ВПР 1 №30 Алгебра = ВПТ 1 №30 Математика
Подайте у вигляді дробу:
1. $2x-\frac{1}{x};$
2. $4p-\frac{4p^2-1}{p};$
3. $\frac{2}{m}+\frac{3}{m-1};$
4. $\frac{m}{1-m}+\frac{1+m}{m};$
5. $\frac{c}{3c-1}+\frac{c}{3c+1};$
6. $\frac{x}{x-y}-\frac{x}{x+y}.$
Розв'язок:
1. $2x-\frac{1}{x}=\frac{2x}{1}-\frac{1}{x}=\frac{2x^2-1}{x};$
2. $4p-\frac{4p^2-1}{p}=\frac{4p}{1}-\frac{4p^2-1}{p}=$
$= \frac{4p^2-\left(4p^2-1\right)}{p}=\frac{4p^2-4p^2+1}{p}=$
$= \frac{1}{p};$
3. $\frac{2}{m}+\frac{3}{m-1}=\frac{2\left(m-1\right)+3m}{m\left(m-1\right)}=$
$= \frac{2m-2+3m}{m\left(m-1\right)}=\frac{5m-2}{m\left(m-1\right)};$
4. $\frac{m}{1-m}+\frac{1+m}{m}=$
$= \frac{m^2+\left(1-m\right)\left(1+m\right)}{m\left(1-m\right)}= \frac{m^2+1-m^2}{m\left(1-m\right)}=$
$= \frac{1}{m\left(1-m\right)}=\frac{1}{m-m^2};$
5. $\frac{c}{3c-1}+\frac{c}{3c+1}=$
$= \frac{c\left(3c+1\right)+c\left(3c-1\right)}{\left(3c-1\right)\left(3c+1\right)}=$
$= \frac{3c^2+c+3c^2-c}{\left(3c-1\right)\left(3c+1\right)}=\frac{6c^2}{9c^2-1};$
6. $\frac{x}{x-y}-\frac{x}{x+y}=\frac{x\left(x+y\right)-x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}=$
$= \frac{x^2+xy-x^2+xy}{\left(x+y\right)\left(x-y\right)}=\frac{2xy}{x^2-y^2}.$