Упр.1345 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) a:b — ab, если a=-0,5, b=2/3;
2) (b+c)/(b-c), если b=2/7, c=-4/9;
3) (x2+y2)/(x-y), если x=-0,3, y=-0,4.

1) При $$a=-0{,}5$$ и $$b=\frac{2}{3}$$:

$$ a:b-ab=-0{,}5:\frac{2}{3}-(-0{,}5)\cdot\frac{2}{3} $$
$$ =-\frac{1}{2}\cdot\frac{3}{2}+\frac{1}{2}\cdot\frac{2}{3} $$
$$ =-\frac{3}{4}+\frac{1}{3} =-\frac{9}{12}+\frac{4}{12} =-\frac{5}{12} $$

2) При $$b=\frac{2}{7}$$ и $$c=-\frac{4}{9}$$:

$$ \frac{b+c}{b-c} = \frac{\frac{2}{7}+ \left(-\frac{4}{9}\right)}{\frac{2}{7}-\left(-\frac{4}{9}\right)} = \frac{\frac{18}{63}-\frac{28}{63}}{\frac{18}{63}+\frac{28}{63}} = \frac{-\frac{10}{63}}{\frac{46}{63}} = -\frac{10}{63}\cdot\frac{63}{46} = -\frac{5}{23} $$

3) При $$x=-0{,}3$$ и $$y=-0{,}4$$:

$$ \frac{x^2+y^2}{x-y} = \frac{(-0{,}3)^2+(-0{,}4)^2}{-0{,}3-(-0{,}4)} = \frac{0{,}09+0{,}16}{-0{,}3+0{,}4} = \frac{0{,}25}{0{,}1} =2{,}5 $$

Ответ

1) $$-\frac{5}{12}$$; 2) $$-\frac{5}{23}$$; 3) $$2{,}5$$.