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How do you simplify #(x+5)/(x^-4)-3/(x^2-4)#?

Answer 1

Julia Adams

#color(crimson)(=> (x^7 + 5x^6 -4x^5 - 20x^4 - 3) / (x^2 -4)#

#(x+5) / x^(-4) - 3 / (x^2 - 4)#

#=> x^4 (x+5) - 3 / (x^2-4)#

#=> ((x^5 + 5x^4) (x^2-4) - 3)/(x^2-4)#

#color(crimson)(=> (x^7 + 5x^6 -4x^5 - 20x^4 - 3) / (x^2-4)#

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Answer 2

Hazel Anglin

To simplify the expression (x+5)/(x^-4)-3/(x^2-4), we need to find a common denominator and combine the fractions. The common denominator is (x^-4)(x^2-4).

To combine the fractions, we multiply the numerator and denominator of the first fraction (x+5) by (x^2-4), and the numerator and denominator of the second fraction (-3) by (x^-4).

This gives us ((x+5)(x^2-4))/((x^-4)(x^2-4)) - ((-3)(x^2-4))/((x^-4)(x^2-4)).

Simplifying further, we get (x^3+x^2-4x-20)/(1-3x^2).

Therefore, the simplified expression is (x^3+x^2-4x-20)/(1-3x^2).

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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.