Question

Докажите тождество:
$frac{ {b}^{2} }{ {a}^{2} - ab} = frac{a}{a - b} - frac{b}{a} - 1$

Answer 1

а/(a-b) - b/a - 1 = (a*a-b(a-b)-1(a(a-b))/(a(a-b)) = (a²-ab+b²-a²+ab)/(a(a-b)) = b²/(a²-ab)