Question
Answer
$$\dfrac{\dfrac{\dfrac{x}{9x^2-8x-1}}{8}}{7}=\dfrac{x}{504x^2-448x-56}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\frac{x}{9x^2-8x-1}}{8}}{7}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{x}{72x^2-64x-8}}{7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{x}{504x^2-448x-56}\end{aligned} $$ | |
| ① | Divide $ \dfrac{x}{9x^2-8x-1} $ by $ 8 $ to get $ \dfrac{ x }{ 72x^2-64x-8 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{x}{9x^2-8x-1} }{8} & \xlongequal{\text{Step 1}} \frac{x}{9x^2-8x-1} \cdot \frac{\color{blue}{1}}{\color{blue}{8}} \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ \left( 9x^2-8x-1 \right) \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x }{ 72x^2-64x-8 } \end{aligned} $$ |
| ② | Divide $ \dfrac{x}{72x^2-64x-8} $ by $ 7 $ to get $ \dfrac{ x }{ 504x^2-448x-56 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{x}{72x^2-64x-8} }{7} & \xlongequal{\text{Step 1}} \frac{x}{72x^2-64x-8} \cdot \frac{\color{blue}{1}}{\color{blue}{7}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ \left( 72x^2-64x-8 \right) \cdot 7 } \xlongequal{\text{Step 3}} \frac{ x }{ 504x^2-448x-56 } \end{aligned} $$ |
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Simplify Rational Expressions