Найдите значение выражения: (5b+3)/(b^2-16)-(6b-1)/(b^2-16) при b=4,1; b=-3.

Ответ:

\[\frac{5b + 3}{b^{2} - 16} - \frac{6b - 1}{b^{2} - 16} =\]

\[= \frac{5b + 3 - 6b + 1}{b^{2} - 16} =\]

\[= \frac{- b + 4}{(b - 4)(b + 4)} =\]

\[= \frac{- (b - 4)}{(b - 4)(b + 4)} = - \frac{1}{b + 4}\ \]

\[b = 4,1:\]

\[- \frac{1}{4,1 + 4} = - \frac{1}{8,1} = - \frac{10}{81}.\]

\[b = - 3:\]

\[\frac{- 1}{- 3 + 4} = \frac{- 1}{1} = - 1.\]