The given expression is:

\[
11x^2 + 4x + \frac{12}{(2x+1)(x^2+4)}
\]

This expression contains a quadratic polynomial term \(11x^2 + 4x\) and a fraction with a product of polynomials in the denominator.

Would you like to simplify this expression further, or are you looking for specific operations, such as evaluating it for a particular value of \(x\) or solving it in another context?

Here are some possible directions:

1. Simplifying the rational expression.
2. Factoring if possible.
3. Determining limits or asymptotes.
4. Substituting a value for \(x\).
5. Solving for \(x\) if set equal to another value.

**Tip**: When simplifying complex expressions, break down the problem step-by-step, and focus on the polynomials and rational functions separately.

Learn how to simplify the expression 11x^2 + 4x + 12 / (2x+1)(x²+4). This problem explores key algebraic concepts, such as quadratic expressions and rational function simplification. Suitable for students in Grades 10-12.

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