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2x3 x²-16*

2x3 x²-16*

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find all linear asymptotes of the graph of y(see attached)

Certainly! Here's the transcription of the mathematical expression seen in the image for an educational website: --- ### Simplifying Rational Expressions Consider the following rational expression: \[ \frac{2x^3}{x^2 - 16} \] To simplify this expression, we need to perform the following steps: 1. **Factor the Denominator**: The denominator \( x^2 - 16 \) is a difference of squares, which can be factored as: \[ x^2 - 16 = (x + 4)(x - 4) \] 2. **Rewrite the Expression**: Substitute the factored form of the denominator back into the expression: \[ \frac{2x^3}{(x + 4)(x - 4)} \] 3. **Simplify if Possible**: Check if any factors in the numerator can cancel out with the factors in the denominator. In this case, there are no common factors to cancel out. Therefore, the expression is already in its simplest form when written as: \[ \frac{2x^3}{(x + 4)(x - 4)} \] This simplified expression cannot be reduced further. --- By factoring the denominator and attempting to simplify, we ensure that the rational expression is presented in its most elementary form. Understanding this process is essential for solving more complex algebraic expressions efficiently.
Transcribed Image Text:Certainly! Here's the transcription of the mathematical expression seen in the image for an educational website: --- ### Simplifying Rational Expressions Consider the following rational expression: \[ \frac{2x^3}{x^2 - 16} \] To simplify this expression, we need to perform the following steps: 1. **Factor the Denominator**: The denominator \( x^2 - 16 \) is a difference of squares, which can be factored as: \[ x^2 - 16 = (x + 4)(x - 4) \] 2. **Rewrite the Expression**: Substitute the factored form of the denominator back into the expression: \[ \frac{2x^3}{(x + 4)(x - 4)} \] 3. **Simplify if Possible**: Check if any factors in the numerator can cancel out with the factors in the denominator. In this case, there are no common factors to cancel out. Therefore, the expression is already in its simplest form when written as: \[ \frac{2x^3}{(x + 4)(x - 4)} \] This simplified expression cannot be reduced further. --- By factoring the denominator and attempting to simplify, we ensure that the rational expression is presented in its most elementary form. Understanding this process is essential for solving more complex algebraic expressions efficiently.
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