Выполните сложение или вычитание дробей:
а)

\frac{c}{b - c} + \frac{b^{2} - 3 b c}{b^{2} - c^{2}}

;
б)

\frac{a + 3}{a^{2} - 1} - \frac{1}{a^{2} + a}

Выполните сложение или вычитание дробей: а) c b − c + b 2 − 3 b c b 2 − c 2 ; б) a + 3 a 2 − 1 − 1 a 2 + a .

\frac{c}{b - c} + \frac{b^{2} - 3 b c}{b^{2} - c^{2}} = \frac{c}{b - c} + \frac{b^{2} - 3 b c}{(b - c) (b + c)} = \frac{c (b + c) + b^{2} - 3 b c}{(b - c) (b + c)} = \frac{b c + c^{2} + b^{2} - 3 b c}{(b - c) (b + c)} = \frac{b^{2} - 2 b c + c^{2}}{(b - c) (b + c)} = \frac{(b - c)^{2}}{(b - c) (b + c)} = \frac{b - c}{b + c}

\frac{a + 3}{a^{2} - 1} - \frac{1}{a^{2} + a} = \frac{a + 3}{(a - 1) (a + 1)} - \frac{1}{a (a + 1)} = \frac{a (a + 3) - (a - 1)}{a (a - 1) (a + 1)} = \frac{a^{2} + 3 a - a + 1}{a (a - 1) (a + 1)} = \frac{a^{2} + 2 a + 1}{a (a - 1) (a + 1)} = \frac{(a + 1)^{2}}{a (a - 1) (a + 1)} = \frac{a + 1}{a (a - 1)}