Cho biểu thức M

To solve the given mathematical expressions, we need to simplify each one step by step. Let's break down each expression:

### 1. Expression \( M \)
\[
M = \left( \frac{x^3 - 1 + x^3 + 1 - 4}{x^3 - x} \right) \cdot \left( \frac{x + 1}{x - 1} \right)
\]
Combine the like terms in the numerator:
\[
M = \left( \frac{2x^3 - 4}{x^3 - x} \right) \cdot \left( \frac{x + 1}{x - 1} \right)
\]
Factor the numerator \( 2(x^3 - 2) \) and the denominator \( x(x^2 - 1) = x(x-1)(x+1) \):
\[
M = \left( \frac{2(x^3 - 2)}{x(x - 1)(x + 1)} \right) \cdot \left( \frac{x + 1}{x - 1} \right)
\]
Next, simplify:
\[
M = \frac{2(x^3 - 2)(x + 1)}{x(x - 1)(x + 1)(x - 1)}
\]
Cancel \( (x + 1) \):
\[
M = \frac{2(x^3 - 2)}{x(x - 1)^2}
\]

### 2. Expression \( N \)
\[
N = \left( \frac{x - 4 + 3}{x^2 - 2x} \right) \cdot \left( \frac{x + 2}{x - 2} \right) \cdot \left( -\frac{x + 2}{x - 2} \right)
\]
First, simplify the first part:
\[
N = \left( \frac{x - 1}{x^2 - 2x} \right) \cdot \left( -\frac{(x + 2)^2}{(x - 2)^2} \right)
\]
Now factor:
\[
N = -\frac{(x - 1)(x + 2)^2}{x(x - 2)^2}
\]

### 3. Expression \( P \)
\[
P = \left( \frac{x^2 + 3x + 2 - x}{x^2 + x - 2} \right) \cdot \left( \frac{1}{x + 1} + \frac{1}{x - 1} \right)
\]
First, combine the fraction in \( P \):
\[
P = \left( \frac{x^2 + 2x + 2}{(x + 2)(x - 1)} \right) \cdot \left( \frac{2}{(x + 1)(x - 1)} \right)
\]
So,
\[
P = \frac{2(x^2 + 2x + 2)}{(x + 2)(x^2 - 1)}
\]
You can keep simplifying further depending on what you're looking for.

### Summary
So the simplified forms of the expressions are:
- \( M = \frac{2(x^3 - 2)}{x(x - 1)^2} \)
- \( N = -\frac{(x - 1)(x + 2)^2}{x(x - 2)^2} \)
- \( P = \frac{2(x^2 + 2x + 2)}{(x + 2)(x^2 - 1)} \)

If you have a specific goal, like solving for specific values or further simplifications, let me know!