Question

How do solve `(x^2-4)/(3-x)>=0` graphically?

Answer 1

A fine Socratic graph is inserted. Glory to this software developers.

See more in the explanation

Explanation:

By actual division,

`y = -(3+x)+5/(3-x)`

The graph has two asymptotes `x+y+3=0 and x-3 = 0.`

What I could give as the interpretation, to the graphical depiction of

the the solution as the shaded region, is as follows.

The equation has asymptotes-revealing form of the hyperbola

`(y+x+3)(x-3)=-5`.

y >=0, with respect to each branch of the hyperbola,

Now, look at the graph. Do you agree that the graph is precise, in

shading the region, for our solution.

Also, see the asymptotic conduit ( gap ) above and the the

asymptotic etching ( thin painting ) below, about the asymptote x = 3.

graph{y-(x^2-4)/(3-x)>=0 [-40, 40, -35, 25]}