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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

2 (x + 5) = 3 x + 1

\frac{2}{5} (x - 1) + \frac{5}{2} (x + 2) = \frac{3}{4} (x - 2)

5^{- 10}

(3 y)^{4}

- 8 ∣ 10 + 4 x ∣ = - 112

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