18. Найдите значение выражения \(\frac{a^2-25b^2}{5ab}:(\frac{1}{5b}-\frac{1}{a})\) при a = 8-\(\frac{1}{16}\), b = 6\(\frac{3}{16}\)

Упростим выражение:

\(\frac{a^2-25b^2}{5ab}:(\frac{1}{5b}-\frac{1}{a}) = \frac{(a-5b)(a+5b)}{5ab}:(\frac{a-5b}{5ab}) = \frac{(a-5b)(a+5b)}{5ab}\cdot\frac{5ab}{a-5b} = a+5b\)

Найдем его значение при a = 8-\(\frac{1}{16}\), b = 6\(\frac{3}{16}\):

a = 8-\(\frac{1}{16}\) = \(\frac{128}{16}-\frac{1}{16} = \frac{127}{16}\)

b = 6\(\frac{3}{16}\) = \(\frac{96}{16}+\frac{3}{16} = \frac{99}{16}\)

a + 5b = \(\frac{127}{16}+5\cdot\frac{99}{16} = \frac{127}{16}+\frac{495}{16} = \frac{622}{16} = \frac{311}{8} = 38.875\)

Ответ: 38,875