Simplifying Rational Expressions

To simplify a rational expression:

  1. Completely factor numerators and denominators.

  2. Reduce common factors.

Example 1

Simplify equation.

equation

Example 2

Simplify equation.

equation

Whenever possible, try to write all polynomials in descending order with a positive leading coefficient. To have a positive leading coefficient, occasionally –1 has to be factored out of the polynomial.

Example 3

Simplify equation.

equation

Example 4

Simplify equation.

equation

This answer can be expressed in other ways.

equation

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