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How do you evaluate #3/(16-a^2) - 5/(12+3a)#?

Answer 1

I tried factorizing and using a common denominator:

You can write it as: #3/((4+a)(4-a))-5/(3(4+a))=# #=(9-5(4-a))/(3(4+a)(4-a))=# #=(9-20+5a)/(3(4+a)(4-a))=(5a-11)/(3(4+a)(4-a))#

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Answer 2

Julia Adams

#(5a-11)/(3(4+a)(4-a))#

Assuming you want to evaluate to a single expression:

Factoring the denominators we have: #3/(16-a^2)-5/(12+3a)=3/((4+a)(4-a))-5/(3(4+a))#

we can then make the denominators identical: #3/((4+a)(4-a))-5/(3(4+a))=#

#3/((4+a)(4-a))-(5/3(4-a))/((4+a)(4-a))=#

#(3-5/3(4-a))/((4+a)(4-a))=(5a-11)/(3(4+a)(4-a))#

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Answer 3

Jameson Allen

To evaluate the expression 3/(16-a^2) - 5/(12+3a), we need to find a common denominator and simplify the expression. The common denominator is (16-a^2)(12+3a). Simplifying the expression gives (3(12+3a) - 5(16-a^2))/(16-a^2)(12+3a). Expanding and simplifying further, we get (36+9a - 80 + 5a^2)/(16-a^2)(12+3a). Combining like terms, the expression simplifies to (5a^2 + 9a - 44)/(16-a^2)(12+3a).

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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.