Question

How do you simplify `(k^2-4)/(3k^2) ÷ (2-k)/(11k)`?

Answer 1

`-11/3((k+2)/k)`

Explanation:

First convert the division to a multiplication by inverting the second fraction:
`(k^2-4)/(3k^2)÷(2-k)/(11k)=(k^2-4)/(3k^2)(11k)/(2-k)`

Factor all the terms:
`(k^2-4)/(3k^2)*(11k)/(2-k)=-((k-2)(k+2))/(3k^2)(11k)/(k-2)`

Cancel similar terms:
`-((k-2)(k+2))/(3k^2)(11k)/(k-2)=-11/3((k+2)/k)`