Question

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(2а²-а/а²-а+1):(1/а+1-а-1/а²-а+1)

Answer 1

Объяснение:

$( \frac{2a {}^{2} - a}{a {}^{2} - a + 1} - 2) \div ( \frac{1}{a + 1} - \frac{a - 1}{a {}^{2} - a + 1} ) =\frac{\frac{2a^{2}-a}{a^{2}-a+1}-\frac{2\left(a^{2}-a+1\right)}{a^{2}-a+1}}{\frac{1}{a+1}-\frac{a-1}{a^{2}-a+1}} =\frac{\frac{2a^{2}-a-2\left(a^{2}-a+1\right)}{a^{2}-a+1}}{\frac{1}{a+1}-\frac{a-1}{a^{2}-a+1}} =\frac{\frac{2a^{2}-a-2a^{2}+2a-2}{a^{2}-a+1}}{\frac{1}{a+1}-\frac{a-1}{a^{2}-a+1}} =\frac{\frac{a-2}{a^{2}-a+1}}{\frac{1}{a+1}-\frac{a-1}{a^{2}-a+1}} =\frac{\frac{a-2}{a^{2}-a+1}}{\frac{a^{2}-a+1}{\left(a+1\right)\left(a^{2}-a+1\right)}-\frac{\left(a-1\right)\left(a+1\right)}{\left(a+1\right)\left(a^{2}-a+1\right)}} =\frac{\frac{a-2}{a^{2}-a+1}}{\frac{a^{2}-a+1-\left(a-1\right)\left(a+1\right)}{\left(a+1\right)\left(a^{2}-a+1\right)}} =\frac{\frac{a-2}{a^{2}-a+1}}{\frac{a^{2}-a+1-a^{2}-a+a+1}{\left(a+1\right)\left(a^{2}-a+1\right)}} =\frac{\frac{a-2}{a^{2}-a+1}}{\frac{-a+2}{\left(a+1\right)\left(a^{2}-a+1\right)}} =\frac{\left(a-2\right)\left(a+1\right)\left(a^{2}-a+1\right)}{\left(a^{2}-a+1\right)\left(-a+2\right)} =\frac{-\left(a+1\right)\left(-a+2\right)\left(a^{2}-a+1\right)}{\left(-a+2\right)\left(a^{2}-a+1\right)} =-\left(a+1\right) =-a-1$