Decide whether the given statement is always, sometimes, or never true.
The domain of a rational expression and any simplified form are equivalent.
a. sometimes true
b. never true
c. always true
well, what about zero factors?
Integers are also whole numbers_____ Always, Somtimes, Never True
c. always true
To determine whether the statement "The domain of a rational expression and any simplified form are equivalent" is always, sometimes, or never true, we need to first understand what the domain of a rational expression is and how it relates to its simplified form.
A rational expression is a fraction of two polynomials, where the denominator cannot be zero. The domain of a rational expression consists of all the values that the variable can take without causing the denominator to become zero.
When we simplify a rational expression, we aim to cancel out common factors between the numerator and the denominator, thereby reducing the expression to its simplest form. In the simplified form, any factors that could result in the denominator becoming zero should have been removed.
Based on these definitions, we can conclude that the statement is ALWAYS TRUE. The domain of a rational expression and its simplified form are indeed equivalent, meaning that they both allow the same set of values for the variable without causing division by zero.
So, the correct answer is c. always true.