Solve the inequality (x-3)/(2x+1)>0

Answer 1

either
A:
x-3 > 0 and 2x+1 > 0
or
B:
x-3<0 and 2x+1<0

In case A:
x-3 > 0 means x > 3
2x+1 > 0 means x > -1/2
so, x > 3 satisfies A:

In case B:
x-3 < 0 means x < 3
2x+1 < 0 means x < -1/2
so, x < -1/2 satisfies B:

So, either x < -1/2 or x > 3
satisfies the original inequality