Question
Answer
$$\dfrac{\dfrac{\dfrac{60}{4x^2-36}}{12}}{x^2+3x}=\dfrac{60}{48x^4+144x^3-432x^2-1296x}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\frac{60}{4x^2-36}}{12}}{x^2+3x}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{60}{48x^2-432}}{x^2+3x} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{60}{48x^4+144x^3-432x^2-1296x}\end{aligned} $$ | |
| ① | Divide $ \dfrac{60}{4x^2-36} $ by $ 12 $ to get $ \dfrac{ 60 }{ 48x^2-432 } $. 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. $$ \begin{aligned} \frac{ \frac{60}{4x^2-36} }{12} & \xlongequal{\text{Step 1}} \frac{60}{4x^2-36} \cdot \frac{\color{blue}{1}}{\color{blue}{12}} \xlongequal{\text{Step 2}} \frac{ 60 \cdot 1 }{ \left( 4x^2-36 \right) \cdot 12 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 60 }{ 48x^2-432 } \end{aligned} $$ |
| ② | Divide $ \dfrac{60}{48x^2-432} $ by $ x^2+3x $ to get $ \dfrac{ 60 }{ 48x^4+144x^3-432x^2-1296x } $. 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. $$ \begin{aligned} \frac{ \frac{60}{48x^2-432} }{x^2+3x} & \xlongequal{\text{Step 1}} \frac{60}{48x^2-432} \cdot \frac{\color{blue}{1}}{\color{blue}{x^2+3x}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 60 \cdot 1 }{ \left( 48x^2-432 \right) \cdot \left( x^2+3x \right) } \xlongequal{\text{Step 3}} \frac{ 60 }{ 48x^4+144x^3-432x^2-1296x } \end{aligned} $$ |
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Simplify Rational Expressions