Simplify numerator

$$ \color{blue}{15x} + \color{blue}{70x} = \color{blue}{85x} $$

Add $ \dfrac{85x}{x^2} $ and $ 4x $ to get $ \dfrac{ \color{purple}{ 4x^3+85x } }{ x^2 }$.

Step 1: Write $ 4x $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{85x}{x^2} +4x & \xlongequal{\text{Step 1}} \frac{85x}{x^2} + \frac{4x}{\color{red}{1}} = \frac{ 85x }{ x^2 } + \frac{ 4x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 85x } }{ x^2 } + \frac{ \color{purple}{ 4x^3 } }{ x^2 }=\frac{ \color{purple}{ 4x^3+85x } }{ x^2 } \end{aligned} $$

Subtract $21$ from $ \dfrac{4x^3+85x}{x^2} $ to get $ \dfrac{ \color{purple}{ 4x^3-21x^2+85x } }{ x^2 }$.

Step 1: Write $ 21 $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{4x^3+85x}{x^2} -21 & \xlongequal{\text{Step 1}} \frac{4x^3+85x}{x^2} - \frac{21}{\color{red}{1}} = \frac{ 4x^3+85x }{ x^2 } - \frac{ 21 \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^3+85x } }{ x^2 } - \frac{ \color{purple}{ 21x^2 } }{ x^2 }=\frac{ \color{purple}{ 4x^3-21x^2+85x } }{ x^2 } \end{aligned} $$