The expression provided can be written more clearly as:

$\frac{1}{4x^2 - 3x + 6}$

Would you like me to:

1. Simplify or factorize the expression?
2. Integrate or differentiate the expression?
3. Evaluate the expression for a specific value of $x$?
4. Determine the behavior of the function as $x$ approaches a particular value?
5. Analyze the roots or zeros of the quadratic polynomial in the denominator?

Please specify what you need or choose from the above options. Here are some questions you might want to ask:

1. How do you simplify $\frac{1}{4x^2 - 3x + 6}$?
2. What is the integral of $\frac{1}{4x^2 - 3x + 6}$?
3. What is the derivative of $\frac{1}{4x^2 - 3x + 6}$?
4. How do you evaluate $\frac{1}{4x^2 - 3x + 6}$ at $x = 1$?
5. What are the roots of the quadratic polynomial $4x^2 - 3x + 6$?

Tip: When dealing with complex fractions, it's often helpful to consider if the denominator can be factorized or simplified further.