Hello, I would. like to check my answer with this problem. I was to simplify - please see attached image Below is a mathematical expression commonly found in algebra dealing with rational functions. This specific expression represents a fraction where both the numerator and the denominator are polynomials:\[\frac{3x^2 - 12}{x^2 + 9x + 14}\]### Explanation:- **Numerator (Top Part):** The numerator of the fraction is \(3x^2 - 12\). This is a quadratic polynomial where the coefficient of the \(x^2\) term is 3, and there is a constant term of -12. - **Denominator (Bottom Part):** The denominator of the fraction is \(x^2 + 9x + 14\). This is also a quadratic polynomial. It consists of an \(x^2\) term with a coefficient of 1, a linear \(x\) term with a coefficient of 9, and a constant term of 14.### Potential Applications:- **Simplification:** The expression can be simplified if common factors are identified in the numerator and the denominator.- **Evaluation:** By plugging in specific values of \(x\), the fraction can be evaluated.- **Graphing Rational Functions:** Understanding the behavior of the graph of this function, including asymptotes and intercepts, is crucial for more advanced studies in algebra and calculus.### Graph/Diagram Explanation:There are no specific graphs or diagrams related to this image, but if one were to graph this function, it would be a rational function with potential vertical asymptotes where the denominator equals zero and horizontal or oblique asymptotes to indicate the function's end behavior.This content is typically included in high school or early college-level algebra curricula and can be useful for students experiencing rational functions for the first time.

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Answered: 3x²-12 2 x²+9x+14

Math

Algebra

3x²-12 2 x²+9x+14

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Hello, I would. like to check my answer with this problem.

I was to simplify - please see attached image

Below is a mathematical expression commonly found in algebra dealing with rational functions. This specific expression represents a fraction where both the numerator and the denominator are polynomials:

\[
\frac{3x^2 - 12}{x^2 + 9x + 14}
\]

### Explanation:
- **Numerator (Top Part):** The numerator of the fraction is \(3x^2 - 12\). This is a quadratic polynomial where the coefficient of the \(x^2\) term is 3, and there is a constant term of -12.

- **Denominator (Bottom Part):** The denominator of the fraction is \(x^2 + 9x + 14\). This is also a quadratic polynomial. It consists of an \(x^2\) term with a coefficient of 1, a linear \(x\) term with a coefficient of 9, and a constant term of 14.

### Potential Applications:
- **Simplification:** The expression can be simplified if common factors are identified in the numerator and the denominator.
- **Evaluation:** By plugging in specific values of \(x\), the fraction can be evaluated.
- **Graphing Rational Functions:** Understanding the behavior of the graph of this function, including asymptotes and intercepts, is crucial for more advanced studies in algebra and calculus.

### Graph/Diagram Explanation:
There are no specific graphs or diagrams related to this image, but if one were to graph this function, it would be a rational function with potential vertical asymptotes where the denominator equals zero and horizontal or oblique asymptotes to indicate the function's end behavior.

This content is typically included in high school or early college-level algebra curricula and can be useful for students experiencing rational functions for the first time.

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