№ 7.1 Алгебра = № 12.1 Математика
Виконайте дії:
1. $\frac{12a+b}{3a}-\frac{7b^2}{a^2}·\frac{a}{21b};$
2. $\frac{m^2-n^2}{x^2-9}\cdot\frac{x-3}{m-n}-\frac{m}{x+3};$
3. $\frac{a-b}{2a+b}+\frac{1}{a-b}:\frac{2a+b}{a^2-b^2};$
4. $x-\frac{x^2-xy}{x+y}\cdot\frac{x}{x-y}.$
Розв'язок:
1. $\frac{12a+b}{3a}-\frac{7b^2}{a^2}·\frac{a}{21b}=$
$= \frac{12a+b}{3a}-\frac{7b^2·a}{a^2·21b}=$
$= \frac{12a+b}{3a}-\frac{b}{3a}=$
$= \frac{12a+b-b}{3a}=\frac{12a}{3a}=4;$
2. $\frac{m^2-n^2}{x^2-9}\cdot\frac{x-3}{m-n}-\frac{m}{x+3}=$
$= \frac{\left(m-n\right)\left(m+n\right)(x-3)}{(x-3)(x+3)(m-n)}-\frac{m}{x+3}=$
$= \frac{m+n}{x+3}\ -\frac{m}{x+3}=\frac{m+n-m}{x+3}=$
$= \ \frac{n}{x+3};$
3. $\frac{a-b}{2a+b}+\frac{1}{a-b}:\frac{2a+b}{a^2-b^2}=$
$= \frac{a-b}{2a+b}+\frac{1\cdot\left(a-b\right)\left(a+b\right)}{\left(a-b\right)\left(2a+b\right)}=$
$= \frac{a-b}{2a+b}+\frac{a+b}{2a+b}=\frac{a-b+a+b}{2a+b}=$
$= \frac{2a}{2a+b};$
4. $x-\frac{x^2-xy}{x+y}\cdot\frac{x}{x-y}=$
$= x-\frac{x\left(x-y\right)\cdot x}{\left(x+y\right)\left(x-y\right)}=$
$= x-\frac{x^2}{x+y}=\frac{x^2+xy-x^2}{x+y}=\frac{xy}{x+y}.$