Question

A rectangular prism has a length of 2x^2+2x-24 over 4x^2+x, a width of x^2+x-6 over x+4, and a height of 8x^2+2x over x^2-9. For all values of x for which it is defined , express, in terms of x, the volume of the prism in simplest form.

1. 4(x-2)
2. 2(x-2)
3.2(x+2)
4.4(x+2) please show work.

Answer 1

`V=abc\\\\ V=(2x^2+2x-24)/(4x^2+x)\cdot(x^2+x-6)/(x+4)\cdot(8x^2+2x)/(x^2-9)\\ V=(2(x^2+x-12))/(x(4x+1))\cdot(x^2+3x-2x-6)/(x+4)\cdot(2x(4x+1))/((x-3)(x+3))\\ V=2(x^2+4x-3x-12)\cdot(x(x+3)-2(x+3))/(x+4)\cdot(2)/((x-3)(x+3))\\ V=2(x(x+4)-3(x+4))\cdot((x-2)(x+3))/(x+4)\cdot(2)/((x-3)(x+3))\\ V=2(x-3)(x+4)\cdot(x-2)/(x+4)\cdot(2)/(x-3)\\ V=2\cdot(x-2)\cdot2\\ V=4(x-2)`