Преобразуйте в дробь выражение:
а)

\frac{2 a + b}{2 a^{2} - a b} - \frac{16 a}{a^{2} - b^{2}} - \frac{2 a - b}{2 a^{2} + a b}

;
б)

\frac{1}{(a - 3^{2})} - \frac{2}{a^{2} - 9} + \frac{1}{(a + 3)^{2}}

;
в)

\frac{x - 2}{x^{2} + 2 x + 4} - \frac{6 x}{x^{3} - 8} + \frac{1}{x - 2}

;
г)

\frac{2 a^{2} + 7 a + 3}{a^{3} - 1} - \frac{1 - 2 a}{a^{2} + a + 1} - \frac{3}{a - 1}

Преобразуйте в дробь выражение: а) 2 a + b 2 a 2 − a b − 16 a a 2 − b 2 − 2 a − b 2 a 2 + a b ; б) 1 ( a − 3 2 ) − 2 a 2 − 9 + 1 ( a + 3 ) 2 ; в) x − 2 x 2 + 2 x + 4 − 6 x x 3 − 8 + 1 x − 2 ; г) 2 ...

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

\frac{1}{(a - 3^{2})} - \frac{2}{a^{2} - 9} + \frac{1}{(a + 3)^{2}} = \frac{(a + 3)^{2} - 2 (a^{2} - 9) + (a - 3)^{2}}{(a - 3)^{2} (a + 3)^{2}} = \frac{a^{2} + 6 a + 9 - 2 a^{2} + 18 + a^{2} - 6 a + 9}{(a - 3)^{2} (a + 3)^{2}} = \frac{36}{(a - 3)^{2} (a + 3)^{2}} = \frac{36}{(a^{2} - 9)^{2}}

\frac{x - 2}{x^{2} + 2 x + 4} - \frac{6 x}{x^{3} - 8} + \frac{1}{x - 2} = \frac{(x - 2)^{2} - 6 x + x^{2} + 2 x + 4}{(x - 2) (x^{2} + 2 x + 4)} = \frac{x^{2} - 4 x + 4 - 6 x + x^{2} + 2 x + 4}{(x - 2) (x^{2} + 2 x + 4)} = \frac{2 x^{2} - 8 x + 8}{(x - 2) (x^{2} + 2 x + 4)} = \frac{2 (x - 2)^{2}}{(x - 2) (x^{2} + 2 x + 4)} = \frac{2 (x - 2)}{x^{2} + 2 x + 4}

\frac{2 a^{2} + 7 a + 3}{a^{3} - 1} - \frac{1 - 2 a}{a^{2} + a + 1} - \frac{3}{a - 1} = \frac{2 a^{2} + 7 a + 3 - (1 - 2 a) (a - 1) - 3 (a^{2} + a + 1)}{(a - 1) (a^{2} + a + 1)} = \frac{2 a^{2} + 7 a + 3 + 2 a^{2} - 3 a + 1 - 3 a^{2} - 3 a - 3}{(a - 1) (a^{2} + a + 1)} = \frac{a^{2} + a + 1}{(a - 1) (a^{2} + a + 1)} = \frac{1}{a - 1}