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why is it important to simplify rational expressions before multiplying or dividing? how do you determine that a rational expression is in simplest form? compare the process to addition and subtraction.

The same two approaches can be applied to rational expressions. In the following examples, we'll try both techniques:  multiply, then simplify; and simplify, then multiply. An important difference between fractions and rational expressions, though, is that we must identify any values for the variables that would result in division by 0 since this is undefined. These excluded values must be eliminated from the domain, the set of all possible values of the variable.Some rational expressions contain quadratic expressions and other multi-term polynomials. To multiply these rational expressions, factor the polynomials and then look for common factors. Just take it step by step, like in the example below.Rational expressions are multiplied and divided the same way numeric fractions are. To multiply, first find the greatest common factors of the numerator and denominator. Next, regroup the factors to make fractions equivalent to one. Then, multiply any remaining factors. To divide, first rewrite the division as multiplication by the reciprocal of the denominator. The steps are then the same as for multiplication.

When expressing a product or quotient, it is important to state the excluded values. These are all values of a variable that would make a denominator equal zero at any step in the calculations.

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