Answer
$$(\frac{1}{2}+sqrt\cdot\frac{3}{2})^2-(\frac{1}{2}+sqrt\cdot\frac{3}{2})+1=(\frac{1}{2}+sqrt\cdot\frac{3}{2})^2-\frac{3qrst+1}{2}+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(\frac{1}{2}+sqrt\cdot\frac{3}{2})^2-(\frac{1}{2}+sqrt\cdot\frac{3}{2})+1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(\frac{1}{2}+sqrt\cdot\frac{3}{2})^2-(\frac{1}{2}+\frac{3qrst}{2})+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(\frac{1}{2}+sqrt\cdot\frac{3}{2})^2-\frac{3qrst+1}{2}+1\end{aligned} $$ | |
| ① | Multiply $qrst$ by $ \dfrac{3}{2} $ to get $ \dfrac{ 3qrst }{ 2 } $. Step 1: Write $ qrst $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} qrst \cdot \frac{3}{2} & \xlongequal{\text{Step 1}} \frac{qrst}{\color{red}{1}} \cdot \frac{3}{2} \xlongequal{\text{Step 2}} \frac{ qrst \cdot 3 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3qrst }{ 2 } \end{aligned} $$ |
| ② | Add $ \dfrac{1}{2} $ and $ \dfrac{3qrst}{2} $ to get $ \dfrac{3qrst+1}{2} $. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{1}{2} + \frac{3qrst}{2} & = \frac{1}{\color{blue}{2}} + \frac{3qrst}{\color{blue}{2}} =\frac{ 1 + 3qrst }{ \color{blue}{ 2 }} = \\[1ex] &= \frac{3qrst+1}{2} \end{aligned} $$ |
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