ВПР 1 №18 Алгебра = ВПТ 1 №18 Математика
Спростіть вираз:
1. $\frac{3m-7}{12m}+\frac{13-5m}{12m}-\frac{6m-2}{12m};$
2. $\frac{m^2+1}{a\left(m-1\right)}-\frac{2}{a\left(m-1\right)};$
3. $\frac{x-8}{x^2-25}+\frac{13}{x^2-25};$
4. $\frac{a-4}{a-2}-\frac{2}{2-a}.$
Розв'язок:
1. $\frac{3m-7}{12m}+\frac{13-5m}{12m}-\frac{6m-2}{12m}=$
$= \frac{3m-7+13-5m-6m+2}{12m}=$
$= \frac{8-8m}{12m}= \frac{8\left(1-m\right)}{12m}=\frac{2\left(1-m\right)}{3m};$
2. $\frac{m^2+1}{a\left(m-1\right)}-\frac{2}{a\left(m-1\right)}=\frac{m^2+1-2}{a\left(m-1\right)}=$
$= \frac{m^2-1}{a\left(m-1\right)}=\frac{\left(m-1\right)\left(m+1\right)}{a\left(m-1\right)}=$
$= \frac{m+1}{a};$
3. $\frac{x-8}{x^2-25}+\frac{13}{x^2-25}=\frac{x-8+13}{x^2-25}=$
$= \frac{x+5}{x^2-25}=\frac{x+5}{\left(x-5\right)\left(x+5\right)}=\frac{1}{x-5};$
4. $\frac{a-4}{a-2}-\frac{2}{2-a}=\frac{a-4}{a-2}+\frac{2}{a-2}=$
$= \frac{a-4+2}{a-2}=\frac{a-2}{a-2}=1.$