Преобразуйте в дробь выражение:
а)

\frac{b - 6}{4 - b^{2}} + \frac{2}{2 b - b^{2}}

;
б)

\frac{b}{a b - 5 a^{2}} - \frac{15 b - 25 a}{b^{2} - 25^{2}}

;
в)

\frac{x - 12 a}{x^{2} - 16 a^{2}} - \frac{4 a}{4 a x - x^{2}}

;
г)

\frac{a - 30 y}{a^{2} - 100 y^{2}} - \frac{10 y}{10 a y - a^{2}}

Преобразуйте в дробь выражение: а) b − 6 4 − b 2 + 2 2 b − b 2 ; б) b a b − 5 a 2 − 15 b − 25 a b 2 − 25 2 ; в) x − 12 a x 2 − 16 a 2 − 4 a 4 a x − x 2 ; г) a − 30 y a 2 − 100 y 2 − 10 y 10 a y − a...

\frac{b - 6}{4 - b^{2}} + \frac{2}{2 b - b^{2}} = \frac{b - 6}{(2 - b) (2 + b)} + \frac{2}{b (2 - b)} = \frac{b (b - 6) + 2 (2 + b)}{b (2 - b) (2 + b)} = \frac{b^{2} - 6 b + 4 + 2 b}{b (2 - b) (2 + b)} = \frac{b^{2} - 4 b + 4}{b (2 - b) (2 + b)} = \frac{(b - 2)^{2}}{b (2 - b) (2 + b)} = \frac{(2 - b)^{2}}{b (2 - b) (2 + b)} = \frac{2 - b}{b (2 + b)}

\frac{b}{a b - 5 a^{2}} - \frac{15 b - 25 a}{b^{2} - 25^{2}} = \frac{b}{a (b - 5 a)} - \frac{15 b - 25 a}{(b - 5 a) (b + 5 a)} = \frac{b (b + 5 a) - a (15 b - 25 a)}{a (b - 5 a) (b + 5 a)} = \frac{b^{2} + 5 a b - 15 a b + 25 a^{2}}{a (b - 5 a) (b + 5 a)} = \frac{b^{2} - 10 a b + 25 a^{2}}{a (b - 5 a) (b + 5 a)} = \frac{(b - 5 a)^{2}}{a (b - 5 a) (b + 5 a)} = \frac{b - 5 a}{a (b + 5 a)}

\frac{x - 12 a}{x^{2} - 16 a^{2}} - \frac{4 a}{4 a x - x^{2}} = \frac{x - 12 a}{(x - 4 a) (x + 4 a)} + \frac{4 a}{x (x - 4 a)} = \frac{x (x - 12 a) + 4 a (x + 4 a)}{x (x - 4 a) (x + 4 a)} = \frac{x^{2} - 12 a x + 4 a x + 16 a^{2}}{x (x - 4 a) (x + 4 a)} = \frac{x^{2} - 8 a x + 16 a^{2}}{x (x - 4 a) (x + 4 a)} = \frac{(x - 4 a)^{2}}{x (x - 4 a) (x + 4 a)} = \frac{x - 4 a}{x (x + 4 a)}

\frac{a - 30 y}{a^{2} - 100 y^{2}} - \frac{10 y}{10 a y - a^{2}} = \frac{a - 30 y}{(a - 10 y) (a + 10 y)} + \frac{10 y}{a (a - 10 y)} = \frac{a (a - 30 y) + 10 y (a + 10 y)}{a (a - 10 y) (a + 10 y)} = \frac{a^{2} - 30 a y + 10 a y + 100 y^{2}}{a (a - 10) (a + 10 y)} = \frac{a^{2} - 20 a y + 100 y^{2}}{a (a - 10 y) (a + 10 y)} = \frac{(a - 10 y^{2})}{a (a - 10 y) (a + 10 y)} = \frac{a - 10 y}{a (a + 10 y)}