How do we reduce Rational Expressions? Do Now: How do we reduce fractions? Reduce these fractions:

What is a Rational Expression? A rational expression is a fraction in the form of P 1 /P 2 where P 1 and P 2 are both polynomials and P 2 ≠0. Examples:

What happens if we divide by zero? If we divide by zero, then the expression is undefined. We CAN NOT divide by zero. If we do divide by zero, mathematics, logic, and the world will blow up! We must constantly be aware of situations that will result in a zero in the denominator in the fraction.

For what values of x are the following rational expressions undefined?

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How do we reduce Rational Expressions? The first thing we must do is FACTOR. –When you factor, make sure each term has a positive x in the front. –Ex. 8–x will be factored –(x–8) Once we have something FACTORED, then we cancel out common terms. –The only terms we can cancel are those that are multiplied Remember to state values of x for which the expression is undefined.

Express in simplest form

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Summary/HW Why can’t we just cancel out the x in the following rational expression to get the stated result? HW: pg 116, 16-20