Solve p/(p-1)>0 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

p \in (- \infty, 0) \cup (1, + \infty)

Evaluate

\frac{p}{p - 1} > 0

Find the domain

More Steps

\frac{p}{p - 1} > 0, p \neq = 1

Set the numerator and denominator of \frac{p}{p - 1} equal to 0 to find the values of p where sign changes may occur

p = 0 p - 1 = 0

Calculate

More Steps

p = 0 p = 1

Determine the test intervals using the critical values

p < 0 0 < p < 1 p > 1

Choose a value form each interval

p_{1} = - 1 p_{2} = \frac{1}{2} p_{3} = 2

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

More Steps

p < 0 is the solution p_{2} = \frac{1}{2} p_{3} = 2

To determine if 0 < p < 1 is the solution to the inequality,test if the chosen value p = \frac{1}{2} satisfies the initial inequality

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p < 0 is the solution 0 < p < 1 is not a solution p_{3} = 2

To determine if p > 1 is the solution to the inequality,test if the chosen value p = 2 satisfies the initial inequality

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p < 0 is the solution 0 < p < 1 is not a solution p > 1 is the solution

The original inequality is a strict inequality,so does not include the critical value ,the final solution is p \in (- \infty, 0) \cup (1, + \infty)

p \in (- \infty, 0) \cup (1, + \infty)

Check if the solution is in the defined range

p \in (- \infty, 0) \cup (1, + \infty), p \neq = 1

Solution

p \in (- \infty, 0) \cup (1, + \infty)

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