To determine which of the given expressions are rational expressions, we need to recall that a rational expression is defined as a fraction where both the numerator and the denominator are polynomials. Let's evaluate each of the expressions you provided:
-
Z + 1/z - 8: This is not a rational expression because it involves division of a variable (1/z) which is not a polynomial.
-
2 + squared 8: This expression does not clearly indicate a rational expression. If it refers to \(2 + 8\) (since squared 8 refers to \(sqrt{8}\)), then it's a constant and not a fraction. If it refers to \(2 + \sqrt{8}\), it is also not a fraction, thus not a rational expression.
-
a^2 + 5a + 6/a + 3: This seems to be a rational expression, but it's ambiguous due to lack of parentheses. If it is intended to be \((a^2 + 5a + 6)/(a + 3)\), then it is a rational expression because both the numerator and the denominator are polynomials. If it is improperly formatted as \(a^2 + 5a + 6/a + 3\), then it would not be clearer without parentheses.
-
3 pie + 7: Assuming 'pie' is just a misspelling for 'pi', \(3\pi + 7\) is a constant and not a fraction, thus not a rational expression.
-
2/9x: This is a rational expression since it is in the form of a fraction with \(2\) (a constant) over \(9x\) (a linear polynomial).
Based on this analysis, the expressions that qualify as rational expressions are:
- \( \frac{a^2 + 5a + 6}{a + 3} \) (assuming the correct formatting)
- \( \frac{2}{9x} \)
Final Answer: The rational expressions are \( \frac{a^2 + 5a + 6}{a + 3} \) and \( \frac{2}{9x} \).
5 answers