Multiply $ \color{blue}{2x} $ by $ \left( x-5\right) $ $$ \color{blue}{2x} \cdot \left( x-5\right) = 2x^2-10x $$

Add $2x^2-10x$ and $ \dfrac{6x^2-2x}{-2x} $ to get $ \dfrac{ \color{purple}{ -4x^3+26x^2-2x } }{ -2x }$.

Step 1: Write $ 2x^2-10x $ 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 $\color{blue}{ -2x }$.

$$ \begin{aligned} 2x^2-10x+ \frac{6x^2-2x}{-2x} & \xlongequal{\text{Step 1}} \frac{2x^2-10x}{\color{red}{1}} + \frac{6x^2-2x}{-2x} = \frac{ \left( 2x^2-10x \right) \cdot \color{blue}{ \left( -2x \right) }}{ 1 \cdot \color{blue}{ \left( -2x \right) }} + \frac{ 6x^2-2x }{ -2x } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -4x^3+20x^2 } }{ -2x } + \frac{ \color{purple}{ 6x^2-2x } }{ -2x }=\frac{ \color{purple}{ -4x^3+26x^2-2x } }{ -2x } \end{aligned} $$