Solve for X, and check the extraneous roots. X/(X + 4) =11/(X2 -16) + 2/1
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
in image
![**Solve for X, and check the extraneous roots.**
\[ \frac{X}{X + 4} = \frac{11}{X^2 - 16} + \frac{2}{1} \]
In this equation, we are asked to solve for \( X \) and check for any extraneous roots. The equation involves rational expressions on both sides. Follow these steps:
1. Identify the denominators: \( X + 4 \) and \( X^2 - 16 \).
2. Note that \( X^2 - 16 \) can be factored as \( (X + 4)(X - 4) \).
3. Find a common denominator to combine the terms.
4. Solve the equation for \( X \).
5. Check the solutions to determine if any are extraneous, considering the denominators cannot be zero.
This problem requires an understanding of operations with rational expressions, factoring, and solving quadratic equations. After simplifying, any solutions that result in division by zero in the original equation are considered extraneous and must be discarded.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33eba9e5-eb7d-44a1-93e3-ed0ee897e17f%2F7d0b6a5f-ecc9-4493-9b76-33e7e4e1f1ca%2F2z75uy_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve for X, and check the extraneous roots.**
\[ \frac{X}{X + 4} = \frac{11}{X^2 - 16} + \frac{2}{1} \]
In this equation, we are asked to solve for \( X \) and check for any extraneous roots. The equation involves rational expressions on both sides. Follow these steps:
1. Identify the denominators: \( X + 4 \) and \( X^2 - 16 \).
2. Note that \( X^2 - 16 \) can be factored as \( (X + 4)(X - 4) \).
3. Find a common denominator to combine the terms.
4. Solve the equation for \( X \).
5. Check the solutions to determine if any are extraneous, considering the denominators cannot be zero.
This problem requires an understanding of operations with rational expressions, factoring, and solving quadratic equations. After simplifying, any solutions that result in division by zero in the original equation are considered extraneous and must be discarded.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning