gina is asked to identify a rational expression. which of the following could she choose?
8x^2+7/0
5.3/2x-1
9x-4/8+√x
x3/2+5/2x^9
Gina could choose the rational expression 5.3/(2x-1).
To identify a rational expression, Gina needs to find an expression that can be written as the ratio of two polynomials.
Out of the options provided, the expression that can be considered rational is:
5.3/2x - 1
This expression can be written as the ratio of two polynomials: 5.3 divided by 2x - 1.
To identify a rational expression, Gina needs to look for an expression that consists of both a numerator and a denominator, where both the numerator and denominator are polynomial expressions and there is no division by zero.
Let's go through the options one by one:
1. 8x^2 + 7/0:
This expression has a division by zero, which is not allowed in rational expressions. So, Gina should not choose this option.
2. 5.3/2x - 1:
This expression has a constant (5.3) as the numerator and a polynomial expression (2x - 1) as the denominator. Both the numerator and denominator are valid, so Gina could choose this option.
3. 9x - 4/8 + √x:
This expression has two separate terms in the denominator, which means it's not a single polynomial expression. Therefore, Gina should not choose this option.
4. x^(3/2) + 5/2x^9:
This expression has a fractional exponent (3/2) for the variable x, which means it's not a polynomial expression. Additionally, the term 5/2x^9 has a variable in the denominator, which is also not allowed in rational expressions. Therefore, Gina should not choose this option.
So, the option that Gina could choose as a rational expression is 5.3/2x - 1.