Precalculus Question

Question

Simplify (a-b)(a^-1b+ab^-1)^-1

Answer 1

Using that for any nonzero number A^(-1)=1/A we may rewrite your expression as

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