How do you graph #y=\frac{x}{2-x^2}-3#?

The graph is below: graph{(x/(2-x^2))-3 [-19.67, 20.33, -10.36, 9.64]}

To graph the equation y = (x/(2-x^2)) - 3, follow these steps:

1. Determine the domain of the function by finding the values of x that make the denominator (2-x^2) equal to zero. In this case, x cannot be equal to ±√2.

2. Find the y-intercept by substituting x = 0 into the equation. y = (0/(2-0^2)) - 3 = -3.

3. Determine the x-intercepts by setting y = 0 and solving for x. In this case, there are no x-intercepts.

4. Analyze the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function approaches y = -3.

5. Plot the points obtained from the above steps on a graph and draw a smooth curve passing through them.

Note: Due to the complexity of the equation, it may be helpful to use a graphing calculator or software to accurately plot the graph.