Given:
Volume of a rectangular prism is:
[tex]V=\dfrac{x^2+2x}{x+1}[/tex]
Dimensions of the rectangular prism are:
[tex]l=2x+4[/tex]
[tex]w=\dfrac{x}{8}[/tex]
To find:
The height of the rectangular prism.
Solution:
The volume of a rectangular prism is:
[tex]V=l\times w\times h[/tex]
After substituting the values, we get
[tex]\dfrac{x^2+2x}{x+1}=(2x+4)\times \dfrac{x}{8}\times h[/tex]
[tex]\dfrac{x(x+2)}{x+1}=\dfrac{2x(x+2)}{8}\times h[/tex]
[tex]\dfrac{x(x+2)}{x+1}\times \dfrac{8}{2x(x+2)}=h[/tex]
[tex]\dfrac{1}{x+1}\times \dfrac{8}{2}=h[/tex]
[tex]\dfrac{4}{x+1}=h[/tex]
Therefore, the correct option is C.
