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How do you simplify #(5)/(x-3) + (x)/(x^2-9)#?

Answer 1

# (6x+15)/(x^2-9)#

#(x^2-9)=(x+3)(x-3)# and #5/(x-3)=5(x+3)/((x-3)(x+3)) =(5x+15)/(x^2-9)# so #5/(x-3)+x/(x^2-9) = (5x+15)/(x^2-9)+x/(x^2-9) = (6x+15)/(x^2-9)#

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Answer 2

Nathan Axel

To simplify the expression (5)/(x-3) + (x)/(x^2-9), we first need to find a common denominator. The common denominator for these two fractions is (x-3)(x+3).

Next, we can rewrite the fractions with the common denominator:

(5)/(x-3) + (x)/(x^2-9) = (5(x+3))/((x-3)(x+3)) + (x)/(x^2-9)

Now, we can combine the fractions by adding the numerators:

(5(x+3) + (x))/(x^2-9) = (5x + 15 + x)/(x^2-9)

Simplifying the numerator:

(6x + 15)/(x^2-9)

This is the simplified form of the expression (5)/(x-3) + (x)/(x^2-9).

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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.