Question

How do you find the quotient of `(b^2+6b+5)/(6b+6)div(b+5)`?

Answer 1

`1/6`

Explanation:

The first step with algebraic fractions is to factorise wherever possible:

`(b^2 +6b+5)/(6b+6) color(blue)(div ((b+5))/1)`

`=((b+5)(b+1))/(6(b+1)) color(blue)(xx 1/((b+5)))" "larr` multiply by the reciprocal

`=(cancel((b+5))cancel((b+1)))/(6cancel((b+1))) xx 1/(cancel((b+5)))" "larr` cancel like factors

`=1/6`