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Question

Answer

$$\dfrac{3}{2h^2-2h}+\dfrac{5}{2h-2}=\dfrac{5h+3}{2h^2-2h}$$

Explanation
$$ \begin{aligned}\frac{3}{2h^2-2h}+\frac{5}{2h-2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5h+3}{2h^2-2h}\end{aligned} $$
①

Add $ \dfrac{3}{2h^2-2h} $ and $ \dfrac{5}{2h-2} $ to get $ \dfrac{ \color{purple}{ 5h+3 } }{ 2h^2-2h }$.

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

$$ \begin{aligned} \frac{3}{2h^2-2h} + \frac{5}{2h-2} & = \frac{ 3 }{ 2h^2-2h } + \frac{ 5 \cdot \color{blue}{ h }}{ \left( 2h-2 \right) \cdot \color{blue}{ h }} = \\[1ex] &=\frac{ \color{purple}{ 3 } }{ 2h^2-2h } + \frac{ \color{purple}{ 5h } }{ 2h^2-2h }=\frac{ \color{purple}{ 5h+3 } }{ 2h^2-2h } \end{aligned} $$
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