Приведите к общему знаменателю дроби:
1) $\frac{2p}{5p - 15}$ и $\frac{1}{p^3 - 27}$;
2) $\frac{3a + 1}{9a^2 - 6a + 1}$ и $\frac{a - 2}{9a^2 - 1}$;
3) $\frac{a}{a^2 - 7a}$ и $\frac{a + 3}{a^2 - 14a + 49}$;
4) $\frac{2x}{x^2 - 1}, \frac{3x}{x^2 - 2x + 1}$ и $\frac{4}{x^2 + 2x + 1}$;
5) $\frac{a^2}{a^2 - ab - ac + bc}, \frac{b}{2a - 2b}$ и $\frac{ab}{4a - 4c}$.
$\frac{2p}{5p - 15} = \frac{2p}{5(p - 3)} = \frac{2p(p^2 + 3p + 9)}{5(p - 3)(p^2 + 3p + 9)} = \frac{2p(p^2 + 3p + 9)}{5(p^3 - 27)}$
$\frac{1}{p^3 - 27} = \frac{1}{(p - 3)(p^2 + 3p + 9)} = \frac{5}{5(p - 3)(p^2 + 3p + 9)} = \frac{5}{5(p^3 - 27)}$
$\frac{3a + 1}{9a^2 - 6a + 1} = \frac{3a + 1}{(3a - 1)^2} = \frac{(3a + 1)(3a + 1)}{(3a - 1)^2(3a + 1)} = \frac{(3a + 1)^2}{(3a - 1)^2(3a + 1)}$
$\frac{a - 2}{9a^2 - 1} = \frac{a - 2}{(3a - 1)(3a + 1)} = \frac{(a - 2)(3a - 1)}{(3a - 1)(3a + 1)(3a - 1)} = \frac{(a - 2)(3a - 1)}{(3a - 1)^2(3a + 1)}$
$\frac{a}{a^2 - 7a} = \frac{a}{a(a - 7)} = \frac{a - 7}{(a - 7)(a - 7)} = \frac{a - 7}{(a - 7)^2}$
$\frac{a + 3}{a^2 - 14a + 49} = \frac{a + 3}{(a - 7)^2} = \frac{a(a + 3)}{a(a - 7)^2} = \frac{a + 3}{(a - 7)^2}$
$\frac{2x}{x^2 - 1} = \frac{2x}{(x - 1)(x + 1)} = \frac{2x(x - 1)(x + 1)}{(x - 1)(x + 1)(x - 1)(x + 1)} = \frac{2x(x^2 - 1)}{(x - 1)^2(x + 1)^2}$
$\frac{3x}{x^2 - 2x + 1} = \frac{3x}{(x - 1)^2} = \frac{3x(x + 1)^2}{(x - 1)^2(x + 1)^2}$
$\frac{4}{x^2 + 2x + 1} = \frac{4}{(x + 1)^2} = \frac{4(x - 1)^2}{(x - 1)^2(x + 1)^2}$
$\frac{a^2}{a^2 - ab - ac + bc} = \frac{a^2}{(a^2 - ab) - (ac - bc)} = \frac{a^2}{a(a - b) - c(a - b)} = \frac{a^2}{(a - b)(a - c)} = \frac{4a^2}{4(a - b)(a - c)}$
$\frac{b}{2a - 2b} = \frac{b}{2(a - b)} = \frac{2 * b(a - c)}{2 * 2(a - b)(a - c)} = \frac{2b(a - c)}{4(a - b)(a - c)}$
$\frac{ab}{4a - 4c} = \frac{ab}{4(a - c)} = \frac{ab(a - b)}{4(a - b)(a - c)}$
Пожауйста, оцените решение
