Solve 2x-1/x+1>0

$$\frac{ 2x-1 }{ x+1 } > 0$$

Solve for x

$$x\in \left(-\infty,-1\right)\cup \left(\frac{1}{2},\infty\right)$$

Solution Steps

For the quotient to be positive, 2x-1 and x+1 have to be both negative or both positive. Consider the case when 2x-1 and x+1 are both negative.

$$2x-1<0 x+1<0$$

The solution satisfying both inequalities is x<-1.

$$x<-1$$

Consider the case when 2x-1 and x+1 are both positive.

$$x+1>0 2x-1>0$$

The solution satisfying both inequalities is x>\frac{1}{2}.

$$x>\frac{1}{2}$$

The final solution is the union of the obtained solutions.

$$x<-1\text{; }x>\frac{1}{2}$$