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

Answer 1

Eva Adamson

#(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.

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Answer 2

Kennedy Adams

To simplify the expression (3m^2 + 9m + 6) / (4m^2 + 12m + 8), we can factor both the numerator and denominator.

The numerator can be factored as 3(m^2 + 3m + 2), and the denominator can be factored as 4(m^2 + 3m + 2).

Now, we can cancel out the common factor of (m^2 + 3m + 2) in both the numerator and denominator.

This leaves us with the simplified expression of 3/4.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.