We have

and

Lets simplify these equations. Assuming p = 1/(x + y) and q = 1/(x – y),

3p + 2q = 2 …(i)

Also,

⇒ 9p – 4q = 1 …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Lets multiply eq.(i) by 3, so that variable p in both the equations have same coefficient.

Recalling equations (i) & (ii),

3p + 2q = 2 [×3

9p – 4q = 1

⇒ 10q = 5

⇒ q = 1/2

Substitute q = 1/2 in eq.(i)/eq.(ii), as per convenience of solving.

Thus, substituting in eq.(i), we get

3p + 2(1/2) = 2

⇒ 3p + 1 = 2

⇒ 3p = 2 – 1 = 1

⇒ p = 1/3

Thus, p = 1/3 and q = 1/2

As p = 1/(x + y),

⇒

⇒ x + y = 3 …(iii)

And q = 1/(x – y)

⇒

⇒ x – y = 2 …(iv)

Adding equations (iii) and (iv) to obtain x and y,

(x + y) + (x – y) = 3 + 2

⇒ 2x = 5

⇒ x = 5/2

Putting the value of x in equation (iii), we get

5/2 + y = 3

⇒ y = 3 – 5/2

⇒ y = 1/2

Hence, we have x = 5/2 and y = 1/2