Question

Dau 100 pct și coroană, efortul este apreciat!

Answer 1

$\frac{2x {}^{2} + 4x + 2}{6x {}^{4} - 12x {}^{3} } \cdot \frac{3x {}^{2} }{ x+ 1} - \frac{x + 4}{x {}^{2} - 4} \\ \\ \frac{2(x {}^{2} + 2x + 1)}{6x {}^{3} (x - 2)} \cdot \frac{3x {}^{2} }{ x+ 1} - \frac{x + 4}{(x - 2)(x + 2)} \\ \\ = \frac{(x + 1) {}^{2} }{3x {}^{3} (x - 2)} \cdot \frac{3x {}^{2} }{ x+ 1} - \frac{x + 4}{(x - 2)(x + 2)} \\ \\ = \frac{ {}^{ {}^{x + 2)} } x + 1}{x(x - 2)} - \frac{ {}^{ {}^{x)} } x + 4}{(x - 2)(x +2) } \\ \\ = \frac{(x + 1)(x + 2) - x(x + 4)}{x(x - 2)(x + 2)} \\ \\ = \frac{x {}^{2} + 2x + x + 2 - x {}^{2} - 4x }{x(x - 2)(x + 2)} \\ \\ = \frac{ - x + 2}{x(x - 2)(x + 2)} \\ \\ = \frac{ - (x - 2)}{x(x - 2)(x + 2)} \\ \\ = - \frac{1}{x(x + 2)} \\ \\ = - \frac{1}{x {}^{2} + 2x }$