Multiply $ \dfrac{9x^2+13x+4}{8} $ by $ x^2 $ to get $ \dfrac{ 9x^4+13x^3+4x^2 }{ 8 } $.

Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{9x^2+13x+4}{8} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{9x^2+13x+4}{8} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 9x^2+13x+4 \right) \cdot x^2 }{ 8 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^4+13x^3+4x^2 }{ 8 } \end{aligned} $$

Add $ \dfrac{9x^4+13x^3+4x^2}{8} $ and $ x $ to get $ \dfrac{ \color{purple}{ 9x^4+13x^3+4x^2+8x } }{ 8 }$.

Step 1: Write $ x $ 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 $\color{blue}{8}$.

$$ \begin{aligned} \frac{9x^4+13x^3+4x^2}{8} +x & \xlongequal{\text{Step 1}} \frac{9x^4+13x^3+4x^2}{8} + \frac{x}{\color{red}{1}} = \frac{ 9x^4+13x^3+4x^2 }{ 8 } + \frac{ x \cdot \color{blue}{ 8 }}{ 1 \cdot \color{blue}{ 8 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9x^4+13x^3+4x^2 } }{ 8 } + \frac{ \color{purple}{ 8x } }{ 8 }=\frac{ \color{purple}{ 9x^4+13x^3+4x^2+8x } }{ 8 } \end{aligned} $$

Subtract $7$ from $ \dfrac{9x^4+13x^3+4x^2+8x}{8} $ to get $ \dfrac{ \color{purple}{ 9x^4+13x^3+4x^2+8x-56 } }{ 8 }$.

Step 1: Write $ 7 $ 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 $\color{blue}{8}$.

$$ \begin{aligned} \frac{9x^4+13x^3+4x^2+8x}{8} -7 & \xlongequal{\text{Step 1}} \frac{9x^4+13x^3+4x^2+8x}{8} - \frac{7}{\color{red}{1}} = \frac{ 9x^4+13x^3+4x^2+8x }{ 8 } - \frac{ 7 \cdot \color{blue}{ 8 }}{ 1 \cdot \color{blue}{ 8 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9x^4+13x^3+4x^2+8x } }{ 8 } - \frac{ \color{purple}{ 56 } }{ 8 }=\frac{ \color{purple}{ 9x^4+13x^3+4x^2+8x-56 } }{ 8 } \end{aligned} $$