Question

How do you divide `\frac { 5} { 3n ^ { 3} + 3n ^ { 2} } \div \frac { 1} { 3n ^ { 2} }`?

Answer 1

`frac{5}{3n^3+3n^2}divfrac{1}{3n^2}=frac{5}{n+1}`

Explanation:

`frac{5}{3n^3+3n^2}divfrac{1}{3n^2}`

Factor the denominator of the first fraction
`=frac{5}{(3n^2)(n+1)}div frac{1}{3n^2}`

Dividing is the same as multiplying by the reciprocal:
`=frac{5}{color(red)((3n^2))(n+1)}*color(red)((3n^2))`

Cancel terms that are repeated on the numerator and denominator:
`=frac{5}{n+1}`