Mathematic Problems

121. példa

$2 x^{- n} {(x^{n} - 1)}^{- 1} - 4 {(x^{2 n} - 1)}^{- 1} + 2 x^{- n} {(x^{n} + 1)}^{- 1}$

$= \frac{2}{x^{n}} \cdot \frac{1}{x^{n} - 1} - \frac{4}{x^{2 n} - 1} + \frac{2}{x^{n}} \cdot \frac{1}{x^{n} + 1}$

$= \frac{2}{x^{n} (x^{n} - 1)} - \frac{4}{(x^{n} - 1) (x^{n} + 1)} + \frac{2}{x^{n} (x^{n} + 1)}$

$= \frac{2 (x^{n} + 1) - 4 x^{n} + 2 (x^{n} - 1)}{x^{n} (x^{n} - 1) (x^{n} + 1)}$

$= \frac{2 x^{n} + 2 - 4 x^{n} + 2 x^{n} - 2}{x^{n} (x^{n} - 1) (x^{n} + 1)}$

$= \frac{4 x^{n} - 4 x^{n} + 2 - 2}{x^{n} (x^{n} - 1) (x^{n} + 1)}$

$= \frac{0}{x^{n} (x^{n} - 1) (x^{n} + 1)}$

= 0

Matematika - Képlettár