How do you divide #(4k^2-29k-24)/(k^2-13k+40)# by #(4k^2+15k+9)/(5k^3-25k^2-3k+15)#?

Answer 1

#((5k^2-3))/((k+3))#

With algebraic fractions, the first approach is to factorise where possible:

#(4k^2-29k-24)/(k^2-13k+40) div(4k^2+15k+9)/(5k^3-25k^2-3k+15)#
#=((4k+3)(k-8))/((k-8)(k-5)) div ((4k+3)(k+3))/(5k^2(k-5) -3(k-5))#

To divide by a fraction, multiply by the reciprocal.

#=((4k+3)(k-8))/((k-8)(k-5)) xx ((k-5)(5k^2 -3))/((4k+3)(k+3))#

Now cancel like factors

#=(cancel((4k+3))cancel((k-8)))/(cancel((k-8))cancel((k-5))) xx (cancel((k-5))(5k^2 -3))/(cancel((4k+3))(k+3))#
#=((5k^2-3))/((k+3))#
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Answer 2

To divide the expression (4k^2-29k-24)/(k^2-13k+40) by (4k^2+15k+9)/(5k^3-25k^2-3k+15), we can simplify the division by multiplying the first expression by the reciprocal of the second expression.

First, factorize the expressions: (4k^2-29k-24) can be factored as (4k+3)(k-8) (k^2-13k+40) can be factored as (k-5)(k-8) (4k^2+15k+9) can be factored as (4k+3)(k+3) (5k^3-25k^2-3k+15) can be factored as (k-1)(5k^2+3)

Now, we can rewrite the division as multiplication: (4k+3)(k-8) / (k-5)(k-8) * (5k^2+3) / (k-1)

Next, we can cancel out the common factors: (4k+3) / (k-5) * (5k^2+3) / (k-1)

Finally, we can multiply the numerators and denominators: (4k+3)(5k^2+3) / (k-5)(k-1)

This is the simplified expression after dividing (4k^2-29k-24)/(k^2-13k+40) by (4k^2+15k+9)/(5k^3-25k^2-3k+15).

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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.

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.

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.

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.

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