Subtract $ \dfrac{1}{8} $ from $ x $ to get $ \dfrac{ \color{purple}{ 8x-1 } }{ 8 }$.

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 first fraction by $\color{blue}{ 8 }$.

$$ \begin{aligned} x- \frac{1}{8} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} - \frac{1}{8} = \frac{ x \cdot \color{blue}{ 8 }}{ 1 \cdot \color{blue}{ 8 }} - \frac{ 1 }{ 8 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 8x } }{ 8 } - \frac{ \color{purple}{ 1 } }{ 8 }=\frac{ \color{purple}{ 8x-1 } }{ 8 } \end{aligned} $$

Add $x$ and $ \dfrac{1}{8} $ to get $ \dfrac{ \color{purple}{ 8x+1 } }{ 8 }$.

Step 1: Write $ x $ 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 $\color{blue}{ 8 }$.

$$ \begin{aligned} x+ \frac{1}{8} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} + \frac{1}{8} = \frac{ x \cdot \color{blue}{ 8 }}{ 1 \cdot \color{blue}{ 8 }} + \frac{ 1 }{ 8 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 8x } }{ 8 } + \frac{ \color{purple}{ 1 } }{ 8 }=\frac{ \color{purple}{ 8x+1 } }{ 8 } \end{aligned} $$

Multiply $ \dfrac{8x-1}{8} $ by $ \dfrac{8x+1}{8} $ to get $ \dfrac{64x^2-1}{64} $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{8x-1}{8} \cdot \frac{8x+1}{8} & \xlongequal{\text{Step 1}} \frac{ \left( 8x-1 \right) \cdot \left( 8x+1 \right) }{ 8 \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 64x^2+ \cancel{8x} -\cancel{8x}-1 }{ 64 } = \frac{64x^2-1}{64} \end{aligned} $$