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Question

Answer

$$\dfrac{y}{x}+1=\dfrac{x+y}{x}$$

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

Add $ \dfrac{y}{x} $ and $ 1 $ to get $ \dfrac{ \color{purple}{ x+y } }{ x }$.

Step 1: Write $ 1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

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

$$ \begin{aligned} \frac{y}{x} +1 & \xlongequal{\text{Step 1}} \frac{y}{x} + \frac{1}{\color{red}{1}} = \frac{ y }{ x } + \frac{ 1 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ y } }{ x } + \frac{ \color{purple}{ x } }{ x }=\frac{ \color{purple}{ x+y } }{ x } \end{aligned} $$
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