Let's evaluate each expression step by step using the given values $a = 4$, $b = -2$, and $c = -3$. We'll carefully follow the order of operations (PEMDAS).

(a) Expression: $-\frac{(a + 2)2 - 4c}{2 - b}$

1. Substitute the values: $-\frac{(4 + 2)2 - 4(-3)}{2 - (-2)}$

2. Simplify inside the parentheses: $-\frac{(6)2 - 4(-3)}{2 + 2}$

3. Multiply inside the numerator: $-\frac{12 + 12}{4} = -\frac{24}{4}$

4. Simplify the division: $-6$

So, the value of expression (a) is -6.

(b) Expression: $6a - \frac{3b}{3} - 5[-7 - c]$

1. Substitute the values: $6(4) - \frac{3(-2)}{3} - 5[-7 - (-3)]$

2. Multiply and simplify: $24 - \frac{-6}{3} - 5[-7 + 3]$

3. Simplify inside the division and brackets: $24 + 2 - 5[-4]$

4. Multiply inside the brackets: $24 + 2 + 20 = 46$

So, the value of expression (b) is 46.

Final Answers:

1. (a): $-6$
2. (b): $46$

Would you like more details on these steps or have any further questions?

Here are 5 related questions for practice:

1. Evaluate $\frac{(a - b)c}{a - 2}$ using $a = 4$, $b = -2$, and $c = -3$.
2. What is the value of $4a - \frac{b}{c} + 2c$ if $a = 4$, $b = -2$, and $c = -3$?
3. Simplify $3a + \frac{b^2 - c^2}{a}$ using $a = 4$, $b = -2$, and $c = -3$.
4. Calculate $7b + \frac{c}{a} - b^2$ when $b = -2$ and $c = -3$.
5. Find the result of $\frac{-2a + 3c}{b + 1}$ given $a = 4$, $b = -2$, and $c = -3$.

Tip: When dealing with complex fractions, simplify the numerator and denominator separately before dividing.