ong>Step-by-step explanation:

Given the square root of x square / y square + Y square by 4 x square minus x by Y + y by 2 x minus 3 by 4 is  

We have the equation as  

So √x^2/y^2 + y^2/4x^2 – x/y + y/2x – ¾

So taking LCM we GET

√4x^4 + y^4 – 4x^3y + 2xy^3 – 3x^2y^2 / 4x^2y^2

Now REARRANGING the x and y TERMS we get

√4x^4 – 4x^3y – 3x^2y^2 + 2xy^3 + y^4 / 4x^2y^2

Now taking the square root we get √(2x^2 – xy – y^2)^2 / 4x^2y^2

            So we get 2x^2 – xy – y^2 / 2x^2y^2

We can write this as x/y – 1/2 – y/2x

                      OR  

   √(x/y)^2 + (y/2x)^2 – x/y + y/2x – ¾ + 1 – 1 (add and subtract 1 to both sides)

 √(x/y)^2 + (y/2x)^2 – 1 – x/y + y/2x + 1/4  

     Let P = √(x/y)^2 + (y/2x)^2 – 2(x/y)(y/2x) – x/y + y/2x + ¼

     Squaring both sides we get

    So p^2 = (x/y – y/2x)^2 – (x/y – y/2x – 1/4)

      Now let x/y – y/2x = a

 So p^2 = a^2 – (a – 1/4 )

    Or p^2 = a^2 – (4a – 1 / 4)

    Or p^2 = 4a^2 – 4a + 1 / 4

     P^2 = (2a – 1 / 2)^2

Or p = 2a – 1 / 2

      Or p = a – 1/2  

     Or p = x/y – y/2x – 1/2