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MathCalculus

Partial Fraction Decomposition of (x² + 1)/[x(x + 1)(x + 2)]

Decompose the rational function with three distinct linear factors, solve its coefficients, and check both the full decomposition and a two-expression grouping.

Question

Express the rational function as a sum or difference of two simpler rational expressions.

x2+1x(x+1)(x+2).\frac{x^2+1}{x(x+1)(x+2)}.

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Evidence boundary

This page solves OpenStax Calculus Volume 2, §3.4, exercise 183 as printed. The shared instruction requests two expressions; we supply that grouped form and the full three-term decomposition. The identity holds only where the original denominator is nonzero. The algebra shown here is independently checked, not presented as a quoted teacher key.