Multiply $ \dfrac{9}{7} $ by $ x^2 $ to get $ \dfrac{ 9x^2 }{ 7 } $.

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.

$$ \begin{aligned} \frac{9}{7} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{9}{7} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x^2 }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^2 }{ 7 } \end{aligned} $$

Add $5x^2+14x$ and $ \dfrac{9x^2}{7} $ to get $ \dfrac{ \color{purple}{ 44x^2+98x } }{ 7 }$.

Step 1: Write $ 5x^2+14x $ 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 $\color{blue}{ 7 }$.

$$ \begin{aligned} 5x^2+14x+ \frac{9x^2}{7} & \xlongequal{\text{Step 1}} \frac{5x^2+14x}{\color{red}{1}} + \frac{9x^2}{7} = \frac{ \left( 5x^2+14x \right) \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} + \frac{ 9x^2 }{ 7 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 35x^2+98x } }{ 7 } + \frac{ \color{purple}{ 9x^2 } }{ 7 }=\frac{ \color{purple}{ 44x^2+98x } }{ 7 } \end{aligned} $$

Subtract $3x$ from $ \dfrac{44x^2+98x}{7} $ to get $ \dfrac{ \color{purple}{ 44x^2+77x } }{ 7 }$.

Step 1: Write $ 3x $ 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 $\color{blue}{7}$.

$$ \begin{aligned} \frac{44x^2+98x}{7} -3x & \xlongequal{\text{Step 1}} \frac{44x^2+98x}{7} - \frac{3x}{\color{red}{1}} = \frac{ 44x^2+98x }{ 7 } - \frac{ 3x \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 44x^2+98x } }{ 7 } - \frac{ \color{purple}{ 21x } }{ 7 }=\frac{ \color{purple}{ 44x^2+77x } }{ 7 } \end{aligned} $$

Subtract $10$ from $ \dfrac{44x^2+77x}{7} $ to get $ \dfrac{ \color{purple}{ 44x^2+77x-70 } }{ 7 }$.

Step 1: Write $ 10 $ 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 $\color{blue}{7}$.

$$ \begin{aligned} \frac{44x^2+77x}{7} -10 & \xlongequal{\text{Step 1}} \frac{44x^2+77x}{7} - \frac{10}{\color{red}{1}} = \frac{ 44x^2+77x }{ 7 } - \frac{ 10 \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 44x^2+77x } }{ 7 } - \frac{ \color{purple}{ 70 } }{ 7 }=\frac{ \color{purple}{ 44x^2+77x-70 } }{ 7 } \end{aligned} $$