Solve |x^2|-x/x<2 - ScanMath

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Type your math problem... |x^2|-x/x<2

x

Question

Solve the inequality

x \in (- 3, 0) \cup (0, 3)

Evaluate

x^{2} - \frac{x}{x} < 2

Find the domain

x^{2} - \frac{x}{x} < 2, x \neq = 0

Simplify

More Steps

Evaluate

x^{2} - \frac{x}{x}

Divide the terms

x^{2} - 1

When the expression in absolute value bars is not negative, remove the bars

x^{2} - 1

x^{2} - 1 < 2

Move the constant to the right side

x^{2} < 2 + 1

Add the numbers

x^{2} < 3

Take the 2 -th root on both sides of the inequality

x^{2} < 3

Calculate

∣ x ∣ < 3

Separate the inequality into 2 possible cases

{x < 3 x > - 3

Find the intersection

- 3 < x < 3

Check if the solution is in the defined range

- 3 < x < 3, x \neq = 0

Solution

x \in (- 3, 0) \cup (0, 3)

Show Solution

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