Question
Answer
$$\dfrac{x^{14}+4x^7+3}{2x^{11}+2x^4}=\dfrac{x^7+3}{2x^4}$$
Explanation
| $$ \begin{aligned}\frac{x^{14}+4x^7+3}{2x^{11}+2x^4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{x^7+3}{2x^4}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{x^{14}+4x^7+3}{2x^{11}+2x^4} $ to $ \dfrac{x^7+3}{2x^4} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x^7+1}$. $$ \begin{aligned} \frac{x^{14}+4x^7+3}{2x^{11}+2x^4} & =\frac{ \left( x^7+3 \right) \cdot \color{blue}{ \left( x^7+1 \right) }}{ 2x^4 \cdot \color{blue}{ \left( x^7+1 \right) }} = \\[1ex] &= \frac{x^7+3}{2x^4} \end{aligned} $$ |
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Simplify Rational Expressions