Упр.3.13 ГДЗ Мордкович 8 класс (Алгебра)

1. $$\frac{2z}{9-z^2}-\frac{6}{9-z^2}=\frac{2z-6}{9-z^2}=\frac{2(z-3)}{-(z-3)(z+3)}=-\frac{2}{z+3}$$

2. $$\frac{x^2+1}{xy-y^2}+\frac{y^2+1}{y^2-xy}=\frac{x^2+1}{xy-y^2}-\frac{y^2+1}{xy-y^2}$$

   $$=\frac{x^2+1-y^2-1}{xy-y^2}=\frac{x^2-y^2}{y(x-y)}=\frac{(x-y)(x+y)}{y(x-y)}=\frac{x+y}{y}$$

3. $$\frac{3t}{49-t^2}-\frac{21}{49-t^2}=\frac{3t-21}{49-t^2}=\frac{3(t-7)}{-(t-7)(t+7)}=-\frac{3}{t+7}$$

4. $$\frac{p^2-2}{p^2-pq}+\frac{q^2-2}{pq-p^2}=\frac{p^2-2}{p^2-pq}-\frac{q^2-2}{p^2-pq}$$

   $$=\frac{p^2-2-q^2+2}{p^2-pq}=\frac{p^2-q^2}{p^2-pq}=\frac{(p-q)(p+q)}{p(p-q)}=\frac{p+q}{p}$$

Ответ

а) $$-\frac{2}{z+3}$$; б) $$\frac{x+y}{y}$$; в) $$-\frac{3}{t+7}$$; г) $$\frac{p+q}{p}$$.