A student writes the following decomposition: 4x+1 (x-2)^ 2 (x^ 2 +3) = A x-2 + B…

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

A student writes the following decomposition: 4x+1(x−2)2(x2+3)=Ax−2+B(x−2)2+Cx2+3.\frac{4x+1}{(x-2)^{2}(x^{2}+3)}=\frac{A}{x-2}+\frac{B}{(x-2)^{2}}+\frac{C}{x^{2}+3}. Identify the error in this decomposition and write the correct decomposition form.

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