# Algebraic Fractions

An algebraic fraction is the quotient of two polynomials and is represented as:

P(x) is the numerator and Q(x), the denominator.

### Equivalent Algebraic Fractions

If two algebraic fractions:

Are equivalent, they are represented as:

**If it verifies that P(x) · S(x) = Q(x) · R(x). **

They are** equivalent** because:

(x+2) · (x−2) = x^{2} − 4

By multiplying the numerator and denominator of a given algebraic fraction by the same nonzero polynomial, the resulting algebraic fraction is equivalent to that given.

### Simplification of Algebraic Fractions

To simplify an algebraic fraction, divide the numerator and the denominator of the fraction by a polynomial that is a common factor of both.

### Amplification of Algebraic Fractions

To amplify an algebraic fraction, multiply the numerator and denominator of the fraction by a polynomial.

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