№ 6.10 Алгебра = № 11.10 Математика
Спростіть вираз:
1. $\frac{ab+b^2}{m-3n}:\frac{a^2-b^2}{2m-6n};$
2. $\frac{x-5}{y^2-4}:\frac{2x-10}{3y-6};$
3. $\frac{x^2-9}{x^2+x}:\frac{x^2+6x+9}{7x+7};$
4. $\frac{x-4y}{a^2-2ab+b^2}:\frac{4xy-x^2}{a-b}.$
Розв'язок:
1. $\frac{ab+b^2}{m-3n}:\frac{a^2-b^2}{2m-6n}=$
$= \frac{b\left(a+b\right)\cdot2\left(m-3n\right)}{\left(m-3n\right)\cdot\left(a-b\right)\left(a+b\right)}= \frac{2b}{a-b};$
2. $\frac{x-5}{y^2-4}:\frac{2x-10}{3y-6}=$
$= \frac{\left(x-5\right)\cdot3\left(y-2\right)}{\left(y-2\right)\left(y+2\right)\cdot2\left(x-5\right)}= \frac{3}{2\left(y+2\right)};$
3. $\frac{x^2-9}{x^2+x}:\frac{x^2+6x+9}{7x+7}=$
$= \frac{\left(x-3\right)\left(x+3\right)\cdot7\left(x+1\right)}{x\left(x+1\right)\left(x+3\right)^2}= \frac{7\left(x-3\right)}{x\left(x+3\right)};$
4. $\frac{x-4y}{a^2-2ab+b^2}:\frac{4xy-x^2}{a-b}=$
$= \frac{\left(x-4y\right)\cdot\left(a-b\right)}{\left(a-b\right)^2\cdot\left(-x\left(x-4y\right)\right)}= $
$= -\frac{1}{x\left(a-b\right)}=\frac{1}{x\left(b-a\right)}.$