## Need help with Complex Fraction

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
bbsa3412
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Joined: Sat Mar 28, 2009 9:46 pm
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### Need help with Complex Fraction

Help me finish this problem....Cant factor by grouping, what other method?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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It looks like the image displays the following:

$\frac{\frac{x\, -\, 2}{x\, +\, 2}\, +\, \frac{x\, -\, 1}{x\, +\, 1}}{\frac{x}{x\, +\, 1}\, -\, \frac{2x\, -\, 3}{x}}$

To simplify, you appear to be multiplying, top and bottom, by the LCM of the various denominators, being:

$x(x\, +\, 2)(x\, +\, 1)$

After multiplying, you get:

$\frac{(x^3\, -\, x^2\, -\, 2x)\, +\, (x^3\, +\, x^2\, -\, 2x)}{(x^3\, +\, 2x^2)\, -\, (2x^3\, +\, 3x^2\, -\, 5x\, -\, 6)}$

So I get the same products that you did. Then:

$\frac{2x^3\, -\, 4x}{-x^3\, -\, x^2\, +\, 5x\, +\, 6}$

Each of the numerator and denominator can be factored, but nothing cancels. You can factor the numerator easily, as you have already displayed. You'll need to use the Rational Roots Test to factor the denominator, and then the remaining quadratic is prime.

$\frac{2x(x\, -\, 2)}{-1(x\, +\, 2)(x^2\, -\, x\, -\, 3)}$

So the above is as "simplified" as you can get.

bbsa3412
Posts: 6
Joined: Sat Mar 28, 2009 9:46 pm
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### Re: Need help with Complex Fraction

Thanks for the quick reply!!! I think the reason I was confused with factoring the denominator is because my book does not refer to the rational roots test in prior sections, so I would never had known how to factor it anyway. Thus far it has only demonstrated factoring by common monomial, special products, grouping, and the AC method.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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Long story short: While you should expect to need to factor and simplify this sort of expression on your next test (it's a common "trick"), it is a fact that most of these expressions do not in fact simplify further. Don't be surprised when most of them don't!

P.S. Thank you for showing your work so nicely!!!