Given, bx + ay = a + b .................1

and ax{1/(a - b) - 1/(a + b)} - by{(1/(b - a) -1/(b + a)} = 2

=> ax[{(a + b) - (a - b)}/{(a - b)*(a + b)}] - by[{(b + a) - (b - a)}/{(b - a)*(b + a)}] = 2

=> ax{(a + b - a + b)/(a² - b² )} - by{(b + a - b + a)/(b² - a² )} = 2

=> ax{2b/(a² - b² )} - by{2a/(b² - a² )} = 2

=> (ax*2b)/(a² - b² ) - (by*2a)/(b² - a² ) = 2

=> 2abx/(a² - b² ) - 2aby/(b² - a² ) = 2

=> 2{abx/(a² - b² ) - aby/(b² - a² )} = 2

=> abx/(a² - b² ) - aby/(b² - a² ) = 2/2

=> abx/(a² - b² ) - aby/(b² - a² ) = 1

=> abx/(a² - b² ) + aby/(a² - b² ) = 1

=> (abx + aby)/(a² - b² ) = 1

=> abx + aby = a² - b² 

=> a(bx + by) = a² - b²

=> bx + by = (a² - b² )/a  ............2

Now, subtract equation 1 and 2, we get

      bx + ay - bx - by = a + b - (a² - b² )/a

=> ay - by = a + b - (a² - b² )/a

=> y(a - b) = {a² + ab - (a² - b² )}/a

=> y(a - b) = {a² + ab - a² + b² )}/a

=> y(a - b) = (ab + b² )/a

=> y = (ab + b² )/{a*(a - b)}

=> y = b(a + b)/{a*(a - b)}

From equation 1, we get

      bx + a*[b(a + b)/{a*(a - b)}] = a + b

=> bx + b(a + b)/(a - b) = a + b

=> bx = (a + b) - {b(a + b)/(a - b)}

=> bx = {(a + b)*(a - b) - b(a + b)}/(a - b)

=> bx = (a + b)*{(a - b) - b}/(a - b)

=> bx = (a + b)*{a - b - b}/(a - b)

=> bx = {(a + b)*(a - 2b)}/(a - b)

=> x = {(a + b)*(a - 2b)}/{a*(a - b)}

So, the value of x and y are {(a + b)*(a - 2b)}/{a*(a - b)} and b(a + b)/{a*(a - b)} respectively.