Номер 125 ГДЗ алгебра 8 класс Макарычев

№125. Представим в виде дроби:
a)

$$
\frac{x^2-1}{a-b} \cdot \frac{7 a-7 b}{a^2+a}=\frac{(x-1)(x+1)}{a-b} \cdot \frac{7(a-b)}{a(a+1)}=\frac{7(x-1)(x+1)(a-b)}{(a-b) a(a+1)}=\frac{7(x-1)(x+1)}{a(a+1)}
$$

б)

$$
\begin{gathered}
\frac{b^2+2 b c}{b+3} \cdot \frac{5 b+15}{b^2-4 c^2}=\frac{b(b+2 c)}{b+3} \cdot \frac{5(b+3)}{(b-2 c)(b+2 c)} \\
=\frac{b(b+2 c) 5(b+3)}{(b+3)(b-2 c)(b+2 c)}=\frac{5 b}{b-2 c}
\end{gathered}
$$

в)

$$
\begin{gathered}
\frac{(x+3)^2}{2 x-4} \cdot \frac{x^2-4}{3 x+9}=\frac{(x+3)(x+3)}{2(x-2)} \cdot \frac{(x-2)(x+2)}{3(x+3)} \\
=\frac{(x+3)(x+3)(x-2)(x+2)}{2(x-2) 3(x+3)}=\frac{x+2}{6}
\end{gathered}
$$

г)

$$
\begin{gathered}
\frac{(5-y)^2}{2 y+12} \cdot \frac{y^2-36}{2 y-10}=\frac{(5-y)(5-y)}{2(y+6)} \cdot \frac{(y-6)(y+6)}{2(y-5)} \\
=\frac{(y+6)(5-y)(5-y)(y-6)}{4(y-5)(y+6)}=\frac{(5-y)(5-y)(y-6)}{4(y-5)} \\
=\frac{(5-y)(y-6)}{4}
\end{gathered}
$$