$$\dfrac{a}{1-\dfrac{s}{770}}=\dfrac{770a}{-s+770}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{a}{1-\frac{s}{770}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{a}{\frac{-s+770}{770}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{770a}{-s+770}\end{aligned} $$ | |
| ① | Subtract $ \dfrac{s}{770} $ from $ 1 $ to get $ \dfrac{ \color{purple}{ -s+770 } }{ 770 }$. Step 1: Write $ 1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |
| ② | Divide $a$ by $ \dfrac{-s+770}{770} $ to get $ \dfrac{ 770a }{ -s+770 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Write $ a $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 3: Multiply numerators and denominators. Step 4: Simplify numerator and denominator. $$ \begin{aligned} \frac{a}{ \frac{\color{blue}{-s+770}}{\color{blue}{770}} } & \xlongequal{\text{Step 1}} a \cdot \frac{\color{blue}{770}}{\color{blue}{-s+770}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{a}{\color{red}{1}} \cdot \frac{770}{-s+770} \xlongequal{\text{Step 3}} \frac{ a \cdot 770 }{ 1 \cdot \left( -s+770 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 770a }{ -s+770 } \end{aligned} $$ |