ВПР 1 №55 Алгебра = ВПТ 3 №18 Математика
Виконайте дії:
1. $\left(\frac{2a}{2a-1}+1\right)\cdot\frac{6a-3}{4a^2-a}=\frac{3}{a};$
2. $\left(m+\frac{m^2}{3-m}\right):\frac{m+3}{m-3}=-\frac{3m}{m+3};$
3. $\left(\frac{a}{a-b}-\frac{a}{a+b}\right):\frac{ab}{a+b};$
4. $\left(p-\frac{p^2-3}{p+1}\right)\cdot\frac{p^2-1}{p+3}.$
Розв'язок:
1. a) $\frac{2a}{2a-1}=\frac{2a+2a-1}{2a-1}=\frac{4a-1}{2a-1};$
б) $\frac{4a-1}{2a-1}\cdot\frac{6a-3}{4a^2-a}=$
$= \frac{\left(4a-1\right)\cdot3\left(2a-1\right)}{\left(2a-1\right)\cdot a\left(4a-1\right)}=\frac{3}{a};$
2. a) $ \frac{m}{1}+\frac{m^2}{3-m}=\frac{m\left(3-m\right)+m}{3-m}=$
$= \frac{3m-m^2+m^2}{3-m}=\frac{3m}{3-m};$
б) $\frac{3m}{3-m}:\frac{m+3}{m-3}=\frac{3m}{3-m}\cdot\frac{m-3}{m+3}=$
$= -\frac{3m}{m-3}\cdot\frac{m-3}{m+3}=-\frac{3m}{m+3};$
3. $\left(\frac{a}{a-b}-\frac{a}{a+b}\right):\frac{ab}{a+b}=$
$= \frac{a^2+ab-a^2+ab}{\left(a-b\right)\left(a+b\right)}:\frac{ab}{a+b}=$
$= \frac{2ab\cdot\left(a+b\right)}{\left(a-b\right)\left(a+b\right)\cdot a b}=$
$= \frac{2}{a-b};$
4. $\left(p-\frac{p^2-3}{p+1}\right)\cdot\frac{p^2-1}{p+3}=$
$= \frac{\left(p^2+p-p^2+3\right)\cdot\left(p-1\right)\left(p+1\right)}{\left(p+1\right)\cdot\left(p+3\right)}=$
$= p-1.$