Question

frac{5}{х-у}-frac{3}{х+y};

 

Answer 1

$frac{5}{x-y}-frac{3}{x+y}=frac{5(x+y)-3(x-y)}{(x+y)(x-y)}=frac{5x+5y-3x+3y}{(x+y)(x-y)}=frac{2x+8y}{x^2-y^2}$

 

 

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Answer 2

$frac{5x+5y-3x+5y}{(x+y)(x-y)}=frac{2x+8y}{(x+y)(x-y)}\ left { {{2x+8y=0 | /2} atop {(x+y)(x-y)neq0}} right.\ left { {{x+4y=0} atop {(x+y)(x-y)neq0}} right.$