Gina is asked to identify a rational expression. Which of the following could she choose? Choose one CORRECT answer

Question

A). 5.3/2x-1
B). x^3/2 + 5/2x^9
C). 8x^2 + 7/0
D). 9x-4/8+√x

Answer 1

A rational expression is defined as a fraction where both the numerator and the denominator are polynomials. Let's evaluate the options:

A) $\frac{5.3}{2x-1}$ - The numerator (5.3) is a constant (which is a polynomial of degree 0) and the denominator (2x - 1) is a polynomial of degree 1. This is a rational expression.

B) $\frac{x^3}{2}+\frac{5}{2x^9}$ - The first part $\frac{x^3}{2}$ is a polynomial term, but the second part $\frac{5}{2x^9}$ does not form a single rational expression because of division by a variable raised to a power in the denominator.

C) $\frac{8x^2+7}{0}$ - Division by zero is undefined, so this does not qualify as a rational expression.

D) $\frac{9x-4}{8+\sqrt{x}}$ - The denominator $8+\sqrt{x}$ is not a polynomial because $\sqrt{x}$ is not a polynomial term.

The only correct answer among the options provided is:

A) $\frac{5.3}{2x-1}$.

Answer 2

Now, let's answer a different question:
Melany was asked to create an equivalent form of the rational expression −3x2−15x−18x+3 . Which of the following is a correct equivalent form?
−3x−24−114x+3
This rational expression does not have any equivalent forms.
−3x−114
−3x−6

Answer 3

To determine an equivalent form of the rational expression $-\frac{3x^2-15x-18}{x+3}$, we should first simplify it.

1. Factor the numerator: $-3x^2-15x-18$ can be factored out:

   $$-3(x^2+5x+6)=-3(x+2)(x+3)$$

So, the expression becomes:

$$-\frac{3(x+2)(x+3)}{x+3}$$

2. Cancel the common factors: As long as $x+3\ne 0$ (or $x\ne -3$), we can cancel $x+3$ from the numerator and the denominator:

$$-3(x+2)$$

3. Final form: This simplifies to:

$$-3x-6$$

Now we can check the provided options:

1. −3x−24−114x+3
2. This rational expression does not have any equivalent forms.
3. −3x−114
4. −3x−6

Among these options, the correct equivalent form of the original rational expression is:

−3x−6.