Question
Answer
$$\dfrac{6-4\dfrac{3^1}{2}}{6+4\dfrac{3^1}{2}}=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6-4\frac{3^1}{2}}{6+4\frac{3^1}{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6-4\cdot\frac{3}{2}}{6+4\cdot\frac{3}{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{6-6}{6+6} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{0}{12} \xlongequal{ } \\[1 em] & \xlongequal{ }0\end{aligned} $$ | |
| ① | A polynomial raised to the power of one equals itself. |
| ② | A polynomial raised to the power of one equals itself. |
| ③ | Multiply $4$ by $ \dfrac{3}{2} $ to get $ 6$. Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Cancel down by $ \color{blue}{2} $ $$ \begin{aligned} 4 \cdot \frac{3}{2} & = \frac{4}{\color{red}{1}} \cdot \frac{3}{2} = \frac{12 : \color{blue}{2}}{2 : \color{blue}{2}} = \\[1ex] &= \frac{6}{1} =6 \end{aligned} $$ |
| ④ | Multiply $4$ by $ \dfrac{3}{2} $ to get $ 6$. Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Cancel down by $ \color{blue}{2} $ $$ \begin{aligned} 4 \cdot \frac{3}{2} & = \frac{4}{\color{red}{1}} \cdot \frac{3}{2} = \frac{12 : \color{blue}{2}}{2 : \color{blue}{2}} = \\[1ex] &= \frac{6}{1} =6 \end{aligned} $$ |
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