Нарисуй график y=1/(x+1)+1/(x-1) что бы его было четко видно и обьясни как его нарисовать

Here's the graph of the function \( y = \frac{1}{x+1} + \frac{1}{x-1} \). It clearly shows important features like the asymptotes and behavior of the function.

### Steps to draw this graph:
1. **Define the function**: The function is a sum of two rational expressions. Identify that the function has vertical asymptotes at \( x = -1 \) and \( x = 1 \) because the denominators become zero at these points.
2. **Identify asymptotes**:
   - As \( x \to -1 \) or \( x \to 1 \), the function becomes undefined, and the graph will approach infinity (asymptotes).
   - Vertical asymptotes are drawn at \( x = -1 \) and \( x = 1 \).
3. **Plot the function**: For values of \( x \), calculate \( y \) and plot points. The graph has a steep curve near the asymptotes and flattens out far from the asymptotes.
4. **Mark axes and asymptotes**: The x-axis is the horizontal asymptote far away from the vertical lines, and the y-axis is used for symmetry.

The graph shows the asymptotic behavior clearly, with steep changes near \( x = -1 \) and \( x = 1 \).

Do you want further explanation or any details on this function?

Here are 5 related questions:
1. How do you find vertical asymptotes for rational functions?
2. What is the behavior of functions near asymptotes?
3. How can you calculate horizontal asymptotes?
4. How do discontinuities affect a graph?
5. How do transformations affect rational functions like this one?

**Tip:** When graphing rational functions, always look for points where the denominator equals zero to locate vertical asymptotes.

Learn how to graph the rational function y = 1/(x+1) + 1/(x-1), including identifying asymptotes at x = -1 and x = 1. Understand the behavior near asymptotes and explore key graphing techniques for rational functions. Suitable for high school students in Grades 10-12.

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