Упр.4.42 ГДЗ Мордкович 8 класс (Алгебра)

4.42

а)

$$ \frac{12x+5y}{20x^2y}-\frac{5y-4x}{25xy^2} = \frac{5y(12x+5y)-4x(5y-4x)}{100x^2y^2} $$

$$ \frac{60xy+25y^2-20xy+16x^2}{100x^2y^2} = \frac{25y^2+40xy+16x^2}{100x^2y^2} $$

$$ \frac{(5y+4x)^2}{100x^2y^2} = \left(\frac{5y+4x}{10xy}\right)^2 $$

Тождество верно.

б)

$$ \frac{2n+3m}{12mn^2}-\frac{9m-2n}{18m^2n} = \frac{3m(2n+3m)-2n(9m-2n)}{36m^2n^2} $$

$$ \frac{6mn+9m^2-18mn+4n^2}{36m^2n^2} = \frac{9m^2-12mn+4n^2}{36m^2n^2} $$

$$ \frac{(3m-2n)^2}{36m^2n^2} = \left(\frac{3m-2n}{6mn}\right)^2 $$

Тождество верно.

Ответ

а) $$\frac{12x+5y}{20x^2y}-\frac{5y-4x}{25xy^2}=\left(\frac{5y+4x}{10xy}\right)^2$$
б) $$\frac{2n+3m}{12mn^2}-\frac{9m-2n}{18m^2n}=\left(\frac{3m-2n}{6mn}\right)^2$$