Domains of Rational Expressions
Domain is a set of all possible input values for the variables of a function or an expression, which produce a valid output from this function or expression. Valid output means that the function or expression with this input value is mathematically defined. Domain for a rational expression is the set of all real numbers, excluding the possible cases when denominator or denominators of this rational expression are equal to zero, which means that this rational expression is mathematically undefined because of the division by zero.
1.[pic]
To factor this polynomial: [pic].
This rational expression is mathematically undefined because of the division by zero when its denominator −6y is equal to zero, i.e., when y = 0, and mathematically defined for all the other possible input values of y.
It means that the domain for this rational expression is a set of all rational numbers, with the excluded value of 0. [pic]
2. [pic]
To factor this polynomial: [pic].
This rational expression is mathematically undefined because of the division by zero when its denominator 2p(1−2p) is equal to zero, i.e., when p = 0 and [pic], and mathematically defined for all the other possible
input values of p. It means that the domain for this rational expression is a set of all rational numbers, with the excluded values of 0 and [pic].
[pic]
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