Just require a substitution!

Algebra Level 4

\[\begin{cases}5 x\left(1+\frac { 1 }{ { x }^{ 2 }+y^{ 2 } } \right)=12\\ 5y \left(1-\frac { 1 }{ { x }^{ 2 }+{ y }^{ 2 } } \right)=4 \end{cases}\] If \(x=a\) and \(y=b\) satisfy the above equations simultaneously for \(a>b>0\), then find \(a+b\).

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