Multiply $t^5$ by $ \dfrac{u^3}{5} $ to get $ \dfrac{ t^5u^3 }{ 5 } $.

Step 1: Write $ t^5 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} t^5 \cdot \frac{u^3}{5} & \xlongequal{\text{Step 1}} \frac{t^5}{\color{red}{1}} \cdot \frac{u^3}{5} \xlongequal{\text{Step 2}} \frac{ t^5 \cdot u^3 }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ t^5u^3 }{ 5 } \end{aligned} $$

Add $ \dfrac{t^5u^3}{5} $ and $ u $ to get $ \dfrac{ \color{purple}{ t^5u^3+5u } }{ 5 }$.

Step 1: Write $ u $ 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 second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{t^5u^3}{5} +u & \xlongequal{\text{Step 1}} \frac{t^5u^3}{5} + \frac{u}{\color{red}{1}} = \frac{ t^5u^3 }{ 5 } + \frac{ u \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ t^5u^3 } }{ 5 } + \frac{ \color{purple}{ 5u } }{ 5 }=\frac{ \color{purple}{ t^5u^3+5u } }{ 5 } \end{aligned} $$

Add $ \dfrac{t^5u^3+5u}{5} $ and $ 8 $ to get $ \dfrac{ \color{purple}{ t^5u^3+5u+40 } }{ 5 }$.

Step 1: Write $ 8 $ 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 second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{t^5u^3+5u}{5} +8 & \xlongequal{\text{Step 1}} \frac{t^5u^3+5u}{5} + \frac{8}{\color{red}{1}} = \frac{ t^5u^3+5u }{ 5 } + \frac{ 8 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ t^5u^3+5u } }{ 5 } + \frac{ \color{purple}{ 40 } }{ 5 }=\frac{ \color{purple}{ t^5u^3+5u+40 } }{ 5 } \end{aligned} $$