Multiply $2$ by $ \dfrac{x}{3} $ to get $ \dfrac{ 2x }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{x}{3} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{x}{3} \xlongequal{\text{Step 2}} \frac{ 2 \cdot x }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 2x }{ 3 } \end{aligned} $$

Subtract $ \dfrac{5}{3} $ from $ x $ to get $ \dfrac{ \color{purple}{ 3x-5 } }{ 3 }$.

Step 1: Write $ x $ 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 first fraction by $\color{blue}{ 3 }$.

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

Subtract $ \dfrac{10}{9} $ from $ \dfrac{2x}{3} $ to get $ \dfrac{ \color{purple}{ 6x-10 } }{ 9 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{2x}{3} - \frac{10}{9} & = \frac{ 2x \cdot \color{blue}{ 3 }}{ 3 \cdot \color{blue}{ 3 }} - \frac{ 10 }{ 9 } = \\[1ex] &=\frac{ \color{purple}{ 6x } }{ 9 } - \frac{ \color{purple}{ 10 } }{ 9 }=\frac{ \color{purple}{ 6x-10 } }{ 9 } \end{aligned} $$

Subtract $ \dfrac{5}{3} $ from $ x $ to get $ \dfrac{ \color{purple}{ 3x-5 } }{ 3 }$.

Step 1: Write $ x $ 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 first fraction by $\color{blue}{ 3 }$.

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

Divide $ \dfrac{6x-10}{9} $ by $ \dfrac{3x-5}{3} $ to get $ \dfrac{ 6 }{ 9 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Factor numerators and denominators.

Step 3: Cancel common factors.

Step 4: Multiply numerators and denominators.

$$ \begin{aligned} \frac{ \frac{6x-10}{9} }{ \frac{\color{blue}{3x-5}}{\color{blue}{3}} } & \xlongequal{\text{Step 1}} \frac{6x-10}{9} \cdot \frac{\color{blue}{3}}{\color{blue}{3x-5}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 2 \cdot \color{blue}{ \left( 3x-5 \right) } }{ 9 } \cdot \frac{ 3 }{ 1 \cdot \color{blue}{ \left( 3x-5 \right) } } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2 }{ 9 } \cdot \frac{ 3 }{ 1 } \xlongequal{\text{Step 4}} \frac{ 6 }{ 9 } \end{aligned} $$

Divide both the top and bottom numbers by $ \color{orangered}{ 3 } $.