Giải các phương trình sau a) \( \frac{2x-1}{x+1} = \frac{2x}{x+1}. \) b) \( \frac{x^2-2}{x+1} = \frac{x^2-2x+3}{x+1}. \) c) \( \frac{x^2+4x}{x-1} = \frac{x^2-3x+2}{x-1}. \) d) \( \frac{2x-1}{x+3} = 1. \) e) \( \frac{5}{x+7} = \frac{-14}{x-5}. \) f) \( \frac{x+3}{x-3} + \frac{x-2}{x} = 2. \)

Let's solve each of the equations step by step.

### a) \( \frac{2x-1}{x+1} = \frac{2x}{x+1} \)

Since both sides have the common denominator \(x + 1\) (assuming \(x \neq -1\)), we can multiply both sides by \(x + 1\):

\[
2x - 1 = 2x
\]

Subtract \(2x\) from both sides:

\[
-1 = 0
\]

This is a contradiction, so there are no solutions.

### b) \( \frac{x^2-2}{x+1} = \frac{x^2-2x+3}{x+1} \)

Multiplying both sides by \(x + 1\) (assuming \(x \neq -1\)):

\[
x^2 - 2 = x^2 - 2x + 3
\]

Subtract \(x^2\) from both sides:

\[
-2 = -2x + 3
\]

Rearranging gives:

\[
2x = 5 \implies x = \frac{5}{2}
\]

### c) \( \frac{x^2+4x}{x-1} = \frac{x^2-3x+2}{x-1} \)

Multiplying both sides by \(x - 1\) (assuming \(x \neq 1\)):

\[
x^2 + 4x = x^2 - 3x + 2
\]

Subtracting \(x^2\) from both sides:

\[
4x = -3x + 2
\]

Rearranging gives:

\[
7x = 2 \implies x = \frac{2}{7}
\]

### d) \( \frac{2x-1}{x+3} = 1 \)

Multiplying both sides by \(x + 3\) (assuming \(x \neq -3\)):

\[
2x - 1 = x + 3
\]

Rearranging gives:

\[
2x - x = 4 \implies x = 4
\]

### e) \( \frac{5}{x+7} = \frac{-14}{x-5} \)

Cross-multiplying:

\[
5(x - 5) = -14(x + 7)
\]

Expanding both sides:

\[
5x - 25 = -14x - 98
\]

Combining like terms:

\[
19x = -73 \implies x = -\frac{73}{19}
\]

### f) \( \frac{x+3}{x-3} + \frac{x-2}{x} = 2 \)

First, find a common denominator, which is \(x(x-3)\):

\[
\frac{(x + 3)x + (x - 2)(x - 3)}{x(x - 3)} = 2
\]

Simplifying the numerator:

\[
x^2 + 3x + x^2 - 5x + 6 = 2x^2 - 2x + 6
\]

So we have:

\[
\frac{2x^2 - 2x + 6}{x(x - 3)} = 2
\]

Cross-multiplying gives:

\[
2x^2 - 2x + 6 = 2x^2 - 6x
\]

This simplifies to:

\[
4x + 6 = 0 \implies x = -\frac{3}{2}
\]

### Summary of Solutions:
a) No solutions
b) \(x = \frac{5}{2}\)
c) \(x = \frac{2}{7}\)
d) \(x = 4\)
e) \(x = -\frac{73}{19}\)
f) \(x = -\frac{3}{2}\)