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