Question

1/b^2-ab - 1/ab-a^2​

Answer 1

$\frac{1}{b^{2}-ab}-\frac{1}{ab-a^{2}}=\frac{1}{b(b-a)}-\frac{1}{a(b-a)}=\frac{a-b}{ab(b-a)}=-\frac{1}{ab}$

Answer 2

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

Answer 3

To simplify the expression:

1/b^2 - ab - 1/ab - a^2

= (a^2 - ab) / (a^2b^2) - (b^2 - ab) / (a^2b^2)

= [(a^2 - ab) - (b^2 - ab)] / (a^2b^2)

= (a^2 - b^2) / (a^2b^2)

Therefore, the simplified expression is (a^2 - b^2) / (a^2b^2).