Question

How do you divide `\frac { 9x - 54} { 7} \div \frac { x - 6} { 3}`?

Answer 1

`27/7=3 6/7`

Explanation:

Factorise first - we would like to be able to simply by cancelling, but this can only happen with factors, not terms.

`(9x-54)/7 div (x-6)/3`

`= (9(x-6))/7 xx 3/(x-6)" "larr` multiply by the reciprocal

`= (9cancel((x-6)))/7 xx 3/cancel((x-6))`

`=27/7`

`=3 6/7`