algebra

We have the equation: \(x - {1 \over x} = 3\)

 

Solve as follows: 

 

\({x^2 \over x} - {1 \over x} = 3\)

\({x^2 - 1 \over x} = 3\)

\(x^2 - 1 = 3x \) 

\(x^2 - 3x - 1 = 0\)

 

Now, just solve the quadratic...

\(x - \frac{1}{x} = 3\)

 

\(x^2 - 1 = 3x\)

 

\(x^2 - 3x -1 = 0\)

 

\(x = \frac{3\pm\sqrt{13}}{2}\)

 

 

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