Question
Answer
$$10\cdot\dfrac{x^2-64}{5x+40}=\dfrac{10x-80}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10 \cdot \frac{x^2-64}{5x+40}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10 \cdot \frac{x-8}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10x-80}{5}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{x^2-64}{5x+40} $ to $ \dfrac{x-8}{5} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x+8}$. $$ \begin{aligned} \frac{x^2-64}{5x+40} & =\frac{ \left( x-8 \right) \cdot \color{blue}{ \left( x+8 \right) }}{ 5 \cdot \color{blue}{ \left( x+8 \right) }} = \\[1ex] &= \frac{x-8}{5} \end{aligned} $$ |
| ② | Multiply $10$ by $ \dfrac{x-8}{5} $ to get $ \dfrac{ 10x-80 }{ 5 } $. 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. $$ \begin{aligned} 10 \cdot \frac{x-8}{5} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{x-8}{5} \xlongequal{\text{Step 2}} \frac{ 10 \cdot \left( x-8 \right) }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x-80 }{ 5 } \end{aligned} $$ |
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