Сократите дробь (2x^2+3xy+y^2)/(x^2-y^2 ).

Ответ:

\[\frac{2x^{2} + 3xy + y^{2}}{x^{2} - y^{2}}\]

\[2x^{2} + 3xy + y^{2}\]

\[a = 2;b = 3y;\ \ c = y^{2}\]

\[D = (3y)^{2} - 4 \cdot 2 \cdot y^{2} = 9y^{2} - 8y^{2} = y^{2}\]

\[x_{1} = \frac{- 3y + y}{4} = - \frac{2y}{4} = - \frac{y}{2};\]

\[x_{2} = \frac{- 3y - y}{4} = - \frac{4y}{4} = - y.\]

\[2x^{2} + 3xy + y^{2} = 2 \cdot \left( x + \frac{y}{2} \right)(x + y) =\]

\[= (2x + y)(x + y)\]

\[\frac{2x^{2} + 3xy + y^{2}}{x^{2} - y^{2}} = \frac{(2x + y)(x + y)}{(x - y)(x + y)} =\]

\[= \frac{2x + y}{x - y}\]