Year 9: Simplification of rational algebraic expressions

What is a rational algebraic expression? A rational algebraic expression is an expression that can be written as a fraction where the numerator and denominator are polynomials. For example: $(2x+3)/(x-1)$ or $(5x\mathrm{²}+2x)/(x+2)$.

Simplifying rational expressions Simplifying a rational expression means reducing it to its simplest form. This is done by dividing out any common factors in the numerator and denominator.

Steps for simplification

• Factor both the numerator and denominator completely.
• Identify common factors.
• Divide out the common factors.
• Ensure the numerator and denominator have no common factors.

Example

• Factor the numerator: $\left(x\right)(x-1)$
• There are no common factors.
• The simplified expression is: $\left(x\right)(x-1)$

Important notes

• Always check your answer by multiplying the simplified expression back together.
• If the numerator and denominator have no common factors, the expression is already simplified.
• Be careful with negative signs!