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

The solution to ((x^2+y^2))/(x^2-y^2)+y/(x+y)-x/(x-y) is 0

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

simplify

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

0

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Simplify

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

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

Cancel

\frac{- y ^{2} x ^{2} + x ^{2} y ^{2}}{( x + y ) ( x - y ) ( x ^{2} - y ^{2} )} : 0

= 0

\frac{n ^{2} + 2 n - 24}{n ^{2} - 11 n + 28}

- 9 x^{2} - 6 x - 1 = 0

\frac{4}{3} \cdot π

\frac{1}{5} x + \frac{1}{3} = \frac{4}{3}

(a^{\frac{1}{2}})^{2}

What is ((x^2+y^2))/(x^2-y^2)+y/(x+y)-x/(x-y) ?
The solution to ((x^2+y^2))/(x^2-y^2)+y/(x+y)-x/(x-y) is 0