R6 - Section R.6 Rational Expressions A rational expression...

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Math 1513 Sec R.6 1 Section R.6 Rational Expressions A rational expression is a fraction of two polynomials. For example: 2 1 2 2 , , 5 6 2 , 3 x x x x . When working with rational expressions we usually are concerned with 4 things. 1. Determine the domain of the expression 2. Simplify it or reduce it to its lowest terms 3. Multiply, divide, add, subtract rational expressions 4. Simplify complex rational expressions The Domain of a Rational Expression A very important, but often overlooked, mathematical principle is that you cannot divided by zero. A rational expression is really a division problem. It is the numerator divided by the denominator. For example, 5 3 x x is really 5 x divided by 3 x . If you cannot divide by zero, then the divisor of this problem, namely, 3 x cannot be zero. For the domain, x can be any number except when 3 0 x   or 3 x . Therefore the domain of 5 3 x x is { | 3} x x .

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Math 1513 Sec R.6 2 Find the domain of 2 2 4 x x . Simplifying/Reducing Rational Expressions It might be helpful to review how you reduce simple fractions. For example, how do you reduce 20 25 ? One way to do it would be: 5 20 4 5 4 5 5 25 5 5 4 5 The same technique can be applied to more complicated rational expressions. For example, reduce:
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R6 - Section R.6 Rational Expressions A rational expression...

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