№ 6.9 Алгебра = № 11.9 Математика
Спростіть вираз:
1. $\frac{m^2-n^2}{p+2q}:\frac{mn+m^2}{2p+4q};$
2. $\frac{6x-30}{2x+5}:\frac{x^2-25}{4x+10};$
3. $\frac{a+2}{a-2}:\frac{a^2+4a+4}{5a-10};$
4. $\frac{x+y}{p-2m}:\frac{x^2+2xy+y^2}{2m^2-mp}.$
Розв'язок:
1. $\frac{m^2-n^2}{p+2q}:\frac{mn+m^2}{2p+4q}=$
$= \frac{\left(m-n\right)\left(m+n\right)\cdot2\left(p+2q\right)}{\left(p+2q\right)\cdot m\left(n+m\right)}=$
$= \frac{2\left(m-n\right)}{m};$
2. $\frac{6x-30}{2x+5}:\frac{x^2-25}{4x+10}=$
$= \frac{6\left(x-5\right)\cdot2\left(x+5\right)}{\left(2x+5\right)\left(x-5\right)\left(x+5\right)}= \frac{12}{x+5};$
3. $\frac{a+2}{a-2}:\frac{a^2+4a+4}{5a-10}=\frac{\left(a+2\right)\cdot5\left(a-2\right)}{\left(a-2\right)\cdot\left(a+2\right)^2}=$
$= \frac{5}{a+2};$
4. $\frac{x+y}{p-2m}:\frac{x^2+2xy+y^2}{2m^2-mp}=$
$= \frac{\left(x+y\right)\cdot m\left(2m-p\right)}{-\left(2m-p\right)\left(x+y\right)^2}= -\frac{m}{x+y}.$