How do you simplify #(m^2-9mn+14n^2 )/(m^2+7mn+12n^2 )#?

1 Answer
George C.
Sep 7, 2016

#(m^2-9mn+14n^2)/(m^2+7mn+12n^2) = ((m-2n)(m-7n))/((m+3n)(m+4n))#

#color(white)((m^2-9mn+14n^2)/(m^2+7mn+12n^2)) = 1+(2n(n-8m))/((m+3n)(m+4n))#

Explanation:

Start by factoring both the numerator and denominator:

#(m^2-9mn+14n^2)/(m^2+7mn+12n^2) = ((m-2n)(m-7n))/((m+3n)(m+4n))#

There are no common factors to cancel.

Alternatively, we can split this rational expression as:

#(m^2-9mn+14n^2)/(m^2+7mn+12n^2) = (m^2+7mn+12n^2-16mn+2n^2)/(m^2+7mn+12n^2)#

#color(white)((m^2-9mn+14n^2)/(m^2+7mn+12n^2)) = ((m^2+7mn+12n^2)-16mn+2n^2)/(m^2+7mn+12n^2)#

#color(white)((m^2-9mn+14n^2)/(m^2+7mn+12n^2)) = 1+(-16mn+2n^2)/(m^2+7mn+12n^2)#

#color(white)((m^2-9mn+14n^2)/(m^2+7mn+12n^2)) = 1+(2n(n-8m))/(m^2+7mn+12n^2)#

#color(white)((m^2-9mn+14n^2)/(m^2+7mn+12n^2)) = 1+(2n(n-8m))/((m+3n)(m+4n))#

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