Multiply:
(x^(2) -4)/x^(2)) * (x^(2)-2x)/x^(2)+3x-10

Question

Multiply:
(x^(2) -4)/x^(2)) * (x^(2)-2x)/x^(2)+3x-10

anonymous · Answer

$$\frac{ x ^{2} -4}{ x ^{2} } * \frac{ x^{2} - 2x }{ x^{2}+3x-10 }$$

anonymous · Answer

So I factored it out to be
$$\frac{ (x-2)(x+2) }{ x(x) }*\frac{ x(x-2) }{ (x+5)(x-2)}$$

anonymous · Answer

And then I divided out to be 
$$\frac{ x+2 }{ x(x+5)}$$ and that x cannot equal -5 and 2, but my homework is saying that's not correct. Can someone help me out?
@phi @dan815

phi · Answer

you have (x-2) in the top twice.  You can cancel one of them with the bottom (x-2), but that still leaves one up top

anonymous · Answer

Alright, that's what I thought. is that all that I did wrong?

phi · Answer

yes,  all you need is multiply by  (x-2) (up top)

anonymous · Answer

So, my final product would look like
{x+2 (x-2)/x(x+5)}

anonymous · Answer

With x not being able to equal -5 or 2, and those two numbers only?

anonymous · Answer

Okay so I got the question wrong because I did not include 0 as a number x cannot equal. Why would I need to include that if it is obvious and I did not need to include it on my other problems?

phi · Answer

maybe because you canceled out an x.  Technically you have a "double 0"

anonymous · Answer

Can you explain that concept to me? I don't remember hearing it.

phi · Answer

I think x/x^2  with x=0 is different from 1/x with x=0
but I am not a mathematician so I have no good explanation.  Just a guess as to why they want x=0 listed in the excluded values.