Multiply $hp$ by $ \dfrac{l^2}{2k} $ to get $ \dfrac{ hl^2p }{ 2k } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} hp \cdot \frac{l^2}{2k} & \xlongequal{\text{Step 1}} \frac{hp}{\color{red}{1}} \cdot \frac{l^2}{2k} \xlongequal{\text{Step 2}} \frac{ hp \cdot l^2 }{ 1 \cdot 2k } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ hl^2p }{ 2k } \end{aligned} $$

Multiply $p$ by $ \dfrac{l^3}{3} $ to get $ \dfrac{ l^3p }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} p \cdot \frac{l^3}{3} & \xlongequal{\text{Step 1}} \frac{p}{\color{red}{1}} \cdot \frac{l^3}{3} \xlongequal{\text{Step 2}} \frac{ p \cdot l^3 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ l^3p }{ 3 } \end{aligned} $$

Subtract $ \dfrac{h}{k} $ from $ 1 $ to get $ \dfrac{ \color{purple}{ -h+k } }{ k }$.

Step 1: Write $ 1 $ 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 $\color{blue}{ k }$.

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

Add $ \dfrac{hl^2p}{2k} $ and $ \dfrac{l^3p}{3} $ to get $ \dfrac{ \color{purple}{ 2kl^3p+3hl^2p } }{ 6k }$.

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}{ 3 }$ and the second by $\color{blue}{ 2k }$.

$$ \begin{aligned} \frac{hl^2p}{2k} + \frac{l^3p}{3} & = \frac{ hl^2p \cdot \color{blue}{ 3 }}{ 2k \cdot \color{blue}{ 3 }} + \frac{ l^3p \cdot \color{blue}{ 2k }}{ 3 \cdot \color{blue}{ 2k }} = \\[1ex] &=\frac{ \color{purple}{ 3hl^2p } }{ 6k } + \frac{ \color{purple}{ 2kl^3p } }{ 6k }=\frac{ \color{purple}{ 2kl^3p+3hl^2p } }{ 6k } \end{aligned} $$

Subtract $ \dfrac{h}{k} $ from $ 1 $ to get $ \dfrac{ \color{purple}{ -h+k } }{ k }$.

Step 1: Write $ 1 $ 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 $\color{blue}{ k }$.

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

Divide $ \dfrac{2kl^3p+3hl^2p}{6k} $ by $ \dfrac{-h+k}{k} $ to get $ \dfrac{ 2k^2l^3p+3hkl^2p }{ -6hk+6k^2 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{2kl^3p+3hl^2p}{6k} }{ \frac{\color{blue}{-h+k}}{\color{blue}{k}} } & \xlongequal{\text{Step 1}} \frac{2kl^3p+3hl^2p}{6k} \cdot \frac{\color{blue}{k}}{\color{blue}{-h+k}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 2kl^3p+3hl^2p \right) \cdot k }{ 6k \cdot \left( -h+k \right) } \xlongequal{\text{Step 3}} \frac{ 2k^2l^3p+3hkl^2p }{ -6hk+6k^2 } \end{aligned} $$