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Question

Answer

$$\dfrac{9}{2z+5}+\dfrac{z}{4z+10}=\dfrac{z+18}{4z+10}$$

Explanation
$$ \begin{aligned}\frac{9}{2z+5}+\frac{z}{4z+10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{z+18}{4z+10}\end{aligned} $$
①

Add $ \dfrac{9}{2z+5} $ and $ \dfrac{z}{4z+10} $ to get $ \dfrac{ \color{purple}{ z+18 } }{ 4z+10 }$.

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

$$ \begin{aligned} \frac{9}{2z+5} + \frac{z}{4z+10} & = \frac{ 9 \cdot \color{blue}{ 2 }}{ \left( 2z+5 \right) \cdot \color{blue}{ 2 }} + \frac{ z }{ 4z+10 } = \\[1ex] &=\frac{ \color{purple}{ 18 } }{ 4z+10 } + \frac{ \color{purple}{ z } }{ 4z+10 }=\frac{ \color{purple}{ z+18 } }{ 4z+10 } \end{aligned} $$
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