Question

Доведіть тотожність
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Answer 1

$\frac{15a + 2.5b}{9a {}^{2} - 1.5ab } - \frac{15a - 2.5b}{9a {}^{2} + 1.5ab } + \frac{60a}{9a {}^{2} - 0.25b {}^{2} } = \frac{40}{6a - b}$

$\frac{15 + \frac{5}{2} b}{9 {a}^{2} - \frac{3}{2}ab } - \frac{15a - \frac{5}{2}b }{9 {a}^{2} + \frac{3}{2}ab } + \frac{60a}{9 {a}^{2} + \frac{3}{2} ab {}^{2} } = \frac{40}{6a - b}$

$\frac{ \frac{30a + 5b}{2} }{9a {}^{2} - \frac{3}{2}ba } - \frac{ \frac{30a - 5b}{2} }{9a {}^{2} + \frac{3}{2}ba } + \frac{60a}{a \times (9a + \frac{3}{2}b {}^{2} )} = \frac{40}{6a - b}$

$\frac{ \frac{30a + 5b}{2} }{ \frac{18a {}^{2} - 3ba}{2} } - \frac{ \frac{30a - 5b}{2} }{ \frac{18a {}^{2} - 3ba}{2} } + \frac{60}{9a + \frac{3}{2}b {}^{2} } = \frac{40}{6a - b}$

$\frac{30a + 5b}{18a {}^{2} - 3ba} - \frac{30a - 5b}{18a {}^{2} + 3ba} + \frac{60}{ \frac{18a + 3b {}^{2} }{2} } = \frac{40}{6a - b}$

$\frac{30a + 5b}{3a \times (6a - b)} - \frac{30a - 5b}{3a \times (6a + b)} + \frac{120}{18a + 3b {}^{2} } = \frac{40}{6a - b}$

$\frac{30a + 5b}{3a \times (6a - b)} - \frac{30a - 5b}{3a \times (6a + b)} + \frac{120}{3(6a + b {}^{2} )} = \frac{40}{6a - b}$

$\frac{30a + 5b}{3a \times (6a - b)} - \frac{30a - 5b}{3a \times (6a + b)} + \frac{40}{6a + b {}^{2} } = \frac{40}{6a - b}$

$\frac{(6a + b) \times (6a + b {}^{2}) \times (30a + 5b) - (6a - b) + (6a + b {}^{2} ) \times (30a - 5b) + 120a \times (6a - b) \times (6a + b)}{3a \times (6a - b) \times (6a + b) \times (6a + b {}^{2}) } = \frac{40}{6a - b}$

$\frac{(36a {}^{2} + 6b {}^{2} a + 6ba + b {}^{3}) \times (30a + 5b) - (36a {}^{2} + 6b {}^{2} a - 6ba - b {}^{3} ) \times (30a - 5b) + 120a \times (36a {}^{2} - b {}^{2} ) }{3a \times (6a - b) \times (6a + b) \times (6a + b {}^{2}) } = \frac{40}{6a - b}$

$a = - \frac{1}{6} \\ a = \frac{1}{6} b$