Power[\(40)1+16.8Power[z,-1]\(41)\(40)1+1.31Power[z,-1]\(41)z,-1]
You asked:
Evaluate the expression: \({\left( \left(1 + 16.8 {z}^{-1}\right) \cdot \left(1 + 1.31 {z}^{-1}\right) \cdot z \right)}^{-1}\)
MathBot Answer:
Evaluated
\(\displaystyle {\left( \left(1 + 16.8 {z}^{-1}\right) \cdot \left(1 + 1.31 {z}^{-1}\right) \cdot z \right)}^{-1} = \frac{1}{z \left(1 + \frac{131}{100 z}\right) \left(1 + \frac{84}{5 z}\right)} \)
Expanded
\[{\left( \left(1 + 16.8 {z}^{-1}\right) \cdot \left(1 + 1.31 {z}^{-1}\right) \cdot z \right)}^{-1} = \frac{1}{z + \frac{1811}{100} + \frac{2751}{125 z}}\]
Factored
\[{\left( \left(1 + 16.8 {z}^{-1}\right) \cdot \left(1 + 1.31 {z}^{-1}\right) \cdot z \right)}^{-1} = \frac{500 z}{\left(5 z + 84\right) \left(100 z + 131\right)}\]