Add $ \dfrac{-x^2}{10} $ and $ 10 $ to get $ \dfrac{ \color{purple}{ -x^2+100 } }{ 10 }$.

Step 1: Write $ 10 $ 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 $\color{blue}{10}$.

$$ \begin{aligned} \frac{-x^2}{10} +10 & \xlongequal{\text{Step 1}} \frac{-x^2}{10} + \frac{10}{\color{red}{1}} = \frac{ -x^2 }{ 10 } + \frac{ 10 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -x^2 } }{ 10 } + \frac{ \color{purple}{ 100 } }{ 10 }=\frac{ \color{purple}{ -x^2+100 } }{ 10 } \end{aligned} $$

Subtract $x^3$ from $ \dfrac{-x^2+100}{10} $ to get $ \dfrac{ \color{purple}{ -10x^3-x^2+100 } }{ 10 }$.

Step 1: Write $ x^3 $ 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 $\color{blue}{10}$.

$$ \begin{aligned} \frac{-x^2+100}{10} -x^3 & \xlongequal{\text{Step 1}} \frac{-x^2+100}{10} - \frac{x^3}{\color{red}{1}} = \frac{ -x^2+100 }{ 10 } - \frac{ x^3 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -x^2+100 } }{ 10 } - \frac{ \color{purple}{ 10x^3 } }{ 10 }=\frac{ \color{purple}{ -10x^3-x^2+100 } }{ 10 } \end{aligned} $$