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Question

Answer

$$\dfrac{9}{4x+12}+\dfrac{2}{x+3}=\dfrac{17}{4x+12}$$

Explanation
$$ \begin{aligned}\frac{9}{4x+12}+\frac{2}{x+3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{17}{4x+12}\end{aligned} $$
①

Add $ \dfrac{9}{4x+12} $ and $ \dfrac{2}{x+3} $ to get $ \dfrac{ \color{purple}{ 17 } }{ 4x+12 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{4}$.

$$ \begin{aligned} \frac{9}{4x+12} + \frac{2}{x+3} & = \frac{ 9 }{ 4x+12 } + \frac{ 2 \cdot \color{blue}{ 4 }}{ \left( x+3 \right) \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 9 } }{ 4x+12 } + \frac{ \color{purple}{ 8 } }{ 4x+12 }=\frac{ \color{purple}{ 17 } }{ 4x+12 } \end{aligned} $$
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