What is (x/y-y/x)*((x+y)/(x-y)-(x-y)/(x+y)) ?

The solution to (x/y-y/x)*((x+y)/(x-y)-(x-y)/(x+y)) is 4

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simplify (x/y-y/x)*((x+y)/(x-y)-(x-y)/(x+y))

simplify

(\frac{x}{y} - \frac{y}{x}) \cdot (\frac{x + y}{x - y} - \frac{x - y}{x + y})

4

Solution steps

(\frac{x}{y} - \frac{y}{x}) (\frac{x + y}{x - y} - \frac{x - y}{x + y})

Join

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

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

Apply the fraction rule:

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

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

Simplify

(x^{2} - y^{2}) (\frac{x + y}{x - y} - \frac{x - y}{x + y}) : 4 x y

= \frac{4 x y}{x y}

Cancel the common factor:

x

= \frac{4 y}{y}

Cancel the common factor:

y

= 4

(9 x^{2} + 10 x + 4) - (9 x^{2} + 5 x - 1)

(1 + 3 i)^{8}

(\frac{a}{b} + \frac{b}{a})^{2} - (\frac{a}{b} - \frac{b}{a})^{2}

8 q^{2}

[\frac{6 \cdot 4 ^{n}}{4 ^{2 n + 1} + 2 ^{4 n + 1}}]^{n^{- 1}}

What is (x/y-y/x)*((x+y)/(x-y)-(x-y)/(x+y)) ?
The solution to (x/y-y/x)*((x+y)/(x-y)-(x-y)/(x+y)) is 4