Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{2(iwcr+1)}-iwc\frac{r}{2(iwcr+1)}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{2cirw+2}-iwc\frac{r}{2cirw+2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{1}{2cirw+2}-\frac{cirw}{2cirw+2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{-cirw+1}{2cirw+2}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( cirw+1\right) $ $$ \color{blue}{2} \cdot \left( cirw+1\right) = 2cirw+2 $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( cirw+1\right) $ $$ \color{blue}{2} \cdot \left( cirw+1\right) = 2cirw+2 $$ |
| ③ | Multiply $ \color{blue}{2} $ by $ \left( cirw+1\right) $ $$ \color{blue}{2} \cdot \left( cirw+1\right) = 2cirw+2 $$ |
| ④ | Multiply $ciw$ by $ \dfrac{r}{2cirw+2} $ to get $ \dfrac{ cirw }{ 2cirw+2 } $. Step 1: Write $ ciw $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} ciw \cdot \frac{r}{2cirw+2} & \xlongequal{\text{Step 1}} \frac{ciw}{\color{red}{1}} \cdot \frac{r}{2cirw+2} \xlongequal{\text{Step 2}} \frac{ ciw \cdot r }{ 1 \cdot \left( 2cirw+2 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ cirw }{ 2cirw+2 } \end{aligned} $$ |
| ⑤ | Subtract $ \dfrac{cirw}{2cirw+2} $ from $ \dfrac{1}{2cirw+2} $ to get $ \dfrac{-cirw+1}{2cirw+2} $. To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{1}{2cirw+2} - \frac{cirw}{2cirw+2} & = \frac{1}{\color{blue}{2cirw+2}} - \frac{cirw}{\color{blue}{2cirw+2}} = \\[1ex] &=\frac{ 1 - cirw }{ \color{blue}{ 2cirw+2 }}= \frac{-cirw+1}{2cirw+2} \end{aligned} $$ |