What is 1/(x+y)-1/(x-y)+(2y)/(x^2+y^2) ?

The solution to 1/(x+y)-1/(x-y)+(2y)/(x^2+y^2) is -(4y^3)/((x+y)(x-y)(x^2+y^2))

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simplify 1/(x+y)-1/(x-y)+(2y)/(x^2+y^2)

simplify

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

- \frac{4 y ^{3}}{( x + y ) ( x - y ) ( x ^{2} + y ^{2} )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(x - y) (x^{2} + y^{2}) - (x + y) (x^{2} + y^{2}) + 2 y (x + y) (x - y) : - 4 y^{3}

= \frac{- 4 y ^{3}}{( x + y ) ( x - y ) ( x ^{2} + y ^{2} )}

Apply the fraction rule:

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

= - \frac{4 y ^{3}}{( x + y ) ( x - y ) ( x ^{2} + y ^{2} )}

5 - k + 12 = 16

- \frac{7}{2} w = 20

x (x - 1) > 0

(\frac{1}{4})^{10}

2 (2 x + 1) - \frac{3 x}{2} = \frac{- 3 ( 4 + x )}{2}

What is 1/(x+y)-1/(x-y)+(2y)/(x^2+y^2) ?
The solution to 1/(x+y)-1/(x-y)+(2y)/(x^2+y^2) is -(4y^3)/((x+y)(x-y)(x^2+y^2))