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Question

Answer

$$\dfrac{8}{3w+2}-\dfrac{1}{9w+6}=\dfrac{23}{9w+6}$$

Explanation
$$ \begin{aligned}\frac{8}{3w+2}-\frac{1}{9w+6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{23}{9w+6}\end{aligned} $$
①

Subtract $ \dfrac{1}{9w+6} $ from $ \dfrac{8}{3w+2} $ to get $ \dfrac{ \color{purple}{ 23 } }{ 9w+6 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{8}{3w+2} - \frac{1}{9w+6} & = \frac{ 8 \cdot \color{blue}{ 3 }}{ \left( 3w+2 \right) \cdot \color{blue}{ 3 }} - \frac{ 1 }{ 9w+6 } = \\[1ex] &=\frac{ \color{purple}{ 24 } }{ 9w+6 } - \frac{ \color{purple}{ 1 } }{ 9w+6 }=\frac{ \color{purple}{ 23 } }{ 9w+6 } \end{aligned} $$
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