Step 1 :The given expression is \(\frac{3}{4 x^{2}-9 x-9}+\frac{1}{4 x^{2}+11 x+6}\)
Step 2 :To simplify this expression, we need to find a common denominator for the two fractions. The common denominator will be the product of the two denominators.
Step 3 :After finding the common denominator, we can combine the two fractions into one.
Step 4 :Then, we can simplify the numerator of the resulting fraction if possible.
Step 5 :Final Answer: The simplified form of the given expression is \(\boxed{\frac{1}{x^{2}-x-6}}\)