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4x/x^2 - 9 all over 8x^2/x^2 + 6x + 9

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I don't see the simplifies result @MarkRijckenberg
Is this the expression you're looking at? \[\frac{\frac{4x}{x^2 - 9}}{\frac{8x^2}{x^2 + 6x + 9}}\]
It's a bit ambiguous when written out horizontally like that. I recommend liberal use of parentheses.

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Other answers:

Yes that is correct.
If you're going to enter it into a calculator (or wolframalpha), then you'll need to express it like this: (4x/(x^2 - 9)) / ((8x^2)/(x^2 + 6x + 9)) Even then, I tried that in wolframalpha, and it didn't give the fully simplified result.
\[1/2\,{\frac {x+3}{ \left( x-3 \right) x}}\]
Best first step is to express the fraction-division as fraction-mulitplication. (Division is defined as multiplication by the reciprcal.) Then factor the crap out of everything and see what cancels.
from wolfram if you type it like this 4*x/((x^2-9)*(8*x^2/(x^2+6*x+9)))
Or you could just write it down and do the algebra . . .
Guys, both your formula's give the same results in WolfRam....
Yep, and neither shows Lindsey how to do it herself.
Intermediate step looks like this: \[\frac{4x}{(x+3)(x-3)} \space \times \space \frac{(x+3)(x+3)}{8x^2}\]

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