Calculate $\underset{x\rightarrow7}{\lim}\frac{\sqrt{x+2}-\sqrt[3]{x+20}}{\sqrt[4]{x+9}-2}$ Please help me calculate this:
$$\underset{x\rightarrow7}{\lim}\frac{\sqrt{x+2}-\sqrt[3]{x+20}}{\sqrt[4]{x+9}-2}$$
Here I've tried multiplying by $\sqrt[4]{x+9}+2$ and few other method. 
Thanks in advance for solution / hints using simple methods.
Edit
Please don't use l'Hosplital rule. We are before derivatives, don't know how to use it correctly yet. Thanks!

$\frac{112}{27}$ which is roughly 4.14815
The derivative of the top at $x=7$ is $\frac{7}{54}$
The derivative of the bottom at $x=7$ is $\frac{1}{32}$
$\frac{(\frac{7}{54})}{(\frac{1}{32})}$ is $\frac{112}{27}$
