Question

спростити вираз
даю 50 балов​

Answer 1

Ответ:

$\frac{x}{x + 2} - \frac{(x - 2) {}^{2} }{2} \times ( \frac{1}{x {}^{2} - 4} + \frac{1}{x {}^{2} - 4x + 4} )= \frac{x}{x+2}-\frac{\left(x-2\right)^{2}}{2}\left(\frac{1}{\left(x-2\right)\left(x+2\right)}+\frac{1}{\left(x-2\right)^{2}}\right) =\frac{x}{x+2}-\frac{\left(x-2\right)^{2}}{2}\left(\frac{x-2}{\left(x+2\right)\left(x-2\right)^{2}}+\frac{x+2}{\left(x+2\right)\left(x-2\right)^{2}}\right) =\frac{x}{x+2}-\frac{\left(x-2\right)^{2}}{2}\times \left(\frac{x-2+x+2}{\left(x+2\right)\left(x-2\right)^{2}}\right) =\frac{x}{x+2}-\frac{\left(x-2\right)^{2}}{2}\times \left(\frac{2x}{\left(x+2\right)\left(x-2\right)^{2}}\right) =\frac{x}{x+2}-\frac{\left(x-2\right)^{2}\times 2x}{2\left(x+2\right)\left(x-2\right)^{2}} =\frac{x}{x+2}-\frac{x}{x+2} =0$