№ 4.22 Алгебра = № 4.22 Математика
Виконайте дію:
1) $\frac{a\ -\ 2}{2(a\ +\ 1)} + \frac{a}{a\ +\ 1}; $
2) $\frac{m}{4(a\ +\ b)} − \frac{3m}{5(a\ +\ b)};$
3) $\frac{a\ -\ 2}{2a\ +\ 6} − \frac{a\ +\ 1}{3a\ +\ 9}; $
4) $\frac{4}{ax\ -\ ay} + \frac{5}{bx\ -\ by}; $
5) $\frac{5}{x} − \frac{30}{x(x\ +\ 6)};$
6) $\frac{6}{x^2\ +\ 3x} − \frac{2}{x}.$
Розв'язок:
1) $\frac{a - 2}{2(a + 1)} + \frac{a}{a + 1} = \frac{a - 2 + 2a}{2(a + 1)} = $
$= \frac{3a - 2}{2a + 2};$
2) $\frac{m}{4(a\ +\ b)} − \frac{3m}{5(a\ +\ b)} = $
$= \frac{5m\ -\ 12m}{20(a\ +\ b)} = \frac{\ -7m}{20(a\ +\ b)} =$
$= − \frac{\ 7m}{20a\ +\ 20b};$
3) $\frac{a - 2}{2a + 6} − \frac{a + 1}{3a + 9} = $
$= \frac{a - 2}{2(a + 3)} − \frac{a + 1}{3(a + 3)} =$
$= \frac{3(a\ -\ 2)\ -\ 2(a\ +\ 1)}{6(a\ +\ 3)} = $
$= \frac{3a\ -\ 6\ -\ 2a\ \ -\ 2}{6(a\ +\ 3)} = \frac{a\ -\ 8}{6a\ +\ 18}; $
4) $\frac{4}{ax - ay} + \frac{5}{bx - by} = $
$= \frac{4}{a(x - y)} + \frac{5}{b(x - y)} = \frac{4b\ +\ 5a}{ab(x\ -\ y)}; $
5) $\frac{5}{x} − \frac{30}{x(x\ +\ 6)} = \frac{5(x\ +\ 6)\ -\ 30\ }{x(x\ +\ 6)} = $
$= \frac{5x + 30 - 30 }{x(x + 6)} = \frac{5x }{x(x + 6)} = \frac{5 }{x + 6};$
6) $\frac{6}{x^2\ +\ 3x} − \frac{2}{x} = \frac{6}{x(x\ +\ 3)} − \frac{2}{x} =$
$= \ \frac{6\ -\ 2(x\ +\ 3)}{x(x\ +\ 3)} = \frac{6\ -\ 2x\ -\ 6}{x(x\ +\ 3)} = $
$= \frac{-2x}{x(x\ +\ 3)} = − \frac{2}{x\ +\ 3}.$