Answer:

x = 4, y = 5

Explanation:

So first, lets make this equation simpler,

Take 1/(x-1) as A and 1/(y-2) as B
So our new Equations are -

5A + B = 2 ---- (i)
6A - 3B = 1 ---- (ii)

Now, lets solve for Linear Equations in Two Variables,

I will be using Elimination method (Eliminating Variable B) -
(i) x 3
(ii) x 1

So now, our New Equations are -

15A + 3B = 6 ---- (iii)

6A - 3B = 1 ---- (iv)

As the signs of the coefficients of B are opposite, I will add the equations -

  15A + 3B = 6

+ 6A - 3B = 1
-----------------------

21A = 7

Now, solve -

A = 7/21, A = 1/3

Putting Value of A into Eqn. (iv)
6/3 - 3B = 1
2 - 3B = 1
-3B = 1-2
-3B = -1
3B = 1
B = 1/3

We know that A = 1/(x-1) and B = 1/(y-2)

Now solve,

A = 1/(x-1)
1/3 = 1/(x-1)

x-1 = 3

x = 4

B = 1/(y-2)
1/3 = 1/(y-2)
y-2 = 3
y = 5

Hope it helps! :)