Answer
$$\frac{5b-5}{5}\cdot\frac{6}{b-1}=6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5b-5}{5}\cdot\frac{6}{b-1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{30}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}} \frac{ 30 : \color{orangered}{ 5 } }{ 5 : \color{orangered}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{6}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6\end{aligned} $$ | |
| ① | Multiply $ \dfrac{5b-5}{5} $ by $ \dfrac{6}{b-1} $ to get $ \dfrac{ 30 }{ 5 } $. Step 1: Factor numerators and denominators. Step 2: Cancel common factors. Step 3: Multiply numerators and denominators. $$ \begin{aligned} \frac{5b-5}{5} \cdot \frac{6}{b-1} & \xlongequal{\text{Step 1}} \frac{ 5 \cdot \color{blue}{ \left( b-1 \right) } }{ 5 } \cdot \frac{ 6 }{ 1 \cdot \color{blue}{ \left( b-1 \right) } } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 5 }{ 5 } \cdot \frac{ 6 }{ 1 } \xlongequal{\text{Step 3}} \frac{ 30 }{ 5 } \end{aligned} $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 5 } $. |
| ③ | Remove 1 from denominator. |
This page was created using
Simplify Rational Expressions