I'm trying to help my sister with her homework. We have the result of a "composite function" that looks like this:

-5 / ( (3/x) - 3 )

So, negative 5 OVER (3 over x) minus 3

Actually, I'll gimp it:



I'm just wondering if it's possible to reduce that any further. The real result looks like this:



Any way to reduce that further?

Thanks,
Brian

I did this in the 9th grade and I am ashamed to say I forgot how to do that :p

Seems like a reasonable answer to me

5x/(3(x-1))

Just multiply the whole thing by x/x to get the fraction out of the denominator, and then also switch the signs around just to make it neater.

That looks perfectly fine to me.

Thanks all.

I was taught to try and get fractions out of denominators too, but when you just have the one x in the original form, and 2 in the 'neater' version I'd tend to stick with the first layout - particularly if I was going to solve for x via any old method. But that's just my preference.

I agree with Darth's simplification.

Also... use OpenOffice Math or a Microsoft Word Equation for math equations. Math (and probably Equation too) uses the TeX syntax, which I've found relatively painless to learn (but maybe it's because I'm a programmer).

[Edit: Actually Equation has this weird "try to be user friendly" thing going on. I'll have to fool with it. Hmmm...]

Though in his sister's case you probably want to get it to that simplified form so you can find the roots and asymptotes easily.

Aye, quite possibly

Arg, Asymptotes, the bain of my existance.

Almost everything else in Maths that I've covered I can handle, but finding the roots and drawing an asymptote I just can't do.

[Note - This problem only seems to occur with a slant asymptote.]

Yes, slant asymptotes suck. They're easier to understand if you think about the limits that cause them, though.

Everything is fine until I have to deal with dividing by infinity.