Consider the rational function

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the rational function 5x2−3(x+1)2(x2+4)\dfrac{5x^{2}-3}{(x+1)^{2}(x^{2}+4)}. Which of the following decompositions is structurally correct? (a) Ax+1+B(x+1)2+Cx2+4\dfrac{A}{x+1}+\dfrac{B}{(x+1)^{2}}+\dfrac{C}{x^{2}+4} (b) Ax+1+B(x+1)2+Cx+Dx2+4\dfrac{A}{x+1}+\dfrac{B}{(x+1)^{2}}+\dfrac{Cx+D}{x^{2}+4} (c) Ax+1+B(x+1)2+Cx+D(x2+4)2\dfrac{A}{x+1}+\dfrac{B}{(x+1)^{2}}+\dfrac{Cx+D}{(x^{2}+4)^{2}} (d) Ax+1+Cx+Dx2+4\dfrac{A}{x+1}+\dfrac{Cx+D}{x^{2}+4}

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