Solve 2a+5/a+1>0

$$\frac { 2 a + 5 } { a + 1 } > 0$$

Solve for a

$$a\in \left(-\infty,-\frac{5}{2}\right)\cup \left(-1,\infty\right)$$

Solution Steps

For the quotient to be positive, 2a+5 and a+1 have to be both negative or both positive. Consider the case when 2a+5 and a+1 are both negative.

$$2a+5<0 a+1<0$$

The solution satisfying both inequalities is a<-\frac{5}{2}.

$$a<-\frac{5}{2}$$

Consider the case when 2a+5 and a+1 are both positive.

$$a+1>0 2a+5>0$$

The solution satisfying both inequalities is a>-1.

$$a>-1$$

The final solution is the union of the obtained solutions.

$$a<-\frac{5}{2}\text{; }a>-1$$