Виконайте дію:
1) $\frac{x+y}{5}-\frac{x}{5};$
2) $\frac{4m^2}{5}+\frac{m^2}{5}; $
3) $\frac{12}{x^2}\cdot\frac{x}{3}; $
4) $\frac{a^2}{3}:\frac{a}{15}.$
Розв'язок:
1) $\frac{x+y}{5}-\frac{x}{5}=\frac{x+y-x}{5}=\frac{y}{5};$
2) $\frac{4m^2}{5}+\frac{m^2}{5}=\frac{4m^2+m^2}{5}=$
$ = \frac{5m^2}{5}=m^2;$
3) $\frac{12}{x^2}\cdot\frac{x}{3}=\frac{12\cdot x}{x^2\cdot3}=\frac{3\cdot4\cdot x}{x\cdot x\cdot3}=\frac{4}{x};$
4) $\frac{a^2}{3} ∶\frac{a}{15}=\frac{a^2}{3}\cdot\frac{15}{a}=\frac{a^2\cdot15}{3\cdot a}=$
$= \frac{a\cdot a\cdot3\cdot5}{3\cdot a}=5a.$