3. Find the partial fraction decomposition of f(x): x² f(x)=x2+2x+1

Match the rational expression on the left with the correct partial fraction decomposition form on the right. 62. x2-2x+3x2x-4x3+5 a. Ax+Bx2+Cx3+Dx4+Ex-4+Fx+Gx2+5 b. Ax+Bx-4+Cx-42+Dx-43+Fx+Gx2+5+Hx+Ix2+52 c. Ax+Bx2+Cx-4+Dx2+Ex+Fx3+5 d. Ax+Bx2+Cx3+Dx-4+Ex-42+Fx+Gx2+5 e. Ax+Bx-4+Cx+Dx2+5 f. Ax+Bx2+Cx-4+Dx+Ex2+5

Can you explain why a partial fraction decomposition is unique? (Hint: Think about it as a system of equations.)

(a) How do we express a rational function r as a partial faction decomposition? (a) Given the form of the partial fraction decomposition. (i) 2x(x5)(x1)2 (ii) 2x(x5)(x21) (iii) 3x+1x(x2+1)2