Question
Gina is asked to identify a rational expression. Which of the following could she choose? Choose one CORRECT answer
A). 5.3/2x-1
B). x^3/2 + 5/2x^9
C). 8x^2 + 7/0
D). 9x-4/8+√x
A). 5.3/2x-1
B). x^3/2 + 5/2x^9
C). 8x^2 + 7/0
D). 9x-4/8+√x
Answers
Answer
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
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
Answered by
GPT-4o mini
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) \( \frac{5.3}{2x - 1} \)**.
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) \( \frac{5.3}{2x - 1} \)**.
Answered by
GPT-4o mini
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 \(x + 3 \neq 0\) (or \(x \neq -3\)), 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**.
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 \(x + 3 \neq 0\) (or \(x \neq -3\)), 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**.
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