Algebraic Fractions

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

Algebraic Fraction

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

Equivalent Algebraic Fractions

If two algebraic fractions:

Equivalent Algebraic Fractions

Are equivalent, they are represented as:

Equivalent Algebraic Fractions

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

Equivalent Algebraic Fractions

They are equivalent because:

(x+2) · (x−2) = x2 − 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.

Equivalent Algebraic Fractions

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.

Simplification of Algebraic Fractions

Amplification of Algebraic Fractions

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

Amplification of Algebraic Fractions