( 2 / ( x + y ) ) - ( 5 / ( x - y ) ) = -9
( 1 / ( x + y ) ) + (3 / ( x - y ) ) = 1
I'm so sorry but i can't type as you do, but can you try to understand it.
And thanks in advance.
Making the indicated substitutions gets you the equations
$\displaystyle 2A-5B=-9,$
$\displaystyle A+3B=1.$
Solve these for $\displaystyle A$ and $\displaystyle B$ and then substitute into the earlier substitutions.
$\displaystyle x+y=1/A,$
$\displaystyle x-y=1/B.$
You should be able to solve both sets easily.