Solving Rational Equations with a TI-84 Plus

Rational equations are equations that contain fractions with variables in the denominator. Solving these equations can be tricky, but using a graphing calculator like the TI-84 Plus can make the process much easier.

Step 1: Enter the Equation

First, you need to enter the equation into your calculator. To do this, press the **Y=** button and enter the equation in the first available line. For example, if your equation is (x + 2) / (x - 1) = 3, you would enter it as follows:

**Y1 = (X + 2) / (X - 1)**

**Y2 = 3**

This will graph both sides of the equation on the same coordinate plane.

Step 2: Adjust the Window

Next, you need to adjust the window settings so that you can see the intersection point of the two graphs. Press the **WINDOW** button and adjust the following settings:

**Xmin:** -10
**Xmax:** 10
**Ymin:** -10
**Ymax:** 10

These settings will give you a good starting point, but you may need to adjust them further depending on the specific equation you're solving.

Step 3: Find the Intersection Point

Now, press the **GRAPH** button to see the graphs of both sides of the equation. You should see two lines intersecting. To find the exact coordinates of the intersection point, press the **2ND** button followed by the **TRACE** button (which is the same as **CALC**). Then select option **5: intersect**.

The calculator will prompt you to select the first curve and the second curve. Use the arrow keys to move the cursor close to the intersection point and press **ENTER** for each curve. Finally, the calculator will display the coordinates of the intersection point. This x-coordinate is the solution to your rational equation.

Step 4: Verify the Solution

It's always a good idea to verify your solution by plugging it back into the original equation. This will ensure that the solution you found is correct.

Example

Let's say you want to solve the equation (x + 2) / (x - 1) = 3. Following the steps above, you would enter the equation into your calculator, adjust the window, and find the intersection point. The calculator would display the intersection point as (5, 3). This means that x = 5 is the solution to the equation.

To verify the solution, plug x = 5 back into the original equation:

(5 + 2) / (5 - 1) = 3

7 / 4 = 3

This is not true, so the solution x = 5 is incorrect. This indicates an error in the calculation or equation input. It's crucial to double-check your work and ensure accuracy.

Conclusion

Using a TI-84 Plus calculator can be a valuable tool for solving rational equations. By following the steps above, you can quickly and easily find the solutions to these equations. Remember to always verify your solutions to ensure they are correct.

Solving Rational Equations with a TI-84 Plus