ВПР 1 №49 Алгебра = ВПТ 3 №12 Математика
Виконайте дію:
1. $\frac{ax-xy}{a}:\frac{a^2-ay}{x};$
2. $\frac{a^2-b^2}{5a}:\frac{3a+3b}{10a^2};$
3. $\frac{x^2-36}{a-2b}:\frac{x^2+12x+36}{2b-a};$
4. $\frac{3a-a^2}{a^2-4a+4}:\frac{3-a}{4-2a}.$
Розв'язок:
1. $\frac{ax-xy}{a}:\frac{a^2-ay}{x}=$
$= \frac{ax-xy}{a}\cdot\frac{x}{a^2-ay}=$
$= \frac{x\cdot\left(a^2-y\right)\cdot x}{a\cdot a\left(a-y\right)}=$
$= \frac{x^2}{a^2};$
2. $\frac{a^2-b^2}{5a}:\frac{3a+3b}{10a^2}=\frac{a^2-b^2}{5a}\cdot\frac{10a^2}{3a+3b}=$
$= \frac{10a^2\left(a-b\right)\left(a+b\right)}{5a\cdot3\left(a+b\right)}=$
$= \frac{2a\left(a-b\right)}{3};$
3. $\frac{x^2-36}{a-2b}:\frac{x^2+12x+36}{2b-a}=$
$= \frac{x^2-36}{a-2b}\cdot\left(-\frac{a-2b}{x^2+12x+36}\right)=$
$= \frac{\left(x-6\right)\left(x+6\right)\cdot\left(2b-a\right)}{\left(a-2b\right)\cdot\left(x+6\right)^2}=$
$= -\frac{x-6}{x+6}=\frac{6-x}{x+6};$
4. $\frac{3a-a^2}{a^2-4a+4}:\frac{3-a}{4-2a}=$
$= \frac{3a-a^2}{a^2-4a+4}\cdot\frac{4-2a}{3-a}=$
$= \frac{a\left(3-a\right)}{\left(a-2\right)^2}\cdot\frac{2\left(2-a\right)}{\left(3-a\right)}=$
$= \frac{a\cdot\left(3-a\right)\cdot2\left(2-a\right)}{\left(2-a\right)^2\cdot\left(3-a\right)}= \frac{2a}{2-a}.$