Tính M

To solve for \( M \), let's break down the expression:

\[
M = \left[ \left( c - \frac{1}{2} \right)^3 - \left( \frac{3}{4} \right)^3 \cdot (-c - 2)^2 \right] : \left[ 2(c - 1)^5 + \left( \frac{3}{4} \right)^2 - \frac{3}{8} \right]
\]

1. **Calculate the numerator**:

- First term: \( \left( c - \frac{1}{2} \right)^3 \)
- Second term: \( -\left( \frac{3}{4} \right)^3 \cdot (-c - 2)^2 \)

Substitute \( \left( \frac{3}{4} \right)^3 = \frac{27}{64} \) to evaluate the second term.

2. **Calculate the denominator**:

- First term: \( 2(c - 1)^5 \)
- Second term: \( \left( \frac{3}{4} \right)^2 = \frac{9}{16} \)
- Combine that with \( -\frac{3}{8} \).

Now you'll need to simplify the numerator and denominator separately, then form the quotient \( M \) by dividing the simplified numerator by the simplified denominator.

If you have specific values for \( c \) or want a final expression, please provide them!