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How do you combine #(x^2 +3x +2)/(x^2-16) + (3x +6)/(x^2-16)#?

Answer 1

When you have a sum or subtraction of two fractions with the same denominator, you just sum/subtract the numerators, as follows:

#(x^2+3x+2+3x+6)/(x^2-16)#

#(x^2+6x+8)/(x^2-16)#

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Answer 2

Isaiah Anthony

To combine the given expressions, we first need to find a common denominator, which in this case is (x^2-16). Then, we can add the numerators together and simplify the resulting expression.

The combined expression is: (x^2 + 3x + 2)/(x^2 - 16) + (3x + 6)/(x^2 - 16)

To add the numerators, we add (x^2 + 3x + 2) and (3x + 6) together, which gives us: x^2 + 3x + 2 + 3x + 6

Simplifying further, we combine like terms: x^2 + 6x + 8

Therefore, the combined expression is: (x^2 + 6x + 8)/(x^2 - 16)

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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.