Question

сравните c и d, если C = b/ a²-ab+a/b²-ab, D= a²-b²/a²-2ab+b²: a-b/a+b, при a>0 и b>0​

Answer 1

$c=\frac{b}{a(a-b)}+\frac{a}{b(b-a)}= \frac{b}{a(a-b)}-\frac{a}{b(a-b)}=\frac{b^2-a^2}{ab(a-b)}=\frac{-(a+b)}{ab} <0\\\\ d=\frac{(a-b)(a+b)}{(a-b)^2}:\frac{a-b}{a+b}= \frac{a+b}{a-b}\cdot\frac{a+b}{a-b}= \frac{(a+b)^2}{(a-b)^2}>0 \\ \\ d>c$