Rational Expressions and Replacements

Rational Expressions and Replacements

 

Rational numbers are quotients of integers. Some examples are

 

\frac{2}{3} , \frac{4}{-5} , \frac{-8}{17}.

The following are called rational expressions or fraction expressions. They are quotients, or ratios, of polynomials:

 

\frac{3}{4}, \frac{z}{6}, \frac{3}{2 + x}

 

A rational expression is also a division. For example,

 

\frac{3}{4} means 3 ÷ 4 and \frac{x-8}{x+2} means (x-8) ÷ (x+2).

 

Because rational expressions indicate division, we must be careful to avoid denominators of zero. When a variable is replaced with a number that produces a denominator equal to zero, the rational expression is not defined.

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