Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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.

Sagot :

konrad509
[tex]V=abc\\\\ V=\frac{2x^2+2x-24}{4x^2+x}\cdot\frac{x^2+x-6}{x+4}\cdot\frac{8x^2+2x}{x^2-9}\\ V=\frac{2(x^2+x-12)}{x(4x+1)}\cdot\frac{x^2+3x-2x-6}{x+4}\cdot\frac{2x(4x+1)}{(x-3)(x+3)}\\ V=2(x^2+4x-3x-12)\cdot\frac{x(x+3)-2(x+3)}{x+4}\cdot\frac{2}{(x-3)(x+3)}\\ V=2(x(x+4)-3(x+4))\cdot\frac{(x-2)(x+3)}{x+4}\cdot\frac{2}{(x-3)(x+3)}\\ V=2(x-3)(x+4)\cdot\frac{x-2}{x+4}\cdot\frac{2}{x-3}\\ V=2\cdot(x-2)\cdot2\\ V=4(x-2)[/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.