Simplifying Rational Expressions

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In this section, we review how to work with rational expressions. A rational number is the quotient of two integers with a non-zero denominator. Following this same concept, a rational expression is the quotient of two polynomials with a non-zero denominator. We previously learned how to find the domain for a rational expression. The domain will include all values for the variable that result in a non-zero denominator. Since we have variables in our denominator and we are never allowed to divide by zero, we must ensure that no value replaces a variable that results in a zero denominator. Next, we will review how to simplify a rational expression. The process is similar to when we simplified with fractions. A fraction can be simplified by factoring the numerator and denominator completely, then canceling common factors. When we work with a rational expression, we use the same process. We factor the numerator and denominator completely, then cancel any common factors between the numerator and denominator.
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