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) = 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.
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.