What is a/(a+b)+b/(a-b) ?

The solution to a/(a+b)+b/(a-b) is (a^2+b^2)/((a+b)(a-b))

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simplify a/(a+b)+b/(a-b)

simplify

\frac{a}{a + b} + \frac{b}{a - b}

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

Solution steps

\frac{a}{a + b} + \frac{b}{a - b}

Least Common Multiplier of

a + b, a - b : (a + b) (a - b)

Adjust Fractions based on the LCM

= \frac{a ( a - b )}{( a + b ) ( a - b )} + \frac{b ( a + b )}{( a + b ) ( a - b )}

Apply the fraction rule:

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

= \frac{a ( a - b ) + b ( a + b )}{( a + b ) ( a - b )}

Simplify

a (a - b) + b (a + b) : a^{2} + b^{2}

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

\frac{1}{5} \div 6

0. 4^{- 2}

\frac{10}{8} + \frac{10}{6}

d^{2} - 5 d + 4

(- 1)^{n} + (- 1)^{n}

What is a/(a+b)+b/(a-b) ?
The solution to a/(a+b)+b/(a-b) is (a^2+b^2)/((a+b)(a-b))