Номер 166 ГДЗ алгебра 8 класс Макарычев

№166.
a)

$$
\frac{1-\frac{1}{x}}{1+\frac{1}{x}}=\frac{\frac{x-1}{x}}{\frac{x+1}{x}}=\frac{x-1}{x+1}
$$

б)

$$
\frac{\frac{2 a-b}{h}+1}{\frac{2 a+b}{b}-1}=\frac{\frac{2 a-b+h}{h}}{\frac{2 a+b-b}{b}}=\frac{\frac{2 a-b+h}{h}}{\frac{2 a}{b}}=\frac{(2 a-b+h) b}{2 a h}
$$

в)

$$
\begin{gathered}
\frac{\frac{x}{x^2+y^2}+\frac{y}{x^2}}{\frac{x}{y^2}-\frac{y}{x^2}} \\
\frac{\frac{x\left(x^2\right)+y\left(x^2+y^2\right)}{\left(x^2+y^2\right) x^2}}{\frac{x\left(x^2\right)-y\left(y^2\right)}{x^2 y^2}}=\frac{x^3+y x^2+y^3}{\left(x^2+y^2\right) x^2} \cdot \frac{x^2 y^2}{x^3-y^3}
\end{gathered}
$$

r)

$$
\begin{gathered}
\frac{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}{\frac{1}{a b}+\frac{1}{b c}+\frac{1}{a c}} \\
\frac{a b+b c+a c}{a b c} \\
\frac{a b b c}{a b c}
\end{gathered}=\frac{a b+b c+a c}{a+b+c}
$$