Rational Expressions
Simplification of rational expressions, reducing to lowest terms

Simplification of rational expressions, reducing to lowest terms
A rational expression is a fraction of which the numerator and the denominator are polynomials.
A rational expression is reduced to lowest terms if all common factors from the numerator and denominator are canceled.
To reduce a rational expression to lowest terms first factorize both the numerator and denominator as much as possible then cancel common factors, i.e., divide their numerator and denominator by common factors.
Examples:  Reduce the following rational expression to lowest terms.

factoring out the minus sign,
 a - b = -(b - a)
or
 - a + b = -(a - b)

Multiplication and division of rational expressions
Use the formulas for the multiplication and the division of fractions.
 and
Notice the two special cases of which should be aware of:
 and
Examples:  Perform the indicated operations and reduce the answer to lowest terms.
proof
Note, since each second line should be subtracted, the sign of each term is reversed.
Beginning Algebra Contents C