Tuesday, November 6, 2012
Simplifying Rational Expressions
Given a rational expression, the quotient of two polynomials, we will factor the numerator and denominator if we can and then cancel factors that are exactly the same.
Tip: To find the restrictions, set each factor in the denominator equal to zero and solve. The factors in the numerator do not contribute to the list of restrictions.
Simplify and state the restrictions to the domain.
Even if the factor cancels it still contributes to the list of restrictions. Basically, it is important to remember the domain of the original expression when simplifying. Also, we must use caution when simplifying, please do not try to take obviously incorrect shortcuts like this:
Since subtraction is not commutative, we must be alert to opposite binomial factors. For example, 5 − 3 = 2 and 3 − 5 = −2. In general,