Processing math: 66%
Home / Aptitude Tests / Further Mathematics / Express \(\frac{x^{2...
Express x2+x+4(1x)(x2+1) in part...

Express x2+x+4(1x)(x2+1) in partial fractions.

A.

x2x2+1+x+41x

B.

31x+2x+1x2+1

C.

x21x+x+4x2+1

D.

31x+2x+2x2+1

Correct answer is B

x2+x+4(1x)(x2+1)=A1x+Bx+Cx2+1

= A(x2+1)+(Bx+C)(1x)(1x)(x2+1)

x2+x+4=A(x2+1)+(Bx+C)(1x)

x2+x+4=Ax2+A+BxBx2Cx+C

(AB)x2=x2;AB=1......(i)

(BC)x=x;BC=1.....(ii)

A+C=4......(iii)

Solving the above simultaneous equations by any of the known methods, we get

A=3,B=2,C=1