Respuesta :

Thagie
You are asked to use the volume formula V = lwh which basically means to find the volume by multiplying the length, width and height of the prism. These are all given to you as expression so you are asked to multiply the expressions. That is, find: [tex]( \frac{ x^{2} -x}{4x+1} )( \frac{2x-5}{1} )( \frac{24 x^{2} +6x}{x-1} )[/tex]

First factor each of the expressions in the numerators and then multiply those in the numerators putting them over those in the denominator. It turns out those in the denominators (in this problem) cannot be factored. When you do this you are left with:
[tex]\frac{(x)(x-1)(2x-5)(6x)(4x+1)}{(4x+1)(x-1)} [/tex]

You can divide out (sometimes called cancelling out) those terms expressions that are in both the numerator and the denominator. That leaves you with:
[tex]\frac{(x)(2x-5)(6x)} {1}[/tex] which we can clean up by multiplying x and 6x in the numerator.

Thus, the volume of the prism is: [tex]6 x^{2} (2x-5)[/tex]
We do not multiply this out because it is now written as a product and thus factored (as you were asked).

The volume of the prism with the given dimensions is;

V = 12x³ - 30x²

We are given that the formula for the volume of a cube is;

V = Lwh

where;

L is length

w is width

h is height

We are given;

L = (24x² + 6x)/(x -1)

w = 2x - 5

h = (x² - x)/(4x + 1)

This means that;

V = [(24x² + 6x)/(x - 1)] × (2x - 5) × [(x² - x)/(4x + 1)]

Now, let us factorize the terms that can be factorized;

(24x² + 6x)/(x - 1) can be factorized into; [6x(4x + 1)/(x - 1)]

Similarly;[(x² - x)/(4x + 1)] can be factorized into [x(x - 1)/(4x - 1)]

Using the factorized terms to get the volume now;

V = [tex]\frac{6x(4x + 1)}{x -1} * (2x - 5) * \frac{x(x - 1)}{4x + 1}[/tex]

(x - 1) will cancel out and also 4x + 1 will cancel out to give;

V = 6x * x * (2x - 5)

V = 6x²(2x - 5)

V = 12x³ - 30x²

Read more at; https://brainly.com/question/3411616

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