Номер 163 ГДЗ алгебра 8 класс Макарычев

№163.
a)

$$
\begin{gathered}
\left(\frac{2 a b}{a^2-b^2}+\frac{a-b}{2 a+2 b}\right) \cdot\left(\frac{2 a}{a+b}+\frac{b}{b-a}\right) \\
\frac{2 a b}{(a-b)(a+b)}+\frac{a-b}{2(a+b)} \\
\frac{2 a b+(a-b)(a+b)}{2(a+b)(a-b)}=\frac{a^2+b^2}{2(a+b)(a-b)} \\
\left(\frac{2 a}{a+b}-\frac{b}{a-b}\right)=\frac{2 a(a-b)-b(a+b)}{(a+b)(a-b)} \\
\frac{2 a^2-2 a b-a b-b^2}{(a+b)(a-b)}=\frac{2 a^2-3 a b-b^2}{(a+b)(a-b)} \\
\frac{a^2+b^2}{2(a+b)(a-b)} \cdot \frac{2(a+b)(a-b)}{a^2+b^2}=1
\end{gathered}
$$

\begin{aligned}
&\text { б) }\\
&\begin{gathered}
\left(\frac{y}{x-y}-\frac{x^3-x y^2}{x^2+y^2}\right) \cdot\left(\frac{x}{(x-y)^2}-\frac{y}{x^2-y^2}\right) \\
\frac{y\left(x^2+y^2\right)-\left(x^3-x y^2\right)}{(x-y)\left(x^2+y^2\right)} \\
\frac{y x^2+y^3-x^3+x y^2}{(x-y)\left(x^2+y^2\right)} \\
\frac{y^3+x y^2-x^3+y x^2}{(x-y)\left(x^2+y^2\right)} \\
\left(\frac{x}{(x-y)^2}-\frac{y}{x^2-y^2}\right)=\frac{x\left(x^2-y^2\right)-y(x-y)^2}{(x-y)^2\left(x^2-y^2\right)} \\
\frac{x^3-x y^2-y x^2+y^3}{(x-y)^2\left(x^2-y^2\right)} \\
\frac{y^3+x y^2-x^3+y x^2}{(x-y)\left(x^2+y^2\right)} \cdot \frac{x^3-x y^2-y x^2+y^3}{(x-y)^2\left(x^2-y^2\right)}=1
\end{gathered}
\end{aligned}