using $v = lwh$, find an expression in factored form for the volume of this prism. explain the general steps…

Explanation:

Step 1: Write the volume formula with given expressions

$$V = \left(\frac{24x^2 + 6x}{x - 1}\right) \left(2x - 5\right) \left(\frac{x^2 - x}{4x + 1}\right)$$

Step 2: Factor numerators and denominators

Factor (24x^2 + 6x = 6x(4x + 1)), (x^2 - x = x(x - 1)):
$$V = \left(\frac{6x(4x + 1)}{x - 1}\right) \left(2x - 5\right) \left(\frac{x(x - 1)}{4x + 1}\right)$$

Step 3: Cancel common factors

Cancel (4x + 1) and (x - 1) from numerator/denominator:
$$V = 6x \cdot (2x - 5) \cdot x$$

Step 4: Multiply remaining terms

Combine (6x \cdot x = 6x^2), then multiply by (2x - 5):
$$V = 6x^2(2x - 5)$$

Answer:

(6x^2(2x - 5))