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How do you combine #(x^2+13x+18)/(x^2-9)+(x+1)/(x+3)#?

Answer 1

Savannah Anderson

#(x^2+13x+18)/(x^2-9)+(x+1)/(x+3)=(2x+5)/(x-3)#

#(x^2+13x+18)/(x^2-9)+(x+1)/(x+3)#

= #(x^2+13x+18)/((x+3)(x-3))+(x+1)/(x+3)#

= #(x^2+13x+18+(x+1)(x-3))/((x+3)(x-3))#

= #(x^2+13x+18+(x^2-3x+x-3))/((x+3)(x-3))#

= #(2x^2+11x+15)/((x+3)(x-3))#

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

= #(x(2x+5)+3(2x+5))/((x+3)(x-3))#

= #((x+3)(2x+5))/((x+3)(x-3))#

= #(2x+5)/(x-3)#

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Answer 2

Genesis Allen

#(2x^2+11x+15)/((x+3)(x-3))#

#(x^2+13x+18)/(x^2-9)+(x+1)/(x+3)# #=(x^2+13x+18)/((x+3)(x-3))+(x+1)/(x+3)# #=(x^2+13x+18+(x+1)(x-3))/((x+3)(x-3))# #=(x^2+13x+18+x^2-3x+x-3)/((x+3)(x-3))# #(2x^2+11x+15)/((x+3)(x-3))#

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Answer 3

Jameson Allen

To combine the given expressions, we need to find a common denominator for both fractions. The common denominator is (x^2 - 9)(x + 3).

Next, we multiply the first fraction by (x + 3)/(x + 3) and the second fraction by (x^2 - 9)/(x^2 - 9).

After simplifying, we can combine the numerators over the common denominator.

The combined expression is (x^2 + 13x + 18)(x + 3) + (x + 1)(x^2 - 9) / (x^2 - 9)(x + 3).

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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.