Упростите выражение (9b-4)/(b+7)-(44-16b)/(b^2+5b-14).

Ответ:

\[\frac{9b - 4}{b + 7} - \frac{44 - 16b}{b^{2} + 5b - 14} =\]

\[= \frac{9b - 4^{\backslash b - 2}}{b + 7} - \frac{44 - 16b}{(b + 7)(b - 2)} =\]

\[= \frac{(9b - 4)(b - 2) - 44 + 16b}{(b + 7)(b - 2)} =\]

\[= \frac{9b^{2} - 4b - 18b + 8 - 44 + 16b}{(b + 7)(b - 2)} =\]

\[= \frac{9b^{2} - 6b - 36}{(b + 7)(b - 2)}\]

\[b^{2} + 5b - 14 = (b + 7)(b - 2)\]

\[b_{1} + b_{2} = - 5;\ \ \ b_{1} \cdot b_{2} = - 14\]

\[b_{1} = - 7;\ \ \ b_{2} = 2.\]