Решите систему уравнений [latex] left { {{ frac{16}{x+y}+ frac{16}{x-y}=3 } atop { frac{8}{x+y}+ frac{12}{x-y}=2 }} ight. [/latex]

[latex] left { {{ frac{16}{x+y}+frac{16}{x-y}=3 } atop {frac{8}{x+y}+frac{12}{x-y}=2}} ight. ; ,; ; u=frac{1}{x+y}; ,; v=frac{1}{x-y}; ,; xe pm y\\ left { {{16u+16v=3} atop {8u+12v=2, |cdot (-2)}} ight. ; ,; left { {{-8v=-1} atop {8u+12v=2}} ight. ; ,; left { {{v=frac{1}{8}} atop {8u+frac{12}{8}=2}} ight. ; ,; left { {{v=frac{1}{8}} atop {u=frac{1}{16}}} ight. \\v=frac{1}{x-y}=frac{1}{8}; ,; x-y=8\\u=frac{1}{x+y}=frac{1}{16}; ,; x+y=16[/latex][latex] left { {{x-y=8} atop {x+y=16}} ight. ; ,; left { {{2x=24} atop {2y=8}} ight. ; ,; left { {{x=12} atop {y=4}} ight. [/latex]