Answer
$$\frac{4}{x+4}+\frac{x}{x+4}=1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4}{x+4}+\frac{x}{x+4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{x+4}{x+4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1\end{aligned} $$ | |
| ① | Add $ \dfrac{4}{x+4} $ and $ \dfrac{x}{x+4} $ to get $ \dfrac{x+4}{x+4} $. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{4}{x+4} + \frac{x}{x+4} & = \frac{4}{\color{blue}{x+4}} + \frac{x}{\color{blue}{x+4}} =\frac{ 4 + x }{ \color{blue}{ x+4 }} = \\[1ex] &= \frac{x+4}{x+4} \end{aligned} $$ |
| ② | Simplify $ \dfrac{x+4}{x+4} $ to $ 1$. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x+4}$. $$ \begin{aligned} \frac{x+4}{x+4} & =\frac{ 1 \cdot \color{blue}{ \left( x+4 \right) }}{ 1 \cdot \color{blue}{ \left( x+4 \right) }} = \\[1ex] &= \frac{1}{1} =1 \end{aligned} $$ |
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Simplify Rational Expressions