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Question

Answer

$$\dfrac{x}{x+4}+\dfrac{3}{5x+20}=\dfrac{5x+3}{5x+20}$$

Explanation
$$ \begin{aligned}\frac{x}{x+4}+\frac{3}{5x+20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5x+3}{5x+20}\end{aligned} $$
①

Add $ \dfrac{x}{x+4} $ and $ \dfrac{3}{5x+20} $ to get $ \dfrac{ \color{purple}{ 5x+3 } }{ 5x+20 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 5 }$.

$$ \begin{aligned} \frac{x}{x+4} + \frac{3}{5x+20} & = \frac{ x \cdot \color{blue}{ 5 }}{ \left( x+4 \right) \cdot \color{blue}{ 5 }} + \frac{ 3 }{ 5x+20 } = \\[1ex] &=\frac{ \color{purple}{ 5x } }{ 5x+20 } + \frac{ \color{purple}{ 3 } }{ 5x+20 }=\frac{ \color{purple}{ 5x+3 } }{ 5x+20 } \end{aligned} $$
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