Question

How do you find the quotient of `(3a)/(a^2+2a+1)div(a-1)/(a+1)`?

Answer 1

`(3a)/((a+1)(a-1))`

Explanation:

`"factor the denominator of the fraction on the left"`

`"Change division to multiplication and turn the fraction"`
`"on the right upside down. Perform any cancelling"`

`=(3a)/((a+1)cancel((a+1)))xxcancel((a+1))/(a-1)`

`=(3a)/((a+1)(a-1))=(3a)/(a^2-1)`

Answer 2

`(3a)/(a^2-1)`

Explanation:

`(3a)/(a^2+2a+1)/((a-1)/(a+1))`

=`(3a)/(a^2+2a+1)*(a+1)/(a-1)`

=`(3a)/(a+1)^2*(a+1)/(a-1)`

=`(3a)/((a+1)*(a-1))`

=`(3a)/(a^2-1)`