DOMAINS OF RATIONAL EXPRESSIONS 1

Domainof Rational Expressions

Thedomainof rational expression is all values that the variable in theequation is allowed to take on. It is the setallreal numbers for which an expression is defined mathematically. Inother words, the domainisall values that make an expression undefined. The only values thatthe variable in the equation cannot take on are those that wouldcause division by zero.

Anexpression is defined in the realnumber systemif the fractions are legal. Fractions that are not legal do not havemeaning and its division cannot find an answer. However, adenominator cannot be zero since the expression is a legal fractionand its overall values are defined. In an expression or in a rationalnumber, a denominator divides the numerator and it cannot be zerosince it is the divider.

Consideringthe given equation, the domain for each of the two rationalexpressions is given by first setting each factorequalto zero.

= 0 divide both sides by a^15 12y = 0 divide both sides by 12 y = 0 D = {y/y € R} D = 0 |
= 0 divide both sides by a^4 = 0 divide both sides by 25 = 0 get the square root on both sides y = 0 D = {y/y € R} D = 0 |

Theexcludedvalue ofthe two expressions is y = zero. They are to be excluded from thedomain because the value will make the denominator of the expressionequal to zero. However, when solving a rational expression, it isvery important to find excluded values since zero cannot divide anexpression.