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

Ответ:

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

\[3x^{2} - 2x - y^{2}:\]

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

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

\[= 4y^{2} + 12y^{2} = 16y^{2}\]

\[x_{1} = \frac{2y + 4y}{6} = \frac{6y}{6} = y;\]

\[x_{2} = \frac{2y - 4y}{6} = - \frac{2}{6}y = - \frac{y}{3}.\]

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

\[= (x - y)(3x + y).\]

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

\[= \frac{3x + y}{x + y}\]