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**A rational expression is the ratio of two polynomials.**

If **f** is a rational expression then** f** can be written in the form **p/q** where **p** and **q** are polynomials. Like polynomials or any other type of expression, the basic arithmetic operations, namely addition, subtraction, multiplication, and division, can be performed on rational expressions. A nice property of rational expressions is that when any of these operations are performed on two rational expressions, the result is always another rational expression. Contrary to polynomials, it is generally easy to multiply or divide but difficult to add or subtract two rational expressions.

To simplify a rational expression: $$\frac{x^2-16}{x^3+64}$$ a) Completely factor numerators and denominators. $$\frac{(x+4)(x-4)}{(x+4)(x^2-4x+16)}$$ b) Reduce common factors. $$\frac{(x-4)}{(x^2-4x+16)}$$

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