Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10(s+\frac{1}{100})(s+6)k& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10 \cdot \frac{100s+1}{100}(s+6)k \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1000s+10}{100}(s+6)k \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{1000s^2+6010s+60}{100}k \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{1000ks^2+6010ks+60k}{100}\end{aligned} $$ | |
| ① | Add $s$ and $ \dfrac{1}{100} $ to get $ \dfrac{ \color{purple}{ 100s+1 } }{ 100 }$. Step 1: Write $ s $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To add raitonal expressions, both fractions must have the same denominator. |
| ② | Multiply $10$ by $ \dfrac{100s+1}{100} $ to get $ \dfrac{ 1000s+10 }{ 100 } $. Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 10 \cdot \frac{100s+1}{100} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{100s+1}{100} \xlongequal{\text{Step 2}} \frac{ 10 \cdot \left( 100s+1 \right) }{ 1 \cdot 100 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1000s+10 }{ 100 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{1000s+10}{100} $ by $ s+6 $ to get $ \dfrac{1000s^2+6010s+60}{100} $. Step 1: Write $ s+6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1000s+10}{100} \cdot s+6 & \xlongequal{\text{Step 1}} \frac{1000s+10}{100} \cdot \frac{s+6}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 1000s+10 \right) \cdot \left( s+6 \right) }{ 100 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1000s^2+6000s+10s+60 }{ 100 } = \frac{1000s^2+6010s+60}{100} \end{aligned} $$ |
| ④ | Multiply $ \dfrac{1000s^2+6010s+60}{100} $ by $ k $ to get $ \dfrac{ 1000ks^2+6010ks+60k }{ 100 } $. Step 1: Write $ k $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1000s^2+6010s+60}{100} \cdot k & \xlongequal{\text{Step 1}} \frac{1000s^2+6010s+60}{100} \cdot \frac{k}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 1000s^2+6010s+60 \right) \cdot k }{ 100 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 1000ks^2+6010ks+60k }{ 100 } \end{aligned} $$ |