https://latex.codecogs.com/png.latex?\dpi{300}%20f(x)=\frac{x^2-5x+6}{x+1}%20\\%20f(x)=ax+b+\frac{c}{x+1}%20\\%20f (x)=\frac{(ax+b)(x+1)+c}{x+1}%20\\%20f(x)=\frac{ax ^2+(a+b)x+b+c}{x+1}%20\\%20\begin{cases}%20a=1%20\ \%20a+b=-5%20\Rightarrow%201+b=-5%20\Rightarrow%20b=-6\\%20b+c=6%20\Rightarrow%20c-6=6%20\Rightarrow%20c=12%20\end{cases}%20\\%20\\%2 0{\color{red}f(x)=x-6+\frac{12}{x+1}}%20\\