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Question

Answer

$$\dfrac{x}{x+2}+\dfrac{5}{6x+12}=\dfrac{6x+5}{6x+12}$$

Explanation
$$ \begin{aligned}\frac{x}{x+2}+\frac{5}{6x+12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6x+5}{6x+12}\end{aligned} $$
①

Add $ \dfrac{x}{x+2} $ and $ \dfrac{5}{6x+12} $ to get $ \dfrac{ \color{purple}{ 6x+5 } }{ 6x+12 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 6 }$.

$$ \begin{aligned} \frac{x}{x+2} + \frac{5}{6x+12} & = \frac{ x \cdot \color{blue}{ 6 }}{ \left( x+2 \right) \cdot \color{blue}{ 6 }} + \frac{ 5 }{ 6x+12 } = \\[1ex] &=\frac{ \color{purple}{ 6x } }{ 6x+12 } + \frac{ \color{purple}{ 5 } }{ 6x+12 }=\frac{ \color{purple}{ 6x+5 } }{ 6x+12 } \end{aligned} $$
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