Knowing how to simplify expressions in calculus is essential to being able to differentiate. The **TI-89 graphing calculator** makes simplifying expressions an easy task. In fact, you don’t even have to access a menu; The TI-89 can perform expression simplification right on the home screen. There is another way—using the **propFrac **command.

## Simplify TI 89 Example 1: Using the HOME screen

If you have a very simple expression, type it into the HOME screen and the calculator will do the rest.

Example problem: simplify the following expression with the TI-89:

**f(x) = 9x + 8x**

Step 1: Press the HOME key.

Step 2: Press 9 X + 8 X to enter the expression.

Step 3: Press Enter. Your answer should be 17x.

## Simplify TI 89 Example 2: Using propFrac

For more complicated equations, like ((x^{2} + 3x + 2)/(x + 1)), entering it as-is on the HOME screen won’t work. All you’ll see is your entry repeated. This is when you’ll want to use propFrac.

Step 1: Press F2, then 7 to select propFrac from the HOME screen.

Step 2: Type your expression in. Make sure you type in a closing parentheses “)”.

Step 3: Press the ENTER key. For ((x^{2} + 3x + 2)/(x + 1)), the simplified expression is x + 2.

**Caution**: Although the calculator returns the correct answer, it might not be formatted in the way you’re accustomed to.

## TI 89 PropFrac Command Example 3: Using PropFrac to convert Rational to Proper Fractions

A **rational fraction** (also called a rational expression) is a fraction that has a numerator and denominator with rational numbers. A **proper fraction** has a top number that is smaller than it’s bottom number. For example, 5/3 and 8/4 are proper fractions. Converting fractions is tedious by hand, not to mention that (if you’re like me) you’ll make small mistakes. Add a variable or two (like x or y) to the mix and the process can be quite time consuming. However, the TI 89 propFrac command makes it a snap to convert to proper fractions.

**Example question**: Convert the following rational function to a proper fraction.

**f(x) = (x>sup>2 + x + 3) / (x – 2)**

Step 1: Press the **Home **key.

Step 2: Press the **F2** button and then press the **7**. This key combination selects the TI 89 propFrac( command.

Step 3: Press the following keys: ( ( x ^ 2 + x + 3 ) / ( x – 2 ) )

**Note**: Make sure you type in *all* of the parentheses. Missing parentheses are the usual culprit for mathematical errors or for the calculating give you an “error domain” or some other ugly error message.

Step 4: Press ENTER.

The calculator will display the solution, which is (9) / (x – 2) + (x) + 3.

That’s it! You’re done! You can now convert any rational function to a proper fraction using the TI-89!

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