Chapter6: Systems Of Equations And Inequalities
Section6.4: Partial Fractions
Problem 59E: Environmental Science The predicted cost C (in thousands of dollars) for a company to remove p of a...
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the partial fraction decomposition of 26x/(8x^2-10x+3) can be written in the form of (f(x))/(2x-1)+(g(x))/(4x-3) where
f(x)=_____
g(x)=______
![### Partial Fraction Decomposition
In this section, we will discuss the partial fraction decomposition of the given rational function. Consider the rational function:
\[ \frac{26x}{8x^2 - 10x + 3} \]
The partial fraction decomposition of this function can be expressed as:
\[ \frac{26x}{8x^2 - 10x + 3} = \frac{f(x)}{2x - 1} + \frac{g(x)}{4x - 3} \]
Here, \(f(x)\) and \(g(x)\) are functions to be determined. To solve for these functions, we can rewrite the equation:
\[ f(x) = \boxed{\phantom{a}}, \]
\[ g(x) = \boxed{\phantom{a}}. \]
In this decomposition, the original rational function is split into simpler fractions with denominators that are factors of the quadratic polynomial in the original denominator. These simpler fractions are easier to integrate or differentiate when solving calculus problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a7c8b7c-6421-40e7-b33a-5c89a0da3579%2Fd18041bc-660d-47e4-b8f5-1a7d290df323%2F39denws.png&w=3840&q=75)
Transcribed Image Text:### Partial Fraction Decomposition
In this section, we will discuss the partial fraction decomposition of the given rational function. Consider the rational function:
\[ \frac{26x}{8x^2 - 10x + 3} \]
The partial fraction decomposition of this function can be expressed as:
\[ \frac{26x}{8x^2 - 10x + 3} = \frac{f(x)}{2x - 1} + \frac{g(x)}{4x - 3} \]
Here, \(f(x)\) and \(g(x)\) are functions to be determined. To solve for these functions, we can rewrite the equation:
\[ f(x) = \boxed{\phantom{a}}, \]
\[ g(x) = \boxed{\phantom{a}}. \]
In this decomposition, the original rational function is split into simpler fractions with denominators that are factors of the quadratic polynomial in the original denominator. These simpler fractions are easier to integrate or differentiate when solving calculus problems.
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