Multiply $ \dfrac{3}{s} $ by $ q $ to get $ \dfrac{ 3q }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3}{s} \cdot q & \xlongequal{\text{Step 1}} \frac{3}{s} \cdot \frac{q}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot q }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 3q }{ s } \end{aligned} $$

Multiply $ \dfrac{1}{s} $ by $ q $ to get $ \dfrac{ q }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{s} \cdot q & \xlongequal{\text{Step 1}} \frac{1}{s} \cdot \frac{q}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot q }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ q }{ s } \end{aligned} $$

Multiply $ \dfrac{3q}{s} $ by $ r $ to get $ \dfrac{ 3qr }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3q}{s} \cdot r & \xlongequal{\text{Step 1}} \frac{3q}{s} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3q \cdot r }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3qr }{ s } \end{aligned} $$

Multiply $ \dfrac{q}{s} $ by $ r $ to get $ \dfrac{ qr }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{q}{s} \cdot r & \xlongequal{\text{Step 1}} \frac{q}{s} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ q \cdot r }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ qr }{ s } \end{aligned} $$

Multiply $ \dfrac{3qr}{s} $ by $ t $ to get $ \dfrac{ 3qrt }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3qr}{s} \cdot t & \xlongequal{\text{Step 1}} \frac{3qr}{s} \cdot \frac{t}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3qr \cdot t }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3qrt }{ s } \end{aligned} $$

Multiply $ \dfrac{qr}{s} $ by $ t $ to get $ \dfrac{ qrt }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{qr}{s} \cdot t & \xlongequal{\text{Step 1}} \frac{qr}{s} \cdot \frac{t}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ qr \cdot t }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ qrt }{ s } \end{aligned} $$

Multiply $ \dfrac{3qrt}{s} $ by $ 10 $ to get $ \dfrac{ 30qrt }{ s } $.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3qrt}{s} \cdot 10 & \xlongequal{\text{Step 1}} \frac{3qrt}{s} \cdot \frac{10}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3qrt \cdot 10 }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30qrt }{ s } \end{aligned} $$

Multiply $ \dfrac{qrt}{s} $ by $ 10 $ to get $ \dfrac{ 10qrt }{ s } $.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{qrt}{s} \cdot 10 & \xlongequal{\text{Step 1}} \frac{qrt}{s} \cdot \frac{10}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ qrt \cdot 10 }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10qrt }{ s } \end{aligned} $$

Multiply $ \dfrac{30qrt}{s} $ by $ h $ to get $ \dfrac{ 30hqrt }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{30qrt}{s} \cdot h & \xlongequal{\text{Step 1}} \frac{30qrt}{s} \cdot \frac{h}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 30qrt \cdot h }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30hqrt }{ s } \end{aligned} $$

Multiply $ \dfrac{10qrt}{s} $ by $ h $ to get $ \dfrac{ 10hqrt }{ s } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{10qrt}{s} \cdot h & \xlongequal{\text{Step 1}} \frac{10qrt}{s} \cdot \frac{h}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 10qrt \cdot h }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10hqrt }{ s } \end{aligned} $$

Add $1$ and $ \dfrac{30hqrt}{s} $ to get $ \dfrac{ \color{purple}{ 30hqrt+s } }{ s }$.

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 $\color{blue}{ s }$.

$$ \begin{aligned} 1+ \frac{30hqrt}{s} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} + \frac{30hqrt}{s} = \frac{ 1 \cdot \color{blue}{ s }}{ 1 \cdot \color{blue}{ s }} + \frac{ 30hqrt }{ s } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ s } }{ s } + \frac{ \color{purple}{ 30hqrt } }{ s }=\frac{ \color{purple}{ 30hqrt+s } }{ s } \end{aligned} $$

Add $2$ and $ \dfrac{10hqrt}{s} $ to get $ \dfrac{ \color{purple}{ 10hqrt+2s } }{ s }$.

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

$$ \begin{aligned} 2+ \frac{10hqrt}{s} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} + \frac{10hqrt}{s} = \frac{ 2 \cdot \color{blue}{ s }}{ 1 \cdot \color{blue}{ s }} + \frac{ 10hqrt }{ s } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2s } }{ s } + \frac{ \color{purple}{ 10hqrt } }{ s }=\frac{ \color{purple}{ 10hqrt+2s } }{ s } \end{aligned} $$

Divide $ \dfrac{30hqrt+s}{s} $ by $ \dfrac{10hqrt+2s}{s} $ to get $ \dfrac{ 30hqrt+s }{ 10hqrt+2s } $.

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

Step 2: Cancel $ \color{red}{ s } $ in first and second fraction.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{30hqrt+s}{s} }{ \frac{\color{blue}{10hqrt+2s}}{\color{blue}{s}} } & \xlongequal{\text{Step 1}} \frac{30hqrt+s}{s} \cdot \frac{\color{blue}{s}}{\color{blue}{10hqrt+2s}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{30hqrt+s}{\color{red}{1}} \cdot \frac{\color{red}{1}}{10hqrt+2s} \xlongequal{\text{Step 3}} \frac{ \left( 30hqrt+s \right) \cdot 1 }{ 1 \cdot \left( 10hqrt+2s \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 30hqrt+s }{ 10hqrt+2s } \end{aligned} $$