Question

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

Answer 1

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