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# Rational Functions

## Equivalent Rational Functions

We assume that you are familiar with the arithmetic operations of fractions of numbers.

A rational function is the ratio of two polynomials.

### Examples

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The top part of a rational function is called the numerator and the bottom part the denominator.

## Reduction

As with fractional numbers, we can simplify (reduce) a rational function by cancelling common factors found in both the numerator and denominator of the function (dividing by a common factor):

### Example

More Examples (this opens in another window)

### Exercise

Simplify the rational function below.  Use computer notation.

 (x2+ ) ( x+ ) ( x+ ) = (x2+ ) ( x+ ) ( x+ )

The technique of factorization of a polynomial is often needed.

### Exercise

Simplify the rational function below.

 x2  x = x2  x

A common mistake: Cancelling part of a sum or difference.  ONLY common factors can be cancelled.

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