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

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

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

simplify

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

\frac{4 x y}{( x - y ) ( x + y )}

Solution steps

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

Least Common Multiplier of

x - y, x + y : (x - y) (x + y)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

= \frac{4 x y}{( x - y ) ( x + y )}

\frac{x + 3}{6} - \frac{x - 2}{30}

612 - 123 + 100

\frac{1}{2} \times \frac{5}{2}

5 - 3

5 x^{2} + 500

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