How do you factor a division problem?

Question

I tried taking out $2\pi r$ from $$\frac{2\pi r h}{2\pi rh+2\pi r^2}$$ Now I have $$2\pi r\left(\frac{h}{h+r}\right)$$

But the final answer said it's: $$\frac{h}{h+r}$$

If we're left with $h/(h+r)$ without the $2\pi r$ how would we reverse and get back to

$$\frac{2\pi r h}{2\pi rh+ 2\pi r^2}$$

Answer 1

There is a copy of $2 \pi r$ in the numerator and another at the denominator.

$$\frac{2\pi rh}{2\pi r h + 2\pi r^2}=\frac{(2\pi r)h}{(2\pi r)( h + r)}$$

cancelling the common term out give you the answer.

Answer 2

You can factor out $2\pi r$ from both numerator and denominator which then cancel each other out. Like $\frac26=\frac{2\times1}{2\times3}=\frac13$.