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

Step 1: Write $ 2 $ 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 $\color{blue}{w}$.

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

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

Step 1: Write $ 2 $ 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 $\color{blue}{w}$.

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

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

Step 1: Write $ 2 $ 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 $\color{blue}{w}$.

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

Multiply $ \dfrac{w}{2} $ by $ \dfrac{-2w+2}{w} $ to get $ \dfrac{ -2w+2 }{ 2 } $.

Step 1: Cancel $ \color{blue}{ w } $ in first and second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{w}{2} \cdot \frac{-2w+2}{w} & \xlongequal{\text{Step 1}} \frac{\color{blue}{1}}{2} \cdot \frac{-2w+2}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( -2w+2 \right) }{ 2 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ -2w+2 }{ 2 } \end{aligned} $$

Multiply $ \dfrac{w}{2} $ by $ \dfrac{-2w+2}{w} $ to get $ \dfrac{ -2w+2 }{ 2 } $.

Step 1: Cancel $ \color{blue}{ w } $ in first and second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{w}{2} \cdot \frac{-2w+2}{w} & \xlongequal{\text{Step 1}} \frac{\color{blue}{1}}{2} \cdot \frac{-2w+2}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( -2w+2 \right) }{ 2 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ -2w+2 }{ 2 } \end{aligned} $$

Multiply $ \dfrac{w^2}{4} $ by $ \dfrac{-2w+2}{w} $ to get $ \dfrac{ -2w^3+2w^2 }{ 4w } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{w^2}{4} \cdot \frac{-2w+2}{w} & \xlongequal{\text{Step 1}} \frac{ w^2 \cdot \left( -2w+2 \right) }{ 4 \cdot w } \xlongequal{\text{Step 2}} \frac{ -2w^3+2w^2 }{ 4w } \end{aligned} $$

Subtract $l$ from $ \dfrac{-2w+2}{2} $ to get $ \dfrac{ \color{purple}{ -2l-2w+2 } }{ 2 }$.

Step 1: Write $ l $ 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 $\color{blue}{2}$.

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

Add $ \dfrac{w^2}{4} $ and $ \dfrac{-2w+2}{2} $ to get $ \dfrac{ \color{purple}{ w^2-4w+4 } }{ 4 }$.

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

$$ \begin{aligned} \frac{w^2}{4} + \frac{-2w+2}{2} & = \frac{ w^2 }{ 4 } + \frac{ \left( -2w+2 \right) \cdot \color{blue}{ 2 }}{ 2 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ w^2 } }{ 4 } + \frac{ \color{purple}{ -4w+4 } }{ 4 }=\frac{ \color{purple}{ w^2-4w+4 } }{ 4 } \end{aligned} $$

Multiply $ \dfrac{-2w^3+2w^2}{4w} $ by $ \dfrac{w}{2} $ to get $ \dfrac{ -2w^4+2w^3 }{ 8w } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-2w^3+2w^2}{4w} \cdot \frac{w}{2} & \xlongequal{\text{Step 1}} \frac{ \left( -2w^3+2w^2 \right) \cdot w }{ 4w \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ -2w^4+2w^3 }{ 8w } \end{aligned} $$

Subtract $l$ from $ \dfrac{-2w+2}{2} $ to get $ \dfrac{ \color{purple}{ -2l-2w+2 } }{ 2 }$.

Step 1: Write $ l $ 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 $\color{blue}{2}$.

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

Subtract $l$ from $ \dfrac{w^2-4w+4}{4} $ to get $ \dfrac{ \color{purple}{ w^2-4l-4w+4 } }{ 4 }$.

Step 1: Write $ l $ 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 $\color{blue}{4}$.

$$ \begin{aligned} \frac{w^2-4w+4}{4} -l & \xlongequal{\text{Step 1}} \frac{w^2-4w+4}{4} - \frac{l}{\color{red}{1}} = \frac{ w^2-4w+4 }{ 4 } - \frac{ l \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ w^2-4w+4 } }{ 4 } - \frac{ \color{purple}{ 4l } }{ 4 }=\frac{ \color{purple}{ w^2-4l-4w+4 } }{ 4 } \end{aligned} $$

Multiply $ \dfrac{-2w^3+2w^2}{4w} $ by $ \dfrac{w}{2} $ to get $ \dfrac{ -2w^4+2w^3 }{ 8w } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-2w^3+2w^2}{4w} \cdot \frac{w}{2} & \xlongequal{\text{Step 1}} \frac{ \left( -2w^3+2w^2 \right) \cdot w }{ 4w \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ -2w^4+2w^3 }{ 8w } \end{aligned} $$

Multiply $ \dfrac{-2l-2w+2}{2} $ by $ \dfrac{w^2-4l-4w+4}{4} $ to get $ \dfrac{-2lw^2-2w^3+8l^2+16lw+10w^2-16l-16w+8}{8} $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-2l-2w+2}{2} \cdot \frac{w^2-4l-4w+4}{4} & \xlongequal{\text{Step 1}} \frac{ \left( -2l-2w+2 \right) \cdot \left( w^2-4l-4w+4 \right) }{ 2 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ -2lw^2+8l^2+8lw-8l-2w^3+8lw+8w^2-8w+2w^2-8l-8w+8 }{ 8 } = \frac{-2lw^2-2w^3+8l^2+16lw+10w^2-16l-16w+8}{8} \end{aligned} $$

Multiply $ \dfrac{-2w^3+2w^2}{4w} $ by $ \dfrac{w}{2} $ to get $ \dfrac{ -2w^4+2w^3 }{ 8w } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-2w^3+2w^2}{4w} \cdot \frac{w}{2} & \xlongequal{\text{Step 1}} \frac{ \left( -2w^3+2w^2 \right) \cdot w }{ 4w \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ -2w^4+2w^3 }{ 8w } \end{aligned} $$

Subtract $ \dfrac{-2w^4+2w^3}{8w} $ from $ \dfrac{-2lw^2-2w^3+8l^2+16lw+10w^2-16l-16w+8}{8} $ to get $ \dfrac{ \color{purple}{ -16lw^3+64l^2w+128lw^2+64w^3-128lw-128w^2+64w } }{ 64w }$.

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}{ 8w }$ and the second by $\color{blue}{ 8 }$.

$$ \begin{aligned} \frac{-2lw^2-2w^3+8l^2+16lw+10w^2-16l-16w+8}{8} - \frac{-2w^4+2w^3}{8w} & = \frac{ \left( -2lw^2-2w^3+8l^2+16lw+10w^2-16l-16w+8 \right) \cdot \color{blue}{ 8w }}{ 8 \cdot \color{blue}{ 8w }} - \frac{ \left( -2w^4+2w^3 \right) \cdot \color{blue}{ 8 }}{ 8w \cdot \color{blue}{ 8 }} = \\[1ex] &=\frac{ \color{purple}{ -16lw^3-16w^4+64l^2w+128lw^2+80w^3-128lw-128w^2+64w } }{ 64w } - \frac{ \color{purple}{ -16w^4+16w^3 } }{ 64w } = \\[1ex] &=\frac{ \color{purple}{ -16lw^3-16w^4+64l^2w+128lw^2+80w^3-128lw-128w^2+64w - \left( -16w^4+16w^3 \right) } }{ 64w } = \\[1ex] &=\frac{ \color{purple}{ -16lw^3+64l^2w+128lw^2+64w^3-128lw-128w^2+64w } }{ 64w } \end{aligned} $$