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

Answer 1

#x-3#

#"since the fractions have a "color(blue)"common denominator"# #"we can subtract the numerators leaving the denominator"#

#rArrx^2/(x+3)-9/(x+3)#

#=(x^2-9)/(x+3)larrcolor(blue)"combined"#

#"this may be simplified further"#

#x^2-9" is a "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#rArrx^2-9=(x-3)(x+3)#

#rArr(x^2-9)/(x+3)#

#=((x-3)cancel((x+3)))/cancel((x+3))=x-3#

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Answer 2

Julia Adams

To combine the expressions (x^2)/(x+3) and -9/(x+3), you need to have a common denominator. In this case, the common denominator is (x+3).

To combine the fractions, you subtract the numerators while keeping the common denominator.

Therefore, the combined expression is (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.