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Question

Answer

$$\dfrac{5}{2x+1}+\dfrac{8}{4x+2}=\dfrac{18}{4x+2}$$

Explanation
$$ \begin{aligned}\frac{5}{2x+1}+\frac{8}{4x+2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{18}{4x+2}\end{aligned} $$
①

Add $ \dfrac{5}{2x+1} $ and $ \dfrac{8}{4x+2} $ to get $ \dfrac{ \color{purple}{ 18 } }{ 4x+2 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{5}{2x+1} + \frac{8}{4x+2} & = \frac{ 5 \cdot \color{blue}{ 2 }}{ \left( 2x+1 \right) \cdot \color{blue}{ 2 }} + \frac{ 8 }{ 4x+2 } = \\[1ex] &=\frac{ \color{purple}{ 10 } }{ 4x+2 } + \frac{ \color{purple}{ 8 } }{ 4x+2 }=\frac{ \color{purple}{ 18 } }{ 4x+2 } \end{aligned} $$
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