SOLUTION: express the following rational expression in simplest form: 9 - x^2 ___________ ___ 10x^2 - 28x - 6

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Question 20701: express the following rational expression in simplest form:
9 - x^2
_______________
10x^2 - 28x - 6
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
numerator, 9+-+x%5E2 can be thought of as 3%5E2-x%5E2, which is difference of 2 squares. This factorises into (3-x)(3+x)

denominator, 10x%5E2+-+28x+-+6 can be simplified into 2%285x%5E2-14x-3%29. This can then be factorised, by thinking about it a little as 2(5x+1)(x-3)

So we have, %28%283-x%29%283%2Bx%29%29%2F%282%285x%2B1%29%28x-3%29%29

This can be simplified further by realising that (3-x) is really just -(x-3).. this sort of thing is very useful to remember in manipulation of algebra terms.

So, %28-%28x-3%29%283%2Bx%29%29%2F%282%285x%2B1%29%28x-3%29%29 which then simplifies to %28-%283%2Bx%29%29%2F%282%285x%2B1%29%29

cheers
Jon.