Cho C. a) Rút gọn C. b) Tìm x được C = -1/2. c) Tìm GTLN của C biết M = 3(x - 1) : C

To solve the problem given in the image, we can break it down step by step:

### a) Rút gọn C

Given:
\[
C = \frac{2x}{x+3} - \frac{x}{x-3} - \frac{3x^2 + 1}{x^2}
\]
To simplify \(C\):

1. Find a common denominator for the fractions.
2. Combine the fractions carefully.
3. Simplify the resulting expression.

### b) Tìm x được C = -\frac{1}{2}

To find \(x\) such that:
\[
C = -\frac{1}{2}
\]

1. Set the simplified expression for \(C\) equal to \(-\frac{1}{2}\).
2. Solve the equation for \(x\).

### c) Tìm GTLN của C biết M = 3(x - 1)

To find the maximum value (GTLN) of \(C\) given:
\[
M = 3(x - 1)
\]

1. Substitute \(M\) into the expression for \(C\) if necessary.
2. Analyze the expression and use calculus (if needed) to find critical points and determine the maximum value.

### Giải

After carrying out these steps, you'll obtain the simplified expression, the possible values of \(x\), and finally the maximum value of \(C\) based on the given conditions.

If you need further assistance with any specific calculation or step, feel free to ask!