How do you multiply #(3m^2-12m)div(m^2-4m)/(m^2-6m+8)#?

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Answer 1 · 2017-07-02T20:05:03

#3m^2-18m+24#

Let's factorise everything we've got:

#(3m^2-12m)/1 div (m^2-4m)/(m^2-6m+8)#

When we are dividing fractions, we can multiply by the reciprocal of the second fraction, so our expression really is

#(3m^2-12m)/1 xx (m^2-6m+8)/(m^2-4m)#

Let's factorise everything we can:

#(3m(m-4))/1 xx ((m-2)(m-4))/(m(m-4))#

Now, let's see what cancels out, meaning what has the same factor in the numerator as the denominator

#(3cancel(m)cancel((m-4)))/1 xx ((m-2)(m-4))/(cancel(m)cancel((m-4)))#

Now let's multiply the fractions. Remember, it's straight across!

#(3 xx (m-2)(m-4))/1#

#3 xx (m^2-6m+8)#

#3m^2-18m+24#