Question

(b/a+a/b-2)÷(1/b-1/a)​

Answer 1

$\left(\dfrac{b}{a} +\dfrac{a}{b}-2\right):\left(\dfrac{1}{b}-\dfrac{1}{a}\right)=\dfrac{b\cdot b+a\cdot a-2\cdot ab}{ab}:\dfrac{a-b}{ab}=$

$=\dfrac{a^2-2ab+b^2}{ab}\cdot\dfrac{ab}{a-b}=\dfrac{(a-b)^2}{ab}\cdot\dfrac{ab}{a-b}=\dfrac{(a-b)^2\cdot ab}{ab\cdot(a-b)}=a-b$