A rectangular prism has the following dimensions:

- Length: \(\frac{2x^2 + 2x - 24}{4x^2 + x}\)
- Width: \(\frac{x^2 + x - 6}{x + 4}\)
- Height: \(\frac{8x^2 + 2x}{x^2 - 9}\)

For all values of \(x\) for which it is defined, express the volume of the prism in simplest form in terms of \(x\).

1. \(4(x-2)\)
2. \(2(x-2)\)
3. \(2(x+2)\)
4. \(4(x+2)\)

Please show your work.

V = ab c V = 4 x 2 + x 2 x 2 + 2 x − 24 ​ ⋅ x + 4 x 2 + x − 6 ​ ⋅ x 2 − 9 8 x 2 + 2 x ​ V = x ( 4 x + 1 ) 2 ( x 2 + x − 12 ) ​ ⋅ x + 4 x 2 + 3 x − 2 x − 6 ​ ⋅ ( x − 3 ) ( x + 3 ) 2 x ( 4 x + 1 ) ​ V = 2 ( x 2 + 4 x − 3 x − 12 ) ⋅ x + 4 x ( x + 3 ) − 2 ( x + 3 ) ​ ⋅ ( x − 3 ) ( x + 3 ) 2 ​ V = 2 ( x ( x + 4 ) − 3 ( x + 4 )) ⋅ x + 4 ( x − 2 ) ( x + 3 ) ​ ⋅ ( x − 3 ) ( x + 3 ) 2 ​ V = 2 ( x − 3 ) ( x + 4 ) ⋅ x + 4 x − 2 ​ ⋅ x − 3 2 ​ V = 2 ⋅ ( x − 2 ) ⋅ 2 V = 4 ( x − 2 )

Answered by konrad509 | 2024-06-10

The volume of the rectangular prism is V = 4 ( x − 2 ) . Therefore, the correct answer is option 1: 4 ( x − 2 ) .
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Answered by konrad509 | 2024-12-26