Solve t+6/t-1<0

$$\frac { t + 6 } { t - 1 } < 0$$

Solve for t

$$t\in \left(-6,1\right)$$

Solution Steps

For the quotient to be negative, t+6 and t-1 have to be of the opposite signs. Consider the case when t+6 is positive and t-1 is negative.

$$t+6>0 t-1<0$$

The solution satisfying both inequalities is t\in \left(-6,1\right).

$$t\in \left(-6,1\right)$$

Consider the case when t-1 is positive and t+6 is negative.

$$t-1>0 t+6<0$$

This is false for any t.

$$t\in \emptyset$$

The final solution is the union of the obtained solutions.

$$t\in \left(-6,1\right)$$