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Express 5x12(x2)(x3) in partial fracti...

Express 5x12(x2)(x3) in partial fractions

A.

2x+23x3

B.

2x2+3x3

C.

2x33x2

D.

5x34x2

Correct answer is B

5x12(x2)(x3)=Ax2+Bx3

= A(x3)+B(x2)(x2)(x3)

5x12=Ax3A+Bx2B

A+B=5...(i)

(3A+2B)=123A+2B=12...(ii)

From (i), A=5B

3(5B)+2B=12

153B+2B=12B=3

A+3=5A=2

5x12(x2)(x3)=2x2+3x3