https://file.aiquickdraw.com/mathbot/file/1728509499179zw9b8mkh.jpg

The equation shown in the image is:

\[
y = \frac{x^4 + 6}{x^2}
\]

We can simplify this expression by dividing each term in the numerator by \( x^2 \):

\[
y = \frac{x^4}{x^2} + \frac{6}{x^2}
\]

Simplifying further:

\[
y = x^2 + \frac{6}{x^2}
\]

So, the simplified form of the equation is:

\[
y = x^2 + \frac{6}{x^2}
\]

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. What happens to the function \( y = x^2 + \frac{6}{x^2} \) as \( x \) approaches infinity?
2. How would you find the derivative of this function?
3. What are the critical points of this function, and how do you find them?
4. How would you determine the behavior of the function around \( x = 0 \)?
5. How would you plot this function and identify key features such as asymptotes?

**Tip:** When simplifying rational functions, always check if the numerator and denominator have common factors that can simplify the expression.

Simplify the expression y = (x^4 + 6) / x^2

Learn how to simplify the rational expression y = (x^4 + 6) / x^2 with a detailed step-by-step solution. This problem covers key algebraic concepts such as simplifying rational expressions and using the laws of exponents. Suitable for high school students in Grades 9-12.

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