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Question

Answer

$$\dfrac{4x-3}{3}+\dfrac{5x-1}{6}=\dfrac{13x-7}{6}$$

Explanation
$$ \begin{aligned}\frac{4x-3}{3}+\frac{5x-1}{6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{13x-7}{6}\end{aligned} $$
①

Add $ \dfrac{4x-3}{3} $ and $ \dfrac{5x-1}{6} $ to get $ \dfrac{ \color{purple}{ 13x-7 } }{ 6 }$.

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

$$ \begin{aligned} \frac{4x-3}{3} + \frac{5x-1}{6} & = \frac{ \left( 4x-3 \right) \cdot \color{blue}{ 2 }}{ 3 \cdot \color{blue}{ 2 }} + \frac{ 5x-1 }{ 6 } = \\[1ex] &=\frac{ \color{purple}{ 8x-6 } }{ 6 } + \frac{ \color{purple}{ 5x-1 } }{ 6 }=\frac{ \color{purple}{ 13x-7 } }{ 6 } \end{aligned} $$
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