Question
Answer
$$\dfrac{c\cdot(1+x)-o\cdot(1-x)}{c\cdot(1+x)+o\cdot(1-x)}=\dfrac{c+cx-o+ox}{cx-ox+c+o}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{c\cdot(1+x)-o\cdot(1-x)}{c\cdot(1+x)+o\cdot(1-x)}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{c+cx-(1o-ox)}{c+cx+o-ox} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{c+cx-o+ox}{cx-ox+c+o}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{c} $ by $ \left( 1+x\right) $ $$ \color{blue}{c} \cdot \left( 1+x\right) = c+cx $$ |
| ② | Multiply $ \color{blue}{o} $ by $ \left( 1-x\right) $ $$ \color{blue}{o} \cdot \left( 1-x\right) = o-ox $$ |
| ③ | Multiply $ \color{blue}{c} $ by $ \left( 1+x\right) $ $$ \color{blue}{c} \cdot \left( 1+x\right) = c+cx $$ |
| ④ | Multiply $ \color{blue}{o} $ by $ \left( 1-x\right) $ $$ \color{blue}{o} \cdot \left( 1-x\right) = o-ox $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( o-ox \right) = -o+ox $$ |
| ⑥ | Combine like terms: $$ c+cx+o-ox = cx-ox+c+o $$ |
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