Answer
$$z^2-\frac{4}{2}(z-1)=z^2-2z+2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}z^2-\frac{4}{2}(z-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}z^2 - \frac{ 4 : \color{orangered}{ 2 } }{ 2 : \color{orangered}{ 2 }} \cdot \left(z-1\right) \xlongequal{ } \\[1 em] & \xlongequal{ }z^2-\frac{2}{1}(z-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}z^2-2(z-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}z^2-(2z-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}z^2-2z+2\end{aligned} $$ | |
| ① | Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $. |
| ② | Remove 1 from denominator. |
| ③ | Multiply $ \color{blue}{2} $ by $ \left( z-1\right) $ $$ \color{blue}{2} \cdot \left( z-1\right) = 2z-2 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2z-2 \right) = -2z+2 $$ |
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Simplify Rational Expressions