Question

How can i find the volume of this expression

Answer 1

the volume of a rectangular prism is just the length * width * height, so, we know all three, so let's just get their product, and that's the volume


`\bf \cfrac{x^2-1}{6x^3+30x^2}\cdot \cfrac{x^2+11x+30}{x^2+7x+6}\cdot \cfrac{3x}{8} \\\\\\ \cfrac{x^2-1^2}{6x^2\underline{(x+5)}}\cdot \cfrac{\underline{(x+6)}\underline{(x+5)}}{(x+1)\underline{(x+6)}}\cdot \cfrac{3x}{8} \\\\\\ \cfrac{(x-1)\underline{(x+1)}}{6x^2}\cdot \cfrac{1}{\underline{x+1}}\cdot \cfrac{3x}{8}\implies \cfrac{x-1}{(2x)\underline{(3x)}}\cdot \cfrac{1}{1}\cdot \cfrac{\underline{3x}}{8} \\\\\\ \cfrac{x-1}{2x}\cdot \cfrac{1}{1}\cdot \cfrac{1}{8} \implies \cfrac{x-1}{16x}`