Question
Answer
$$6\cdot\dfrac{x}{x-7}\dfrac{x-7}{x}=\dfrac{6x}{x}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6 \cdot \frac{x}{x-7}\frac{x-7}{x}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6x}{x-7}\frac{x-7}{x} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6x}{x}\end{aligned} $$ | |
| ① | Multiply $6$ by $ \dfrac{x}{x-7} $ to get $ \dfrac{ 6x }{ x-7 } $. Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 6 \cdot \frac{x}{x-7} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{x}{x-7} \xlongequal{\text{Step 2}} \frac{ 6 \cdot x }{ 1 \cdot \left( x-7 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x }{ x-7 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{6x}{x-7} $ by $ \dfrac{x-7}{x} $ to get $ \dfrac{ 6x }{ x } $. Step 1: Cancel $ \color{red}{ x-7 } $ in first and second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{6x}{x-7} \cdot \frac{x-7}{x} & \xlongequal{\text{Step 1}} \frac{6x}{\color{red}{1}} \cdot \frac{\color{red}{1}}{x} \xlongequal{\text{Step 2}} \frac{ 6x \cdot 1 }{ 1 \cdot x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x }{ x } \end{aligned} $$ |
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