# Simplify TI 89: How To Simplify An Expression

TI 89 for Statistics > Simplify TI 89

Knowing how to simplify expressions in calculus is essential to being able to differentiate functions. 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.
Sample problem: simplify the following expression with the TI-89:
f(x) = 9x + 8x

Step 1: Press the key.

Step 2: Press to enter the expression.

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

## Simplify TI 89 Example 2: Using propFrac

For more complicated equations, like ((x2 + 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 ((x2 + 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 rational functions to proper fractions.

Sample 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 .
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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