# Solving Rational Equations on a Graphing Calculator

## Key Questions

#### Explanation:

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

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

For example, let there be a trigonometric function $f \left(x\right) = \sin x$, the graph shows its solution as $x = n \pi$, where $n$ is an integer.

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

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

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]}