What are you looking for when you are solving a rational equation on a graphing calculator?
Usually, the intersection of the equation line with the x-axis.
What most expressions and equations are trying to find is a particular unknown value (variable) related to the other values in the expression. Numerically, we simply derive the number value from algebraic manipulations and properties. Graphically, with nominal "x" and "y" axes the usual unknown value is designated as the "x".
So, plotting the equation on a graph will result in one of the points being ON the x-axis (or maybe it will be the ONLY point in the solution). That is the point where the value of "x" satisfies the equation.