Which one of the following expressions is identically equal to ?

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

Problem

Which one of the following expressions is identically equal to 3x3+2x+1(x2+4x+5)2\dfrac{3x^{3}+2x+1}{(x^{2}+4x+5)^{2}}? (a) Ax2+4x+5+B(x2+4x+5)2\dfrac{A}{x^{2}+4x+5}+\dfrac{B}{(x^{2}+4x+5)^{2}} (b) Ax+Bx2+4x+5+Cx+D(x2+4x+5)2\dfrac{Ax+B}{x^{2}+4x+5}+\dfrac{Cx+D}{(x^{2}+4x+5)^{2}} (c) Ax+Bx2+4x+5\dfrac{Ax+B}{x^{2}+4x+5} (d) Ax+Bx2+4x+5+C(x2+4x+5)2\dfrac{Ax+B}{x^{2}+4x+5}+\dfrac{C}{(x^{2}+4x+5)^{2}}

Related theory

Browse the problem library