Номер 170 ГДЗ алгебра 8 класс Макарычев

№170.
a)

$$
\frac{\frac{a^2}{4}-\frac{b^2}{9}}{\frac{a+b}{12}+\frac{a}{18}}
$$


Подставляем $a=\frac{2}{3}, b=-\frac{1}{2}$ :

$$
\begin{gathered}
a^2=\left(\frac{2}{3}\right)^2=\frac{4}{9}, \quad b^2=\left(-\frac{1}{2}\right)^2=\frac{1}{4} \\
\frac{\frac{4}{9} \div 4-\frac{1}{4} \div 9}{\frac{\frac{2}{3}-\frac{1}{2}}{12}+\frac{2}{3}} 1 \\
\frac{\frac{4}{36}-\frac{1}{36}}{\frac{4}{36}-3}+\frac{4}{54} \\
\frac{\frac{3}{36}}{\frac{4-3}{36}+\frac{4}{54}} \\
\frac{\frac{3}{36}}{\frac{1}{36}+\frac{2}{27}}=\frac{\frac{1}{12}}{\frac{3}{36}}=1
\end{gathered}
$$

б)

$$
0.2 \frac{a-b}{\frac{a^2}{25}-b^2}
$$


Подставляем $a=-8, b=0.6$ :

$$
\begin{gathered}
a^2=(-8)^2=64 \\
\frac{-8-0.6}{\frac{64}{25}-(0.6)^2} \\
\frac{-8.6}{\frac{64}{25}-\frac{0.36}{1}} \\
\frac{-8.6}{\frac{64-9}{25}}=\frac{-8.6}{\frac{55}{25}} \\
\frac{-8.6 \times 25}{55}=\frac{-215}{55}=-3.91 \\
0.2 \times(-3.91)=-0.782
\end{gathered}
$$