Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{9}{2}-3sqrt\cdot\frac{7}{2}i}{-3sqrt\cdot7i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{9}{2}-\frac{21qrst}{2}i}{-21qrsti} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\frac{9}{2}-\frac{21iqrst}{2}}{-21qrsti} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{\frac{-21iqrst+9}{2}}{-21qrsti} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{-21iqrst+9}{-42iqrst}\end{aligned} $$ | |
| ① | Multiply $3qrst$ by $ \dfrac{7}{2} $ to get $ \dfrac{ 21qrst }{ 2 } $. Step 1: Write $ 3qrst $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 3qrst \cdot \frac{7}{2} & \xlongequal{\text{Step 1}} \frac{3qrst}{\color{red}{1}} \cdot \frac{7}{2} \xlongequal{\text{Step 2}} \frac{ 3qrst \cdot 7 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 21qrst }{ 2 } \end{aligned} $$ |
| ② | $$ 3 s q r t \cdot 7 = 21 q r s t $$ |
| ③ | Multiply $ \dfrac{21qrst}{2} $ by $ i $ to get $ \dfrac{ 21iqrst }{ 2 } $. Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{21qrst}{2} \cdot i & \xlongequal{\text{Step 1}} \frac{21qrst}{2} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 21qrst \cdot i }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 21iqrst }{ 2 } \end{aligned} $$ |
| ④ | $$ 3 s q r t \cdot 7 = 21 q r s t $$ |
| ⑤ | Subtract $ \dfrac{21iqrst}{2} $ from $ \dfrac{9}{2} $ to get $ \dfrac{-21iqrst+9}{2} $. To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{9}{2} - \frac{21iqrst}{2} & = \frac{9}{\color{blue}{2}} - \frac{21iqrst}{\color{blue}{2}} =\frac{ 9 - 21iqrst }{ \color{blue}{ 2 }} = \\[1ex] &= \frac{-21iqrst+9}{2} \end{aligned} $$ |
| ⑥ | $$ 3 s q r t \cdot 7 = 21 q r s t $$ |
| ⑦ | Divide $ \dfrac{-21iqrst+9}{2} $ by $ -21iqrst $ to get $ \dfrac{ -21iqrst+9 }{ -42iqrst } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{-21iqrst+9}{2} }{-21iqrst} & \xlongequal{\text{Step 1}} \frac{-21iqrst+9}{2} \cdot \frac{\color{blue}{1}}{\color{blue}{-21iqrst}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( -21iqrst+9 \right) \cdot 1 }{ 2 \cdot \left( -21iqrst \right) } \xlongequal{\text{Step 3}} \frac{ -21iqrst+9 }{ -42iqrst } \end{aligned} $$ |