1. ## fraction

Express $\displaystyle \frac{3+h}{h} \times \frac{4h^2}{9-h^2}$ as a single fraction in its simplest form.

2. $\displaystyle \frac{3 + h}{h} \times \frac{4h^2}{9 - h^2} = \frac{3 + h}{h} \times \frac{4h^2}{(3 - h)(3 + h)}$

$\displaystyle = \frac{4h^2(3 + h)}{h(3 - h)(3 + h)}$

$\displaystyle = \frac{4h}{3 - h}$.

3. If you multiply two fractions, you multiply the numerators and the denominators.

$\displaystyle \frac{3+h}{h} * \frac{4h^2}{9-h^2}$
$\displaystyle \frac{(3+h)*(4h^2)}{h*(9-h^2)}$
$\displaystyle \frac{12h^2+4h^3}{9h-h^3}$

You will still need to simplify this and I'd like to encourage you to try that, but if you can't figure it out, feel free to post that.

Edit: Ah well, never mind xD

4. I find that annoying as well... you try to post an answer to help but someone else beats you to it.

5. Originally Posted by Pim
If you multiply two fractions, you multiply the numerators and the denominators.

$\displaystyle \frac{3+h}{h} * \frac{4h^2}{9-h^2}$
$\displaystyle \frac{(3+h)*(4h^2)}{h*(9-h^2)}$
$\displaystyle \frac{12h^2+4h^3}{9h-h^3}$

You will still need to simplify this and I'd like to encourage you to try that, but if you can't figure it out, feel free to post that.

Edit: Ah well, never mind xD
Multiplying out and then simplifying is typically harder than simplifying first and then multiplying.

6. Yeah, I figure you're right on that.