Divide $4x^2-13x+10$ by $ \dfrac{x-3}{x-2} $ to get $ \dfrac{4x^3-21x^2+36x-20}{x-3} $.

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

Step 2: Write $ 4x^2-13x+10 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{4x^2-13x+10}{ \frac{\color{blue}{x-3}}{\color{blue}{x-2}} } & \xlongequal{\text{Step 1}} 4x^2-13x+10 \cdot \frac{\color{blue}{x-2}}{\color{blue}{x-3}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{4x^2-13x+10}{\color{red}{1}} \cdot \frac{x-2}{x-3} \xlongequal{\text{Step 3}} \frac{ \left( 4x^2-13x+10 \right) \cdot \left( x-2 \right) }{ 1 \cdot \left( x-3 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 4x^3-8x^2-13x^2+26x+10x-20 }{ x-3 } = \frac{4x^3-21x^2+36x-20}{x-3} \end{aligned} $$