What is (x-1/x)/(x+1/x) ?

The solution to (x-1/x)/(x+1/x) is (x^2-1)/(x^2+1)

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simplify (x-1/x)/(x+1/x)

simplify

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

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

Solution steps

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

Join

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

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

Join

x + \frac{1}{x} : \frac{x ^{2} + 1}{x}

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

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

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

Cancel the common factor:

x

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

2 π (2)

\frac{5 x ^{2} + 30 x}{x ^{2} + 8 x + 12}

(- 3 x^{2} y^{3} + 2 x y^{2})^{2}

\frac{4}{5} n - 3 + \frac{7}{10} n

- 5.9 g - (- 10 h + 2.7)