10/x+y+2/x-y=4 15÷x+y-15/x-y=-2

$\frac { 10 } { x + y } + \frac { 2 } { x - y } = 4$
$\frac { 15 } { x + y } - \frac { 9 } { x - y } = - 2$.
Putting $\frac 1{x+y}$=u and $\frac 1{x-y}$= v ,the given equations
$10u + 2v= 4$........(i)
$15u - 9v = -2$.......(ii)

Multiplying (i) by 9 and (ii) by 2 and adding them,
$\Rightarrow$ $90 u + 18 v = 36\ and\ 30u - 18v = -4$
$\Rightarrow 120u = 32$
$\Rightarrow u = \frac{4}{15}$
Substituting u = $\frac{4}{15}$ in (i), we get v = $\frac { 2 } { 3 }$
$\Rightarrow \frac { 1 } { x + y } = \frac { 4 } { 15 } \text { and } \frac { 1 } { x - y } = \frac { 2 } { 3 }$
$\Rightarrow x + y = \frac { 15 } { 4 }$ .......(iii)
and $x - y = \frac { 3 } { 2 }$ ......(iv)
Adding (iii) and (iv), 
$\Rightarrow 2 x = \frac { 21 } { 4 } \Rightarrow x = \frac { 21 } { 8 }$
Substituting x =$\frac { 21 } { 8}$ in (iii), we get $y = \frac { 9 } { 8 }$
Hence, the solution is $x = \frac { 21 } { 8 } \text { and } v = \frac { 9 } { 8 }$