How do you simplify #(3m^2 + 9m + 6) / (4m^2 + 12m + 8)#?

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Answer 1 · 2015-07-04T08:11:41

#(3m^2+9m+6)/(4m^2+12m+8)=3/4#

with exclusions #m != -1# and #m != -2#

#(3m^2+9m+6)/(4m^2+12m+8)#

#=(3(m^2+3m+2))/(4(m^2+3m+2))#

#=3/4*(m^2+3m+2)/(m^2+3m+2)#

#=3/4#

However, it is possible for #m^2+3m+2 = 0#.

#m^2+3m+2 = (m+1)(m+2)#

which is zero when #m = -1# or #m = -2#.

For these values of #m# the original rational expression is not defined.