Question

1/3x+y + 1/3x-y = 3/4​

Answer 1

Answer:

Step-by-step explanation:1/(3x + y) + 1/(3x - y) = 3/4

1/2(3x + y) - 1/2(3x - y) = -1/8

put (3x + y) = P and (3x - y) = Q

then, equations convert into

1/P + 1/Q = 3/4 -----(1)

1/2P - 1/2Q = -1/8-----(2)

multiply 2 with equation (2) and then add with equation (1),

1/P + 1/Q + 2/2P - 2/2Q = 3/4 - 2/8

= > 1/P + 1/Q + 1/P - 1/Q = 3/4 - 1/4

=> 2/P = 2/4

=> 2/P = 1/2 , P = 4 put it in equation (1),

1/4 + 1/Q = 3/4

=> 1/Q = 3/4 - 1/4 = 1/2

so, Q = 2

now, P = 3x + y = 4 ----(3)

Q = 3x - y = 2 --------(4)

adding equations (3) and (4),

3x + y + 3x - y = 4 + 2

6x = 6 => x = 1

y = 1

hence, x = 1 and y = 1