Упр.4.18 ГДЗ Мордкович 8 класс (Алгебра)

а)

$$\frac{m+2}{m^2n}-\frac{n-3}{mn^2} = \frac{n(m+2)-m(n-3)}{m^2n^2} = \frac{mn+2n-mn+3m}{m^2n^2} = \frac{2n+3m}{m^2n^2}$$

б)

$$\frac{z^2+3t}{3z^2t}+\frac{z-2}{2z^2} = \frac{2(z^2+3t)+3t(z-2)}{6z^2t}$$
$$= \frac{2z^2+6t+3zt-6t}{6z^2t} = \frac{2z^2+3zt}{6z^2t} = \frac{z(2z+3t)}{6z^2t} = \frac{2z+3t}{6zt}$$

в)

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

г)

$$\frac{m^3-3n^2}{3m^3n^2}-\frac{m-5}{5m^3} = \frac{5(m^3-3n^2)-3n^2(m-5)}{15m^3n^2}$$
$$= \frac{5m^3-15n^2-3mn^2+15n^2}{15m^3n^2} = \frac{5m^3-3mn^2}{15m^3n^2} = \frac{m(5m^2-3n^2)}{15m^3n^2} = \frac{5m^2-3n^2}{15m^2n^2}$$

Ответ

а) $$\frac{2n+3m}{m^2n^2}$$; б) $$\frac{2z+3t}{6zt}$$; в) $$-\frac{x+2y}{x^2y^2}$$; г) $$\frac{5m^2-3n^2}{15m^2n^2}$$.