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# Rational Expressions vs. Rational Numbers

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The description below tells of the properties of rational numbers is very good and comprehensive. However, please describe how it relates to RATIONAL EXPRESSIONS?

A rational number is a number that can be expressed as a fraction, ratio of two integers or decimal number. Rational numbers can be ordered in a number line.

A rational number can be written in infinitely many forms, such as 3/6 = 2/4 = 1/2= a/b, but it is said to be in simplest form when a and b have no common divisors except one.

Every non-zero rational number has exactly one simplest form of this type with a positive denominator. A fraction in this simplest form is said to be an irreducible fraction or a fraction in reduced form.

The decimal expansion of a rational number is eventually periodic (in the case of a finite expansion the zeroes which implicitly follow it form the periodic part). A real number that is not a rational number is called an irrational number.

Fractions are included in the rational numbers, and the rational numbers can be used in many things for every day life situations, such as dividing a cake, giving directions (you are 4.5 miles away from a certain place).

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Rational expressions are simply fractions that use polynomials instead of numbers. In both cases - when dividing fractions and when dividing rational expressions - dividing is the same as multiplying by the reciprocal.

A rational number is a ratio of two integers; a rational expression is a ratio of two polynomials.

A rational number can be written in infinitely many forms; the same is true for rational expressions. For example,

(x + 1)/(x + 2) = (2x + 2)(2x + 4) = (5x + 5)/(5x + 10)

Remember that you can't divide a number by 0. The same is true for rational expressions. In the example above, (x + 1)/(x + 2), the expression is undefined for x = -2. This is because if you plug x = -2 into the expression, the denominator becomes x + 2 = -2 + 2 = 0, and you can't divide by zero.

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