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

To solve the equation 1/4 = 3 - 2x - 1/x + 2, we need to eliminate the fractions by finding a common denominator and then simplify the equation.

Step 1: Find a common denominator for the fractions on the right side of the equation. The denominators are 4 and x. The common denominator is 4x.

Step 2: Rewrite the equation with the common denominator:

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

Simplifying the equation gives us:

1/4 = (12x - 8x - 4 + 8) / (4x)

Step 3: Combine like terms:

1/4 = (4x - 4) / (4x)

Step 4: Cross-multiply:

(1)(4x) = (4)(4x - 4)

4x = 16x - 16

Step 5: Move the variables to one side and the constants to the other side of the equation:

4x - 16x = -16

-12x = -16

Step 6: Solve for x by dividing both sides of the equation by -12:

x = (-16) / (-12)

x = 4/3

Therefore, the solution to the equation 1/4 = 3 - 2x - 1/x + 2 is x = 4/3.