Question

How do you solve a rational equation by using a graph?

Answer 1

Please see below.

Explanation:

To solve any equation `f(x)=0`, we have to just draw a graph of the function in Cartesian coordinates so that `y=f(x)`.

Now, the value of `x` at points where graph of `f(x)` cuts `x`-axis gives the solution of equation `f(x)=0`, whatever it is trigonometric or rational.

For example, let there be a trigonometric function `f(x)=sinx`, the graph shows its solution as `x=npi`, where `n` is an integer.

graph{sinx [-10, 10, -5, 5]}

or if the function is rational such as `f(x)=x(x+0.75)(x+0.25)(x-0.5)(x-1.5)(x-2.3)`, solution of `x(x+0.75)(x+0.25)(x-0.5)(x-1.5)(x-2.3)=0` is `{-0.75,-0.25,0,0.5,1.5,2.3)`

graph{x(x+0.75)(x+0.25)(x-0.5)(x-1.5)(x-2.3) [-1.385, 3.615, -1.06, 1.44]}