Tính

To simplify the expression \(\frac{x^2 + 2}{4x + 6} \cdot \frac{x^2 - 36}{x^2 + x - 2}\), we can follow these steps:

1. Factor where possible.
2. Simplify the expression.

**Step 1: Factor the components.**

First, factor \(x^2 - 36\) and \(x^2 + x - 2\):

- \(x^2 - 36\) is a difference of squares:
\[
x^2 - 36 = (x - 6)(x + 6)
\]

- To factor \(x^2 + x - 2\), we need numbers that multiply to \(-2\) and add to \(1\):
\[
x^2 + x - 2 = (x + 2)(x - 1)
\]

- For the numerator \(x^2 + 2\), it does not factor over the integers.

The denominator \(4x + 6\) can be factored as:
\[
4x + 6 = 2(2x + 3)
\]

**Step 2: Write the expression with the factors:**

The expression becomes:
\[
\frac{x^2 + 2}{2(2x + 3)} \cdot \frac{(x - 6)(x + 6)}{(x + 2)(x - 1)}
\]

**Step 3: Combine the fractions:**

Now we can multiply the fractions:
\[
= \frac{(x^2 + 2)(x - 6)(x + 6)}{2(2x + 3)(x + 2)(x - 1)}
\]

**Step 4: Simplify if possible:**

\((x^2 + 2)\) does not have common factors with the other terms, so we leave it as is.

The final simplified form is:
\[
\frac{(x^2 + 2)(x - 6)(x + 6)}{2(2x + 3)(x + 2)(x - 1)}
\]

This is the simplified version of the expression \(\frac{x^2 + 2}{4x + 6} \cdot \frac{x^2 - 36}{x^2 + x - 2}\).