3/4 = 1 - (3x-2)/(x+1)

Taking L.C.M on right side of the equation

3/4 = [(x + 1) - (3x -2) ]/ (x + 1)

3/4 = [ x + 1 - ( 3x -2 )]/ (x + 1)

3/4 = [ x + 1 - 3x + 2 ]/ (x + 1)

By cross multiplication;

3/4 (x + 1) = (x + 1 - 3x + 2)

Simplify the right side of the equation

3/4 (x + 1) = (-2x + 3)

Use distributive property of multiplication over addition on the left side of the equation

3/4x + 3/4*1 = -2x + 3

3/4 x + 3/4 = -2x + 3

Make right side is equal to zero

3/4 x + 2x + 3/4 - 3 = 0

[3/4 + 2]x + 3/4 - 3 =0

[(3 + 8)/4]x + (3 - 12)/4 = 0

11/4 x -9/4 = 0

(11x - 9)/4 = 0

By cross multiplication

11x - 9= 0

11x =9

x = 9/11

So, the value of x is 9/11.

Taking L.C.M on right side of the equation

3/4 = [(x + 1) - (3x -2) ]/ (x + 1)

3/4 = [ x + 1 - ( 3x -2 )]/ (x + 1)

3/4 = [ x + 1 - 3x + 2 ]/ (x + 1)

By cross multiplication;

3/4 (x + 1) = (x + 1 - 3x + 2)

Simplify the right side of the equation

3/4 (x + 1) = (-2x + 3)

Use distributive property of multiplication over addition on the left side of the equation

3/4x + 3/4*1 = -2x + 3

3/4 x + 3/4 = -2x + 3

Make right side is equal to zero

3/4 x + 2x + 3/4 - 3 = 0

[3/4 + 2]x + 3/4 - 3 =0

[(3 + 8)/4]x + (3 - 12)/4 = 0

11/4 x -9/4 = 0

(11x - 9)/4 = 0

By cross multiplication

11x - 9= 0

11x =9

x = 9/11

So, the value of x is 9/11.