\[\boxed{\text{227\ (227).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ \frac{2m^{2} - 8}{m^{2} + 6m + 8}\]
\[m^{2} + 6m + 8 = 0\]
\[D_{1} = 3^{2} - 8 = 9 - 8 = 1\]
\[m_{1} = - 3 - 1 = - 4;\ \ \ \ m_{2} =\]
\[= - 3 + 1 = - 2;\]
\[\Longrightarrow m^{2} + 6m + 8 =\]
\[= (m + 4)(m + 2);\]
\[\Longrightarrow \frac{2m^{2} - 8}{m^{2} + 6m + 8} =\]
\[= \frac{2 \cdot \left( m^{2} - 4 \right)}{(m + 4)(m + 2)} =\]
\[= \frac{2 \cdot (m - 2)(m + 2)}{(m + 4)(m + 2)} = \frac{2m - 4}{m + 4}.\]
\[\textbf{б)}\ \frac{2m^{2} - 5m + 2}{mn - 2n - 3m + 6}\]
\[2m^{2} - 5m + 2 = 0\]
\[D = 25 - 4 \cdot 2 \cdot 2 = 25 - 16 = 9\]
\[m_{1} = \frac{5 + 3}{4} = 2;\ \ \ \ m_{2} =\]
\[= \frac{5 - 3}{4} = \frac{1}{2};\]
\[\Longrightarrow 2m^{2} - 5m + 2 =\]
\[= 2 \cdot (m - 2)\left( m - \frac{1}{2} \right) =\]
\[= (m - 2)(2m - 1);\]
\[\Longrightarrow \frac{2m^{2} - 5m + 2}{mn - 2n - 3m + 6} =\]
\[= \frac{(m - 2)(2m - 1)}{n(m - 2) - 3 \cdot (m - 2)} =\]
\[= \frac{(m - 2)(2m - 1)}{(m - 2)(n - 3)} =\]
\[= \frac{2m - 1}{n - 3}.\]