Question

найдите значение выражения  (frac{a}{b}-frac{b}{a}):(1+frac{a}{b}) при а=
9sqrt{7},b=6sqrt{7}

Answer 1

$(frac{a}{b}-frac{b}{a}):(1+frac{a}{b}) = frac{a^2-b^2}{ab}*frac{b}{a+b} = frac{a-b}{a}$

$frac{a-b}{a} = frac{9sqrt{7}-6sqrt{7}}{9sqrt{7}} = frac{3sqrt{7}}{9sqrt{7}} = frac{1}{3}$