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

1 Answer
Mar 6, 2016

Answer:

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#.