Gina is asked to identify a rational expression. Which of the following could she choose?(1 point)
1. 8x^2+7/0
2. 5.3/2x-1
3. x 3/2+5/2x^9
4. 9x-4/8+x
The answer that Gina could choose is option 4: 9x - 4/8 + x.
A rational expression is defined as the ratio of two polynomials. To identify a rational expression, Gina needs to look for expressions that involve variables in the numerator and denominator.
Looking at the options provided:
1. 8x^2+7/0 - This expression has a denominator of 0, which makes it undefined. A rational expression cannot have a denominator of zero.
2. 5.3/2x-1 - This expression is not a rational expression because it involves a constant (5.3) divided by a variable expression (2x-1). A rational expression should involve variables in both the numerator and denominator.
3. x 3/2+5/2x^9 - This expression is not clear as it seems to have a missing operator between "x" and "3/2". If it is meant to be x*(3/2), it simplifies to (3x/2) + (5/2x^9). This is a rational expression because it involves variables (x) in both the numerator and denominator.
4. 9x-4/8+x - This expression is not a rational expression because it involves a constant (8) in the denominator instead of a variable.
Therefore, the correct answer is:
3. x 3/2+5/2x^9
To identify a rational expression, Gina needs to understand what it is. A rational expression is a fraction with a polynomial in the numerator and denominator. The numerator and denominator should both be polynomials, meaning they consist of variables and constants multiplied together using addition, subtraction, multiplication, and exponentiation (raising to a power).
Now, let's analyze the given options:
1. 8x^2+7/0: This expression has 0 in the denominator, which is not allowed in mathematics. Division by zero is undefined, making this option invalid.
2. 5.3/2x-1: This expression is not a fraction since it does not contain a polynomial in the numerator. It is a mathematically valid expression but not a rational expression.
3. x^3/2 + 5/2x^9: This expression consists of two polynomials, x^3/2 and 5/2x^9, in the numerator and denominator respectively. Therefore, it is a rational expression.
4. 9x-4/8+x: This expression has two terms, 9x-4 and 8+x, but it is not a fraction. It does not have a polynomial as the denominator. Therefore, it is not a rational expression.
Based on the analysis, Gina could choose option 3, x^3/2 + 5/2x^9, as a rational expression since it satisfies the definition of a rational expression.