MATH LESSON

SIMPLIFYING: RATIONAL EXPRESSIONS

A rational expression is a fraction where the numerator and denominator are polynomials. Simplify it like a regular fraction!

To simplify a rational algebraic expression, factor both the numerator and denominator, then divide out (cancel) any common factors.

P(x)Q(x) = Factored P(x)Factored Q(x) = Simplified Form

x² - 9x + 3

(x - 3)(x + 3)x + 3

x - 3

What is a Rational Algebraic Expression?

It is a ratio of two polynomials. The denominator cannot be zero.

The "Factor and Cancel" Method

Look at 45x⁶3x⁴. Divide coefficients (45 ÷ 3 = 15) and subtract exponents (x^6-4 = x²). Result: 15x²

Common Mistakes!

Mistake: Forgetting to factor first before canceling.

x² - 9x + 3 = x - 93 × WRONG

x² - 9x + 3 = (x-3)(x+3)x+3 = x - 3 ✓ CORRECT

Worked Examples

Example 1: Simplify: 45x⁶3x⁴
→ 15x²

Example 2: Simplify: x² - 9x + 3
→ x - 3

MATH SEATWORK

Seatwork Time!

Answer all 5 questions. Good luck!

Please select an answer first!

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Made for students who want to master Simplifying Rational Algebraic Expressions