How to solve (x-2)/(x-5) > 0

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (x-2)/(x-5) > 0 | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

$$\frac{ x-2 }{ x-5 } > 0$$

$x\in \left(-\infty,2\right)\cup \left(5,\infty\right)$

For the quotient to be positive, $x-2$ and $x-5$ have to be both negative or both positive. Consider the case when $x-2$ and $x-5$ are both negative.

$$x-2<0$$ $$x-5<0$$

The solution satisfying both inequalities is $x<2$.

$$x<2$$

Consider the case when $x-2$ and $x-5$ are both positive.

$$x-5>0$$ $$x-2>0$$

The solution satisfying both inequalities is $x>5$.

$$x>5$$

The final solution is the union of the obtained solutions.

$$x<2\text{; }x>5$$