Solve x/(x-2) >0 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in (- \infty, 0) \cup (2, + \infty)

Evaluate

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

Find the domain

More Steps

\frac{x}{x - 2} > 0, x \neq = 2

Set the numerator and denominator of \frac{x}{x - 2} equal to 0 to find the values of x where sign changes may occur

x = 0 x - 2 = 0

Calculate

More Steps

x = 0 x = 2

Determine the test intervals using the critical values

x < 0 0 < x < 2 x > 2

Choose a value form each interval

x_{1} = - 1 x_{2} = 1 x_{3} = 3

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is the solution x_{2} = 1 x_{3} = 3

To determine if 0 < x < 2 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

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x < 0 is the solution 0 < x < 2 is not a solution x_{3} = 3

To determine if x > 2 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

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x < 0 is the solution 0 < x < 2 is not a solution x > 2 is the solution

The original inequality is a strict inequality,so does not include the critical value ,the final solution is x \in (- \infty, 0) \cup (2, + \infty)

x \in (- \infty, 0) \cup (2, + \infty)

Check if the solution is in the defined range

x \in (- \infty, 0) \cup (2, + \infty), x \neq = 2

Solution

x \in (- \infty, 0) \cup (2, + \infty)

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