Final answer to the problem
$x+\frac{11}{x+1}$
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Step-by-step Solution
Specify the solving method
1
Add the values $5$ and $6$
$\frac{11+x^2+x}{x+1}$
2
Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$
$\frac{x^2+x+11+\frac{1}{4}-\frac{1}{4}}{x+1}$
3
Factor the perfect square trinomial $x^2+x+\frac{1}{4}$
$\frac{\left(x+\sqrt{\left(\frac{1}{4}\right)}\right)^2+11-\frac{1}{4}}{x+1}$
4
Subtract the values $11$ and $-\frac{1}{4}$
$\frac{\frac{43}{4}+\left(x+\sqrt{\left(\frac{1}{4}\right)}\right)^2}{x+1}$
5
Calculate the square root of $\frac{1}{4}$
$\frac{\frac{43}{4}+\left(x+\frac{1}{2}\right)^2}{x+1}$
6
Expand
$\frac{11+x^2+x}{x+1}$
7
Divide $11+x^2+x$ by $x+1$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{2}+x\phantom{;}+11\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}-x\phantom{;};}\phantom{;}11\phantom{;}\phantom{;}\\\end{array}$
8
Resulting polynomial
$x+\frac{11}{x+1}$
Final answer to the problem
$x+\frac{11}{x+1}$