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Question

Answer

$$(1+\dfrac{x}{2})^3-(1+\dfrac{x}{2})=(1+\dfrac{x}{2})^3-\dfrac{x+2}{2}$$

Explanation
$$ \begin{aligned}(1+\frac{x}{2})^3-(1+\frac{x}{2})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1+\frac{x}{2})^3-\frac{x+2}{2}\end{aligned} $$
①

Add $1$ and $ \dfrac{x}{2} $ to get $ \dfrac{ \color{purple}{ x+2 } }{ 2 }$.

Step 1: Write $ 1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} 1+ \frac{x}{2} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} + \frac{x}{2} = \frac{ 1 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ x }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2 } }{ 2 } + \frac{ \color{purple}{ x } }{ 2 }=\frac{ \color{purple}{ x+2 } }{ 2 } \end{aligned} $$
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