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How do you simplify #(w^3-27)/(4w^2-5w-21)#?

Answer 1

Ethan Adkins

Factorizing the obtained fraction

#(w^3-27)/(4w^2-5w-21)#

#((w - 3) (w^2 + 3 w + 9))/((w - 3) (4 w + 7))#

#((cancel(w - 3) )(w^2 + 3 w + 9))/((cancel(w - 3)) (4 w + 7))#

#(w^2 + 3 w + 9)/(4 w + 7)#

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Answer 2

Avery Alexander

To simplify the expression (w^3-27)/(4w^2-5w-21), we can factor both the numerator and the denominator. The numerator can be factored as the difference of cubes: (w-3)(w^2+3w+9). The denominator can be factored as (w-3)(4w+7).

Now, we can cancel out the common factor of (w-3) from both the numerator and the denominator.

Therefore, the simplified expression is (w^2+3w+9)/(4w+7).

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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.