The cooling efficiency coefficient, E(v)E(v)E(v), of a high-speed fluid turbine is modeled by the function
E(v)=20+8v−5v12−2v324−v E(v) = \frac{20 + 8v - 5v^{\frac{1}{2}} - 2v^{\frac{3}{2}}}{4 - \sqrt{v}} E(v)=4−v20+8v−5v21−2v23where v v\,v is the fluid velocity in ms−1\text{ms}^{-1}ms−1, v>0 v > 0\,v>0 and v≠16v \neq 16v=16.
Simplify the expression for E(v)E(v)E(v) completely, showing each step of your algebraic factorisation.
