Question

Упростите выражение (a/c+c/a-2) * 1/a-c

Answer 1

$(\frac{a}{c} + \frac{c}{a-2} ) * \frac{1}{a-c} = \frac{a(a-2)+c*c}{a(a-2)} * \frac{1}{a-c} = \frac{a^2-2a+c^2}{a(a-2)}* \frac{1}{a-c} = \frac{(a-c)^2*1}{a(a-2)*(a-c)} = \\ \\ = \frac{a-c}{a(a-2)} = \frac{1}{a-2} (1 - \frac{c}{a} )$