gina is asked to identify a rational expression. which of the following could she choose?
x^3/2 + 5/2x^9
5.3/2x-1
8x^2 + 7/0
Gina can choose the rational expression: 5.3/2x-1.
The reason is that a rational expression is defined as a ratio of two polynomials, where the denominator is not equal to zero. In this case, 5.3/2x-1 fits this definition.
To identify a rational expression, Gina should look for an expression that can be written as the quotient of two polynomials, where the denominator is not zero.
Out of the three choices given, the only expression that meets this criteria is:
5.3/(2x - 1)
Therefore, Gina could choose the expression 5.3/(2x - 1) as a rational expression.
To identify a rational expression, Gina needs to look for an expression that can be written as a ratio of two polynomial functions. A polynomial function is a mathematical expression that consists of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication.
Let's analyze each given expression to see if they meet the criteria for a rational expression:
1. x^3/2 + 5/2x^9:
This expression is a sum of two terms. However, the first term, x^3/2, has a fractional exponent, which means it is not a polynomial function. Therefore, this expression is not a rational expression.
2. 5.3/2x-1:
This expression contains a decimal number, 5.3. In a polynomial function, the coefficients (numbers multiplying the variables) should be integers. Therefore, this expression is not a rational expression.
3. 8x^2 + 7/0:
In this expression, there is a division by zero, which is undefined in mathematics. Therefore, this expression is not a rational expression.
In conclusion, none of the given options meet the criteria for a rational expression.