https://file.aiquickdraw.com/mathbot/file/1726649908428fawbjvyq.jpg

The equation you've provided in the image is \( (x+2)y = x \).

To solve this equation for \( y \), we can rearrange it as follows:

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

This equation expresses \( y \) in terms of \( x \). \( y \) will be defined for all values of \( x \) except \( x = -2 \) because at \( x = -2 \), the denominator becomes zero which makes the equation undefined.

Would you like further details on this solution or have any other questions? Here are a few things you might consider asking:

1. How does the graph of \( y = \frac{x}{x+2} \) look?
2. What happens to the value of \( y \) as \( x \) approaches infinity?
3. What is the y-intercept of this equation?
4. Can we determine the x-intercept of the graph of \( y = \frac{x}{x+2} \)?
5. Are there any asymptotes for this function, and if so, what are they?

**Tip:** When solving equations involving fractions, it's helpful to check for values that make the denominator zero, as these are points where the function is not defined.

Explore how to solve the second-order non-homogeneous differential equation (D^2 + D - 2)y = x^2 using the method of undetermined coefficients and the superposition principle. Understand the step-by-step process for finding both the complementary and particular solutions.

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