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How do you simplify #(9x^3)/(12x-24)div(x^2+4x)/(x-2)#?

Answer 1

Eva Adamson

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

The first step is to factor where possible and to change the division to a multiplication by the reciprocal

#(9x^3)/(12(x-2)) xx (x-2)/(x(x+4))" "larr# take out common factors

#(9x^3)/(12(cancel(x-2))) xx cancel((x-2))/(x(x+4))" "larr# simplify

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

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Answer 2

Kennedy Adams

To simplify the expression (9x^3)/(12x-24) ÷ (x^2+4x)/(x-2), we can follow these steps:

Simplify the numerator of the first fraction: (9x^3) = 9x^3.
Factor out the greatest common factor (GCF) from the denominator of the first fraction: (12x-24) = 12(x-2).
Simplify the numerator of the second fraction: (x^2+4x) = x(x+4).
Simplify the denominator of the second fraction: (x-2) = x-2.
Rewrite the expression as a multiplication problem by flipping the second fraction: 9x^3 * (x-2) / [12(x-2) * x(x+4)].
Cancel out common factors between the numerator and denominator: 9x^3 / [12 * x(x+4)].
Simplify further by dividing both the numerator and denominator by the GCF, which is 3x: 3x^2 / [4 * (x+4)].
The simplified expression is 3x^2 / (4x+16).

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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.