1. ## Simplifying complex fraction

I know I shoudl know this, but it's late and for some reason I am drawing a blank. Any help would be appreciated. Thanks

How does $\frac{\frac{3}{x}}{1+\frac{4}{x^2}}$ simplify to $\frac{3x}{x^2+4}$

2. Hello, dbakeg00!

$\text{How does }\,\dfrac{\frac{3}{x}}{1+\frac{4}{x^2}}\,\text{ simplify to }\,\dfrac{3x}{x^2+4}$

Multiply by $\dfrac{x^2}{x^2}$

. . $\displaystyle \frac{x^2}{x^2}\cdot \frac{\frac{3}{x}}{1+\frac{4}{x^2}} \;=\;
\dfrac{x^2\left(\frac{3}{x}\right)}{x^2\left(1 + \frac{4}{x^2}\right)} \;=\;\frac{3x}{x^2+4}$

3. Thanks for the help. I know I need to go to bed when I start struggling with something like this!