Question

How do you divide `{(12m^2n^5)/(m+5)}/{(3m^3n)/(m^2-25)}`?

Answer 1

The answer is `4m^-1n^4(m-5)` Or `(4n^4(m-5))/m`

Explanation:

Basically what you are dealing with here is a fraction,
`(12m^2n^5)/(m + 5 )` , being divided by a second fraction

`(3m^3n)/(m^2 - 25)`. So how do we divide fractions? One simple

technique we can use is to multiply the first fraction by the

reciprocal of the second fraction. So our solution looks like this:

`((12m^2n^5)/(m+5))` `((m^2-25)/(3m^3n))` = `(12m^2n^5(m^2-25))/(3m^3n(m +5)`.
While this is the solution, it is not yet reduced to simplest terms, which is our next step. Notice that in the numerator, `(m^2-25)` is a perfect square binomial, which factors easily into `(m+5)(m-5)`. So our original solution from above can now be factored into:
`((3)(4)(m^2)(n)(n^4)(m+5)(m-5))/(3(m^2)(m)(n)(m+5))`. We can now divide or "cancel" like terms to arrive at the simplified answer of `(4n^4(m-5))/m`.