ВПР 1 №31 Алгебра = ВПТ 1 №31 Математика
Виконайте дію:
1. $\frac{2c-7}{2\left(c+5\right)}+\frac{4-c}{c+5};$
2. $\frac{a-1}{3a+6}-\frac{a}{4a+8};$
3. $\frac{7}{x}-\frac{14}{x\left(x+2\right)};$
4. $\frac{9}{m^2+4m}-\frac{5}{m+4};$
5. $\frac{b}{a^2-b^2}+\frac{1}{a+b};$
6. $\frac{x+3}{x^2+2x+4}-\frac{1}{x+1}.$
Розв'язок:
1. $\frac{2c-7}{2\left(c+5\right)}+\frac{4-c}{c+5}=$
$= \frac{\left(2c-7\right)+2\left(4-c\right)}{2\left(c+5\right)}=$
$= \frac{2c-7+8-2c}{2\left(c+5\right)}=\frac{1}{2c+10};$
2. $\frac{a-1}{3a+6}-\frac{a}{4a+8}=$
$= \frac{a-1}{3\left(a+2\right)}-\frac{a}{4\left(a+2\right)}=$
$= \frac{4\left(a-1\right)-3a}{12\left(a+2\right)}=$
$= \frac{4a-4-3a}{12\left(a+2\right)}=\frac{a-4}{12a+24};$
3. $\frac{7}{x}-\frac{14}{x\left(x+2\right)}=\frac{7\left(x+2\right)-14}{x\left(x+2\right)}=$
$= \frac{7x+14-14}{x\left(x+2\right)}=\frac{7x}{x\left(x+2\right)}=\frac{7}{x+2};$
4. $\frac{9}{m^2+4m}-\frac{5}{m+4}=$
$= \frac{9}{m\left(m+4\right)}-\frac{5m}{m+4}=\frac{9-5m}{m\left(m+4\right)}=$
$= \frac{9-5m}{m^2+4m};$
5. $\frac{b}{a^2-b^2}+\frac{1}{a+b}=$
$= \frac{b}{\left(a-b\right)\left(a+b\right)}+\frac{1}{a+b}=$
$= \frac{b+a-b}{\left(a-b\right)\left(a+b\right)}=\frac{a}{a^2-b^2};$
6. $\frac{x+3}{x^2+2x+4}-\frac{1}{x+1}=$
$= \frac{x+3}{\left(x+1\right)^2}-\frac{1}{x+1}=$
$= \frac{\left(x+3\right)-\left(x+1\right)}{\left(x+1\right)^2}=$
$= \frac{x+1-x-1}{\left(x+1\right)^2}=\frac{2}{\left(x+1\right)^2}.$