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Solve the inequality x22x3...

Solve the inequality x22x3

A.

1x3

B.

x3 and x1

C.

x3 or x<1

D.

1x<3

Correct answer is B

x22x3x22x30

x2+x3x3=(x+1)(x3)0 

x=1;x=3

Check: x=1:(1)22(1)=1+23  (satisfied)

1<x<3:022(0)=03 (not satisfied)

x<1:(2)22(2)=4+4=83 (satisfied)

x=3:322(3)=96=33 (satisfied)

x>3:422(4)=168=83 (satisfied)