SOLUTION: Simplify: {{{((X^2+3x-10)/(6X^2-24)) / ((X^2+X-20)/(X^2+3X+2)) / ((x^2-1)/6)}}}

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: Simplify: {{{((X^2+3x-10)/(6X^2-24)) / ((X^2+X-20)/(X^2+3X+2)) / ((x^2-1)/6)}}}      Log On

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Question 3328: Simplify:
%28%28X%5E2%2B3x-10%29%2F%286X%5E2-24%29%29+%2F+%28%28X%5E2%2BX-20%29%2F%28X%5E2%2B3X%2B2%29%29+%2F+%28%28x%5E2-1%29%2F6%29
Answer by ichudov(499) About Me  (Show Source):
You can put this solution on YOUR website!
Here's your cartoon:
%0D%0Acartoon%28+%0D%0A++%28%28X%5E2%2B3x-10%29%2F%286X%5E2-24%29%29+%2F+%28%28X%5E2%2BX-20%29%2F%28X%5E2%2B3X%2B2%29%29+%2F+%28%28x%5E2-1%29%2F6%29%2C%0D%0A++%28%28X%5E2%2B3x-10%29%2F%286X%5E2-24%29%29+%2F+%28%28X%5E2%2BX-20%29%2Fhighlight%28%28X%5E2%2B3X%2B2%29%29%29+%2F+%28%28x%5E2-1%29%2Fhighlight%286%29%29%2C%0D%0A++6%2A%28x%5E2%2B3x-10%29%2A%28x%5E2%2B3x%2B2%29%2F%286x%5E2-24%29%2F%28x%5E2%2Bx-20%29%2F%28x%5E2-1%29%2C%0D%0A++6%2Ahighlight%28%28x%5E2%2B3x-10%29%29%2A%28x%5E2%2B3x%2B2%29%2F%286x%5E2-24%29%2F%28x%5E2%2Bx-20%29%2F%28x%5E2-1%29%2C%0D%0A++6%2Ahighlight%28%28x-2%29%28x%2B5%29%29%2A%28x%5E2%2B3x%2B2%29%2F%286x%5E2-24%29%2F%28x%5E2%2Bx-20%29%2F%28x%5E2-1%29%2C%0D%0A++6%2A%28x-2%29%28x%2B5%29%2Ahighlight%28%28x%5E2%2B3x%2B2%29%29%2F%286x%5E2-24%29%2F%28x%5E2%2Bx-20%29%2F%28x%5E2-1%29%2C%0D%0A++6%2A%28x-2%29%28x%2B5%29%2Ahighlight%28%28x%2B1%29%2A%28x%2B2%29%29%2F%286x%5E2-24%29%2F%28x%5E2%2Bx-20%29%2F%28x%5E2-1%29%2C%0D%0A++6%2A%28x-2%29%28x%2B5%29%2A%28x%2B1%29%28x%2B2%29%2Fhighlight%28%286x%5E2-24%29%29%2F%28x%5E2%2Bx-20%29%2F%28x%5E2-1%29%2C%0D%0A++6%2A%28x-2%29%28x%2B5%29%2A%28x%2B1%29%28x%2B2%29+%2F+highlight%286%2A%28x-2%29%2A%28x%2B2%29%29%2F%28x%5E2%2Bx-20%29%2F%28x%5E2-1%29%2C%0D%0A++6%2A%28x-2%29%28x%2B5%29%2A%28x%2B1%29%28x%2B2%29+%2F+6%2F%28x-2%29%2F%28x%2B2%29%2Fhighlight%28%28x%5E2%2Bx-20%29%29%2F%28x%5E2-1%29%2C%0D%0A++6%2A%28x-2%29%28x%2B5%29%2A%28x%2B1%29%28x%2B2%29+%2F+6%2F%28x-2%29%2F%28x%2B2%29%2Fhighlight%28%28x-4%29%2A%28x%2B5%29%29%2F%28x%5E2-1%29%2C%0D%0A++6%2A%28x-2%29%28x%2B5%29%2A%28x%2B1%29%28x%2B2%29+%2F+6%2F%28x-2%29%2F%28x%2B2%29%2F%28x-4%29%2F%28x%2B5%29%2Fhighlight%28%28x%5E2-1%29%29%2C%0D%0A++6%2A%28x-2%29%28x%2B5%29%2A%28x%2B1%29%28x%2B2%29+%2F+6%2F%28x-2%29%2F%28x%2B2%29%2F%28x-4%29%2F%28x%2B5%29%2Fhighlight%28%28x-1%29%2A%28x%2B1%29%29%2C%0D%0A++6%2A%28x-2%29%28x%2B5%29%2A%28x%2B1%29%28x%2B2%29+%2F+6%2F%28x-2%29%2F%28x%2B2%29%2F%28x-4%29%2F%28x%2B5%29%2F%28x-1%29%2F%28x%2B1%29%2C%0D%0A++highlight%286%29%2Ahighlight%28%28x-2%29%29%2Ahighlight%28%28x%2B5%29%29%2Ahighlight%28%28x%2B1%29%29%2Ahighlight%28%28x%2B2%29%29+%2F+highlight%286%29%2Fhighlight%28%28x-2%29%29%2Fhighlight%28%28x%2B2%29%29%2F%28x-4%29%2Fhighlight%28%28x%2B5%29%29%2F%28x-1%29%2Fhighlight%28%28x%2B1%29%29%2C%0D%0A++cross%286%29%2Across%28%28x-2%29%29%2Across%28%28x%2B5%29%29%2Across%28%28x%2B1%29%29%2Across%28%28x%2B2%29%29+%2F+cross%286%29%2Fcross%28%28x-2%29%29%2Fcross%28%28x%2B2%29%29%2F%28x-4%29%2Fcross%28%28x%2B5%29%29%2F%28x-1%29%2Fcross%28%28x%2B1%29%29%2C%0D%0A++highlight%281%2F%28x-4%29%2F%28x-1%29%29%0D%0A%29%0D%0A
And here's your full solution.
First, move things around:
+%28%28X%5E2%2B3x-10%29%2F%286X%5E2-24%29%29%2F%28%28X%5E2%2BX-20%29%2F%28X%5E2%2B3X%2B2%29%29%2F%28%28x%5E2-1%29%2F6%29=6%2A%28x%5E2%2B3x-10%29%2A%28x%5E2%2B3x%2B2%29%2F%286x%5E2-24%29%2F%28x%5E2%2Bx-20%29%2F%28x%5E2-1%29
Second, factorize every piece in that formula using Quadratic Equation Solver.
+1x%5E2%2B3x-10+=+%28x-2%29%28x%2B5%29
+6X%5E2-24+=++6%28x-2%29%28x%2B2%29+
+X%5E2%2BX-20+=++%28x-4%29%28x%2B5%29+
+X%5E2%2B3X%2B2+=++%28x%2B1%29%28x%2B2%29+
+x%5E2-1+=+%28x-1%29%2A%28x%2B1%29++++
+%28%28X%5E2%2B3x-10%29%2F%286X%5E2-24%29%29%2F%28%28X%5E2%2BX-20%29%2F%28X%5E2%2B3X%2B2%29%29%2F%28%28x%5E2-1%29%2F6%29%0D%0A=%0D%0A6%2A%28x%5E2%2B3x-10%29%2A%28x%5E2%2B3x%2B2%29%2F%286x%5E2-24%29%2F%28x%5E2%2Bx-20%29%2F%28x%5E2-1%29%0D%0A=%0D%0A6%2A%28x-2%29%28x%2B5%29%2A%28x%2B1%29%28x%2B2%29+%2F+6%2F%28x-2%29%2F%28x%2B2%29%2F%28x-4%29%2F%28x%2B5%29%2F%28x-1%29%2F%28x%2B1%29%0D%0A
Now, similar terms cancel out:
%0D%0A6%2A%28x-2%29%28x%2B5%29%2A%28x%2B1%29%28x%2B2%29+%2F+6%2F%28x-2%29%2F%28x%2B2%29%2F%28x-4%29%2F%28x%2B5%29%2F%28x-1%29%2F%28x%2B1%29%0D%0A=%0D%0Across%286%29%2Across%28%28x-2%29%29%2Across%28%28x%2B5%29%29%2Across%28%28x%2B1%29%29%2Across%28%28x%2B2%29%29+%2F+cross%286%29%2Fcross%28%28x-2%29%29%2Fcross%28%28x%2B2%29%29%2F%28x-4%29%2Fcross%28%28x%2B5%29%29%2F%28x-1%29%2Fcross%28%28x%2B1%29%29%0D%0A=+1%2F%28x-4%29%2F%28x-1%29
So, your answer is
%28%28X%5E2%2B3x-10%29%2F%286X%5E2-24%29%29+%2F+%28%28X%5E2%2BX-20%29%2F%28X%5E2%2B3X%2B2%29%29+%2F+%28%28x%5E2-1%29%2F6%29+=+1%2F%28x-4%29%2F%28x-1%29.
Double check my solution, maybe I got something wrong.
Also, note that for every thing that canceled out, there is a point where the