Least Common Denominator: $ \frac{\sqrt{x}}{x}+\frac{\ln\ x}{2\sqrt{x}} $ $$ \frac{\sqrt{x}}{x}+\frac{\ln \ x}{2\sqrt{x}} $$
I have tried combining these two fractions; however, I keep getting stuck. 
$$\frac{2\sqrt{x}}{2\sqrt{x}}\cdot\frac{\sqrt{x}}{x}+\frac{\ln\ x}{2\sqrt{x}}\cdot \frac{x}{x}$$
So that we get
$$\frac {2x}{2\sqrt{x}\cdot(x)}+\frac {x\ln\ x}{2\sqrt{x}\cdot(x)}$$
What am I doing wrong? The answer is $$ \frac{2+\ln\ x}{2\sqrt{x}}$$

Hint:
$\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$
Sometimes one representation is more convenient for what you're trying to do than the other is.
