ВПР 1 №40 Алгебра = ВПТ 3 №3 Математика
Спростіть вираз:
1. $\frac{x^2-3x}{7}\cdot\frac{21}{x^2-9};$
2. $\frac{-3x-y}{6x+6}\cdot\frac{8x+8}{y-3x};$
3. $\frac{a^2-2a+1}{15m^2}\cdot\frac{5m}{a^2-1};$
4. $\frac{c^2+2c}{12ab}\cdot\frac{20a^2b}{c^2+4c+4}.$
Розв'язок:
1. $\frac{x^2-3x}{7}\cdot\frac{21}{x^2-9}=\frac{21x\left(x-3\right)}{7\left(x-3\right)\left(x+3\right)}=$
$= \frac{3x}{x+3};$
2. $\frac{-3x-y}{6x+6}\cdot\frac{8x+8}{y-3x}=\frac{\left(y-3x\right)\cdot8\left(x+1\right)}{6\left(x+1\right)\left(y-3x\right)}=$
$= \frac{4}{3}=1\frac{1}{3};$
3. $\frac{a^2-2a+1}{15m^2}\cdot\frac{5m}{a^2-1}=$
$= \frac{\left(a-1\right)^2\cdot5m}{15m^2\left(a-1\right)\left(a+1\right)}=$
$= \frac{a-1}{3m\left(a+1\right)};$
4. $\frac{c^2+2c}{12ab}\cdot\frac{20a^2b}{c^2+4c+4}=\frac{c\left(c+2\right)\cdot20a^2b}{12ab\left(c+2\right)^2}=$
$= \frac{5ac}{3\left(c+2\right)}.$