Solve y-1/y-0geq0

$$\frac{ y-1 }{ y-0 } \geq 0$$

Solve for y

$$y\in (-\infty,0)\cup [1,\infty)$$

Solution Steps

For the quotient to be ≥0, y-1 and y have to be both ≤0 or both ≥0, and y cannot be zero. Consider the case when y-1\leq 0 and y is negative.

$$y-1\leq 0 y<0$$

The solution satisfying both inequalities is y<0.

$$y<0$$

Consider the case when y-1\geq 0 and y is positive.

$$y-1\geq 0 y>0$$

The solution satisfying both inequalities is y\geq 1.

$$y\geq 1$$

The final solution is the union of the obtained solutions.

$$y<0\text{; }y\geq 1$$