How do I simplify a fraction with a square root on the numerator?

Question

How do I simplify this fraction :

$$\frac{(3x^2+4x)\sqrt {x+1}}{2(x+1)^2}$$

The final result is $\frac{3x^2+4x} {2(x+1)^{3/2}}$.

Answer 1

You divide the numerator and the denominator by $\sqrt{x+1}$, which gives the desired result.