Question

Find an expression to represent the volume of the rectangular prism below,

Answer 1

Answer:

Step-by-step explanation:

$volume=\frac{x^{2} +11x+30}{x^{2} +7x+6} \times \frac{3x}{8} \times \frac{x^{2} -1}{6x^3+30x^{2} } \\=\frac{x^{2} +6x+5x+30}{x^{2} +6x+x+6} \times \frac{3x}{8} \times \frac{(x+1)(x-1)}{6x^{2} (x+5)} \\=\frac{x(x+6)+5(x+6)}{x(x+6)+1(x+6)} \times \frac{3x}{8} \times \frac{(x+1)(x-1)}{6x^{2} (x+5)} \\=\frac{(x+6)(x+5)}{(x+6)(x+1)} \times \frac{3x}{8} \times \frac{(x+1)(x-1)}{6x^{2} (x+5)} \\=\frac{x-1}{16x}$