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Question

Answer

$$\dfrac{3}{2x+6}+\dfrac{4}{6x+18}=\dfrac{13}{6x+18}$$

Explanation
$$ \begin{aligned}\frac{3}{2x+6}+\frac{4}{6x+18}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{13}{6x+18}\end{aligned} $$
①

Add $ \dfrac{3}{2x+6} $ and $ \dfrac{4}{6x+18} $ to get $ \dfrac{ \color{purple}{ 13 } }{ 6x+18 }$.

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

$$ \begin{aligned} \frac{3}{2x+6} + \frac{4}{6x+18} & = \frac{ 3 \cdot \color{blue}{ 3 }}{ \left( 2x+6 \right) \cdot \color{blue}{ 3 }} + \frac{ 4 }{ 6x+18 } = \\[1ex] &=\frac{ \color{purple}{ 9 } }{ 6x+18 } + \frac{ \color{purple}{ 4 } }{ 6x+18 }=\frac{ \color{purple}{ 13 } }{ 6x+18 } \end{aligned} $$
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