Math Problem Statement

Give the appropriate form of the partial fraction decomposition for the following function. StartFraction 2 x Over left parenthesis x minus 2 right parenthesis squared left parenthesis x squared plus 1 right parenthesis EndFraction Question content area bottom Part 1 Choose the correct answer below. A.StartFraction Upper A Over left parenthesis x minus 2 right parenthesis squared EndFraction plus StartFraction Bx plus Upper C Over x squared plus 1 EndFraction StartFraction Upper A Over left parenthesis x minus 2 right parenthesis squared EndFraction plus StartFraction Bx plus Upper C Over x squared plus 1 EndFraction B.StartFraction Upper A Over x minus 2 EndFraction plus StartFraction Upper B Over left parenthesis x minus 2 right parenthesis squared EndFraction plus StartFraction Cx plus Upper D Over x squared plus 1 EndFraction StartFraction Upper A Over x minus 2 EndFraction plus StartFraction Upper B Over left parenthesis x minus 2 right parenthesis squared EndFraction plus StartFraction Cx plus Upper D Over x squared plus 1 EndFraction C.StartFraction Upper A Over x minus 2 EndFraction plus StartFraction Upper B Over left parenthesis x minus 2 right parenthesis squared EndFraction plus StartFraction Upper C Over x squared plus 1 EndFraction StartFraction Upper A Over x minus 2 EndFraction plus StartFraction Upper B Over left parenthesis x minus 2 right parenthesis squared EndFraction plus StartFraction Upper C Over x squared plus 1 EndFraction D.StartFraction Upper A Over x minus 2 EndFraction plus StartFraction Bx plus Upper C Over left parenthesis x minus 2 right parenthesis squared EndFraction plus StartFraction Dx plus Upper E Over x squared plus 1 EndFraction StartFraction Upper A Over x minus 2 EndFraction plus StartFraction Bx plus Upper C Over left parenthesis x minus 2 right parenthesis squared EndFraction plus StartFraction Dx plus Upper E Over x squared plus 1 EndFraction

Solution

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Math Problem Analysis

Mathematical Concepts

Partial Fraction Decomposition
Rational Functions
Quadratic and Linear Factors

Formulas

Partial Fraction Decomposition: A / (x - r) + B / (x - r)^2 + (Cx + D) / (x^2 + 1)
Factorization: (x - 2)^2 and (x^2 + 1)

Theorems

Partial Fraction Theorem: Decomposing a rational function into simpler fractions with distinct and repeated factors
Factorization of Polynomials: Handling linear and irreducible quadratic factors

Suitable Grade Level

Grades 11-12, College level

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