Subtract $x$ from $ \dfrac{1}{2} $ to get $ \dfrac{ \color{purple}{ -2x+1 } }{ 2 }$.

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

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

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

Subtract $x$ from $ \dfrac{1}{2} $ to get $ \dfrac{ \color{purple}{ -2x+1 } }{ 2 }$.

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

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

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

Multiply $ \dfrac{-2x+1}{2} $ by $ \dfrac{-2x+1}{2} $ to get $ \dfrac{4x^2-4x+1}{4} $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-2x+1}{2} \cdot \frac{-2x+1}{2} & \xlongequal{\text{Step 1}} \frac{ \left( -2x+1 \right) \cdot \left( -2x+1 \right) }{ 2 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 4x^2-2x-2x+1 }{ 4 } = \frac{4x^2-4x+1}{4} \end{aligned} $$