Let's break down and solve each part of the problem you've given:

1. Subtract $\frac{7}{12}$ from $\frac{5}{6}$:

To subtract these fractions, we first need to find a common denominator:

• The common denominator between 12 and 6 is 12.
• $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$

Now, subtract:

$\frac{10}{12} - \frac{7}{12} = \frac{3}{12} = \frac{1}{4}$

2. Simplify the complex expression (not clear from your query). The likely interpretation: $\frac{1}{12} \cdot \frac{1}{32} \cdot \frac{1}{31} \cdot \frac{1}{2}$:

Simplify:

$\frac{1}{12 \times 32 \times 31 \times 2}$

This simplifies to:

$\frac{1}{23808}$

3. Solve for $x$ when $\frac{x}{4} = \frac{3}{5}$:

Cross-multiply:

$5x = 12$

So:

$x = \frac{12}{5} = 2.4$

4. Evaluate expressions using $X = 3a + b$ and $Y = a^2 - a + b$ when $a = 4$ and $b = -1$:

First, calculate $X$ and $Y$:

• $X = 3(4) + (-1) = 12 - 1 = 11$
• $Y = (4)^2 - 4 + (-1) = 16 - 4 - 1 = 11$

Sum $X + Y$:

$X + Y = 11 + 11 = 22$

Difference $X - Y$:

$X - Y = 11 - 11 = 0$

5. Find $X - Y$ in terms of $a$ and $b$:

Given the expression $X = 3a + b$ and $Y = a^2 - a + b$, the difference $X - Y$:

$X - Y = (3a + b) - (a^2 - a + b) = 3a + b - a^2 + a - b = 4a - a^2$

Summary of Solutions:

1. $\frac{1}{4}$
2. $\frac{1}{23808}$
3. $x = 2.4$
4. $X + Y = 22$
5. $X - Y = 4a - a^2$

Would you like a detailed breakdown of any part of these solutions?

Questions:

1. What is the next step to subtract fractions with different denominators?
2. How do you multiply fractions with multiple factors?
3. What is the importance of cross-multiplication when solving proportions?
4. How does the quadratic expression change when substituting values for variables?
5. How can you determine the value of $X - Y$ using algebraic manipulation?

Tip: When dealing with fractions, always ensure that you simplify your result to its lowest terms.