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I'm stuck on this rational expression. I factored and simplified, by what do I do next? Should I divide x/2x and 8/4?

I posted my work below.

Thank you!

My work so far

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    $\begingroup$ You're done! You could, if you want, factor out the $2$ from the denominator, like this: $$\dfrac{x+8}{2(x + 2)}\tag{iii} $$ But what you've arrived at (iii) is fine. $\endgroup$
    – amWhy
    Jan 7, 2015 at 22:36
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    $\begingroup$ Looks good to me. $$\frac{2x^2+12x-32}{4x^2-16} = \frac{x+8}{2x+4}.$$ You could say $$\frac{x+8}{2x+4} = \frac12\frac{x+8}{x+2} = \frac12\frac{(x+2)+6}{x+2} =\frac12\left(\frac{x+2}{x+2}+\frac{6}{x+2}\right) = \frac12 + \frac{3}{x+2}.$$ $\endgroup$
    – Eff
    Jan 7, 2015 at 22:39

3 Answers 3

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That's as much as it can be simplified unless you wish to factor out a 2 in the denominator.

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Since the numerator and denominator share no common factors, that is as far as you can simplify. $\frac{x+8}{2x+4}$ is your answer.

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This is it with additional constraints $x\not=\pm2$,also $$\frac{x+8}{2x+4}\not=\frac{x}{2x}+\frac{8}{4}$$

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