How do you combine #4/(a^2 + 12a +27) + 5/(a^2 +10a +21)#?

Answer 1
Since #a^2+12a+27 = (a+3)(a+9)# and #a^2+10a+21 = (a+3)(a+7)#
The Least Common Divisor needed to combine these two terms is #(a+3)(a+7)(a+9)#
#4/(a^2+12a+27) + 5/(a^2+10a+21)#
#= (4(a+7) + 5(a+9))/((a+3)(a+7)(a+9))#
#= (9a +73)/((a+3)(a+7)(a+9))#
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Answer 2

To combine the given expressions, you need to find a common denominator. In this case, the denominators are (a^2 + 12a + 27) and (a^2 + 10a + 21). The common denominator is the product of these two denominators, which is (a^2 + 12a + 27)(a^2 + 10a + 21).

To add the fractions, you need to multiply the numerator of each fraction by the denominator of the other fraction. Then, add the resulting numerators together and place the sum over the common denominator.

After simplifying the resulting expression, you will have the combined fraction.

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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.

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.

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.

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.

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