Multiply $3$ by $ \dfrac{x}{5x} $ to get $ \dfrac{ 3x }{ 5x } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $ \dfrac{10}{6x-5} $ from $ \dfrac{3x}{5x} $ to get $ \dfrac{ \color{purple}{ 18x^2-65x } }{ 30x^2-25x }$.

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}{ 6x-5 }$ and the second by $\color{blue}{ 5x }$.

$$ \begin{aligned} \frac{3x}{5x} - \frac{10}{6x-5} & = \frac{ 3x \cdot \color{blue}{ \left( 6x-5 \right) }}{ 5x \cdot \color{blue}{ \left( 6x-5 \right) }} - \frac{ 10 \cdot \color{blue}{ 5x }}{ \left( 6x-5 \right) \cdot \color{blue}{ 5x }} = \\[1ex] &=\frac{ \color{purple}{ 18x^2-15x } }{ 30x^2-25x } - \frac{ \color{purple}{ 50x } }{ 30x^2-25x }=\frac{ \color{purple}{ 18x^2-65x } }{ 30x^2-25x } \end{aligned} $$