Question

Simplify:
(a-b)/(a^-1-b^-1)

Answer 1

here is my take:
you know that x^-1 = 1/x

so in the denominator you have
(a^-1) - (b^-1) = 1/a - 1/b

you need to have the same denominator, which you get by multiplying both in the numerator and denominatorby the other fraction's denominatior
so you get:

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

the whole expression looks as this:

(a-b)/[b-a/ab] <=> ab(a-b)/(b-a)

multiplying inside the bracket you get:

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

hope this helps...otherwise some other genious may help u :-D ..goodluck.