Question

Упрастите выражение:

Answer 1

Ответ:

$\frac{ \sqrt{4} - 4a + a {}^{2} }{a - 2} - \frac{a - 2}{a {}^{2} - 4} =\frac{2-4a^{2}+a^{2}}{a-2}-\frac{a-2}{a^{2}-4} =\frac{2-3a^{2}}{a-2}-\frac{a-2}{a^{2}-4} =\frac{2-3a^{2}}{a-2}-\frac{a-2}{\left(a-2\right)\left(a+2\right)} =\frac{2-3a^{2}}{a-2}-\frac{1}{a+2} =\frac{\left(2-3a^{2}\right)\left(a+2\right)}{\left(a-2\right)\left(a+2\right)}-\frac{a-2}{\left(a-2\right)\left(a+2\right)} =\frac{\left(2-3a^{2}\right)\left(a+2\right)-\left(a-2\right)}{\left(a-2\right)\left(a+2\right)} =\frac{2a+4-3a^{3}-6a^{2}-a+2}{\left(a-2\right)\left(a+2\right)} =\frac{a+6-6a^{2}-3a^{3}}{\left(a-2\right)\left(a+2\right)} =\frac{a+6-6a^{2}-3a^{3}}{a^{2}-4}$