Подайте у вигляді дробу:
1) $\frac{x+2y}{5}+\frac{4x-7y}{5};$
2) $\frac{x-y}{x^2-4}-\frac{y-2}{x^2-4};$
3) $\frac{4-2m}{m}-\frac{5-2p}{p};$
4) $\frac{m}{m-4}-\frac{m^2}{m^2-8m+16};$
5) $\frac{p^2-p}{3py}\cdot\frac{3p}{p^2-1};$
6) $10x^2:\left(-\frac{5x}{m}\right).$
Розв'язок:
1) $\frac{x+2y}{5}+\frac{4x-7y}{5}=\frac{x+2y+4x-7y}{5}=$
$= \frac{5x-5y}{5}=\frac{5(x-y)}{5}=x-y;$
2) $\frac{x-y}{x^2-4}-\frac{y-2}{x^2-4}=\frac{x-y-(y-2)}{x^2-4}=$
$= \frac{x-y-y+2}{x^2-4}=\frac{x-2y+2}{x^2-4};$
3) $\frac{4-2m}{m}-\frac{5-2p}{p}=$
$= \frac{p\left(4-2m\right)-m\left(5-2p\right)}{mp}=$
$=\frac{4p-2mp-5m+2mp}{mp}=\frac{4p-5m}{mp};$
4) $\frac{m}{m-4}-\frac{m^2}{m^2-8m+16}=$
$= \frac{m}{m-4}-\frac{m^2}{(m-4)^2}=\frac{m\left(m-4\right)-m^2}{(m-4)^2}=$
$= \frac{m^2-4m-m^2}{(m-4)^2}=\frac{-4m}{(m-4)^2};$
5) $\frac{p^2-p}{3py}\cdot\frac{3p}{p^2-1}=\frac{p(p-1)\cdot3p}{3py\cdot(p-1)(p+1)}=$
$= \frac{p\cdot p}{y(p+1)}=\frac{p^2}{y(p+1)};$
6) $10x^2 ∶\left(-\frac{5x}{m}\right)=-\frac{10x^2\cdot m}{5x}=$
$= -\frac{2\cdot5\cdot x\cdot x\cdot m}{5\cdot x}=-2xm.$