Solve x-1/x-2 - ScanMath

Question

Simplify the expression

\frac{x ^{2} - 1 - 2 x}{x}

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x = 0

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x_{1} = 1 - 2, x_{2} = 1 + 2

Alternative Form

x_{1} \approx - 0.414214, x_{2} \approx 2.414214

Evaluate

x - \frac{1}{x} - 2

To find the roots of the expression,set the expression equal to 0

x - \frac{1}{x} - 2 = 0

Find the domain

x - \frac{1}{x} - 2 = 0, x \neq = 0

Calculate

x - \frac{1}{x} - 2 = 0

Subtract the terms

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\frac{x ^{2} - 1}{x} - 2 = 0

Subtract the terms

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\frac{x ^{2} - 1 - 2 x}{x} = 0

Cross multiply

x^{2} - 1 - 2 x = x \times 0

Simplify the equation

x^{2} - 1 - 2 x = 0

Rewrite in standard form

x^{2} - 2 x - 1 = 0

Substitute a= 1,b= - 2 and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 ( - 1 )}{2}

Simplify the expression

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x = \frac{2 \pm 8}{2}

Simplify the radical expression

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x = \frac{2 \pm 2 2}{2}

Separate the equation into 2 possible cases

x = \frac{2 + 2 2}{2} x = \frac{2 - 2 2}{2}

Simplify the expression

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x = 1 + 2 x = \frac{2 - 2 2}{2}

Simplify the expression

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x = 1 + 2 x = 1 - 2

Check if the solution is in the defined range

x = 1 + 2 x = 1 - 2, x \neq = 0

Find the intersection of the solution and the defined range

x = 1 + 2 x = 1 - 2

Solution

x_{1} = 1 - 2, x_{2} = 1 + 2

Alternative Form

x_{1} \approx - 0.414214, x_{2} \approx 2.414214

Show Solution