Question

\(\frac{x^{-3}+y ^{-3} }{ x ^{-1} +y ^{-1}}\) = ???

A. \(x ^{-2}+y ^{-3}\)
B. \(x ^{-2}-y ^{-3}\)
C. \(x ^{-2} - x ^{-1} y ^{-1}+y ^{-2}\)
D. \(x ^{-2} + x ^{-1} y ^{-1}+y ^{-2}\)

Why C not A????

Answer 1

To make this problem easier, just let \(a = x^{-1}\) and \(b = y^{-1}\)

So now we have \(\dfrac{a^3+b^3}{a+b}~\Longrightarrow~\dfrac{(a+b)(a^2-ab+b^2)}{a+b}\)

I bet you know what to do from here.

Answer 2

oh...

Answer 3

umm, then a+b is cancelled...

Answer 4

Right, leave us \(a^2-ab+b^2\).

Plug back in \(x^{-1}\) and \(y^{-1}\)

And we have \(\boxed{x^{-2}-x^{-1}y^{-1}+y^{-2}}\)

Answer 5

oh i see. clear now. thank you so much

Answer 6

Welcome.