Answer
$$2\cdot(-1-2x)(-\frac{1}{x})=\frac{4x+2}{x}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\cdot(-1-2x)(-\frac{1}{x})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-2-4x)(-\frac{1}{x}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4x+2}{x}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( -1-2x\right) $ $$ \color{blue}{2} \cdot \left( -1-2x\right) = -2-4x $$ |
| ② | Multiply $-2-4x$ by $ \dfrac{-1}{x} $ to get $ \dfrac{4x+2}{x} $. Step 1: Write $ -2-4x $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} -2-4x \cdot \frac{-1}{x} & \xlongequal{\text{Step 1}} \frac{-2-4x}{\color{red}{1}} \cdot \frac{-1}{x} \xlongequal{\text{Step 2}} \frac{ \left( -2-4x \right) \cdot \left( -1 \right) }{ 1 \cdot x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2+4x }{ x } = \frac{4x+2}{x} \end{aligned} $$ |
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