Solve -1/a-1>0

$$- \frac{ 1 }{ a } -1 > 0$$

Solve for a

$$a\in \left(-1,0\right)$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a}{a}.

$$-\frac{1}{a}-\frac{a}{a}>0$$

Since -\frac{1}{a} and \frac{a}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-a}{a}>0$$

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

$$-a-1<0 a<0$$

The solution satisfying both inequalities is a\in \left(-1,0\right).

$$a\in \left(-1,0\right)$$

Consider the case when -a-1 and a are both positive.

$$a>0 -a-1>0$$

This is false for any a.

$$a\in \emptyset$$

The final solution is the union of the obtained solutions.

$$a\in \left(-1,0\right)$$