Question

Using V = lwh, what is an expression for the volume of the following prism?

The dimensions of a prism are shown. The height is StartFraction 2 d minus 6 Over 2 d minus 4 EndFraction. The width is StartFraction 4 Over d minus 4 EndFraction. The length is StartFraction d minus 2 Over 3 d minus 9 EndFraction.
StartFraction 4 (d minus 2) Over 3 (d minus 3)(d minus 4) EndFraction
StartFraction 4 d minus 8 Over 3 (d minus 4) squared EndFraction
StartFraction 4 Over 3 d minus 12 EndFraction
StartFraction 1 Over 3 d minus 3 EndFraction

Answer 1

h = (2d−6)/(2d−4) = (d−3)/(d−2)
l = (d−2)/(3d−9) = (d−2)/[3(d−3)]
w = 4/(d−4)

V = lwh = (d−2)/[3(d−3)] * 4/(d−4) * (d−3)/(d−2)
Cancel (d−2) and (d−3): V = 4/[3(d−4)] = 4/(3d−12).

(Domain: d ≠ 2,3,4.)