$$\eqalign{
& y = {{ - {x^2} + 3x} \over {x + 1}}\,\,\left( {D = R\backslash \left\{ 1 \right\}} \right) \cr
& y' = {{\left( { - 2x + 3} \right)\left( {x + 1} \right) - \left( { - {x^2} + 3x} \right)} \over {{{\left( {x + 1} \right)}^2}}} \cr
& y' = {{ - 2{x^2} - 2x + 3x + 3 + {x^2} - 3x} \over {{{\left( {x + 1} \right)}^2}}} \cr
& y' = {{ - {x^2} - 2x + 3} \over {{{\left( {x + 1} \right)}^2}}} \cr
& y' > 0 \Leftrightarrow - {x^2} - 2x + 3 > 0 \cr
& \Leftrightarrow - 3 < x < 1 \cr
& \Rightarrow Ham\,\,so\,\,DB/\left( { - 3; - 1} \right);\,\,\left( { - 1;1} \right) \cr} $$
$$\eqalign{
& y < 0 \Leftrightarrow - {x^2} - 2x + 3 < 0 \cr
& \left[ \matrix{
x > 1 \hfill \cr
x < - 3 \hfill \cr} \right. \Rightarrow Ham\,\,so\,\,NB/\left( { - \infty ; - 3} \right),\,\,\left( {1; + \infty } \right) \cr} $$
