Determine the partial fraction decomposition of the given rational function 2-10 z(2+16z-60) from the four choices given below. Choose an answer (器)z+(-0) 160 A 2-10 10 z(1²+16z-60) z+60 2+16z-60 2-10 (器)-(-) 10 z(1² +16z–60) 2²+16z–60 z+60 -(-) 10 z+60 2+10 2+16z–60 z(r²+16z–60) 160 ()-(一盟) 2-10 10 z+60 2+16z-60 z(z²+16z-60)
Determine the partial fraction decomposition of the given rational function 2-10 z(2+16z-60) from the four choices given below. Choose an answer (器)z+(-0) 160 A 2-10 10 z(1²+16z-60) z+60 2+16z-60 2-10 (器)-(-) 10 z(1² +16z–60) 2²+16z–60 z+60 -(-) 10 z+60 2+10 2+16z–60 z(r²+16z–60) 160 ()-(一盟) 2-10 10 z+60 2+16z-60 z(z²+16z-60)
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Partial Fraction Decomposition - Educational Resource
---
**Problem:**
Determine the partial fraction decomposition of the given rational function
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} \]
from the four choices given below.
**Options:**
**A.**
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} = \frac{10}{x + 60} \left( \frac{x + \left( \frac{160}{60} \right)}{x^2 + 16x - 60} \right) \]
**B.**
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} = \frac{10}{x + 60} + \frac{\left( \frac{30}{60} \right) x - \left( \frac{160}{60} \right)}{x^2 + 16x - 60} \]
**C.**
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} = \frac{10}{x + 60} \left( \frac{\left( \frac{30}{60} \right)x - \left( \frac{160}{60} \right)}{x^2 + 16x - 60} \right) \]
**D.**
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} = \frac{10}{x + 60} - \frac{30 \left( \frac{10}{60} \right)x - \left( \frac{160}{60} \right)}{x^2 + 16x - 60} \]
These options present various forms of the rational function in partial fraction decomposition.
### Explanation:
Partial fraction decomposition involves expressing the function as a sum of simpler fractions. The given function needs to be decomposed accurately according to the rules of algebraic fractions.
When reviewing these options:
1. Verify whether all terms and expansions are correctly derived.
2. Ensure that each partial fraction correctly represents the original function.
In partial fraction decomposition, the main goal is to simplify the computation and enable easier integration or other mathematical operations.
### Graphs/Diagrams:
There are](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d0bce3f-e315-4955-850f-b265844e3b1e%2F6153a517-7ea1-410a-ad25-616c57154ff1%2Fp7dveco.jpeg&w=3840&q=75)
Transcribed Image Text:### Partial Fraction Decomposition - Educational Resource
---
**Problem:**
Determine the partial fraction decomposition of the given rational function
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} \]
from the four choices given below.
**Options:**
**A.**
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} = \frac{10}{x + 60} \left( \frac{x + \left( \frac{160}{60} \right)}{x^2 + 16x - 60} \right) \]
**B.**
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} = \frac{10}{x + 60} + \frac{\left( \frac{30}{60} \right) x - \left( \frac{160}{60} \right)}{x^2 + 16x - 60} \]
**C.**
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} = \frac{10}{x + 60} \left( \frac{\left( \frac{30}{60} \right)x - \left( \frac{160}{60} \right)}{x^2 + 16x - 60} \right) \]
**D.**
\[ \frac{x^2 - 10}{x(x^2 + 16x - 60)} = \frac{10}{x + 60} - \frac{30 \left( \frac{10}{60} \right)x - \left( \frac{160}{60} \right)}{x^2 + 16x - 60} \]
These options present various forms of the rational function in partial fraction decomposition.
### Explanation:
Partial fraction decomposition involves expressing the function as a sum of simpler fractions. The given function needs to be decomposed accurately according to the rules of algebraic fractions.
When reviewing these options:
1. Verify whether all terms and expansions are correctly derived.
2. Ensure that each partial fraction correctly represents the original function.
In partial fraction decomposition, the main goal is to simplify the computation and enable easier integration or other mathematical operations.
### Graphs/Diagrams:
There are
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