Basic calculus Quotient rule question

Hi iam doin quotient rules in calculus and iam just getting stuck at a certain stage in this question.

The question is

$\displaystyle = \frac{3x+1}{\sqrt{x+1}}$

and the answer they have down is

$\displaystyle =\frac{3x+5}{2\sqrt{(x+1)^3}}$

and iam using the forumula

$\displaystyle y=\frac{vu'-uv'}{v^2}$

and iam getting stuck at

$\displaystyle \frac{3(x+1)^\frac{1}{2}-\frac{1}{2}(x+1)^{-\frac{1}{2}}(3x+1)}{x+1}$

could someone please show me the working out and how you do this question thx