2B%28-6%29-6%29
%28-9%2F-8%29%2B%28-5%2F-3%29+=+%2872-6%2B1%29%2F%2836-6-6%29
%2827%2B40%29%2F24+=+67%2F24
67%2F24+=+67%2F24
x = -6 is correct, not x = 6 as you say your book shows.