SOLUTION: please help Simplify: Simplify: 16 - x^2 / x^3 - 2x^2 - 8x

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Question 22086: please help
Simplify:
Simplify: 16 - x^2 / x^3 - 2x^2 - 8x

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
+%2816+-+x%5E2%29+%2F%28+x%5E3+-+2x%5E2+-+8x%29+

Factor the numerator and denominator. The numerator is the difference of two squares, and the denominator has a common factor, which is also a trinomial:
+%28%284-x%29%2A%284%2Bx%29%29+%2F%28x%2A+%28x%5E2-2x-8%29%29+
The denominator factors again:
+%28%284-x%29%2A%284%2Bx%29%29+%2F%28x%2A+%28x-4%29%2A%28x%2B2%29%29+

Notice that the (4-x) and the (x-4) are negatives of one another, so they divide out, leaving a factor of -1 in the numerator:
+%28-1%2A%284%2Bx%29%29+%2F%28x%2A+%28x%2B2%29%29+
or +-%28x%2B4%29+%2F%28x%2A+%28x%2B2%29%29+

R^2 at SCC