Question: Subtract the following:
1) $\frac{5}{8}a - \frac{2}{8}a$
2) $\frac{7}{3}x - \frac{2}{4}y$
3) $\frac{6}{x} + 4 - \frac{2}{x} - 1$
4) $\frac{4}{x} - 2 - \frac{1}{x} + 5$
5) $\frac{7}{x^2} - 16 - \frac{3}{x} - 4$
1. **Problem:** Subtract $\frac{2}{8}a$ from $\frac{5}{8}a$.
Since both terms have the same denominator and variable, subtract the numerators:
$$\frac{5}{8}a - \frac{2}{8}a = \frac{5-2}{8}a = \frac{3}{8}a$$
2. **Problem:** Subtract $\frac{2}{4}y$ from $\frac{7}{3}x$.
These terms have different variables and denominators, so they cannot be combined. The expression remains:
$$\frac{7}{3}x - \frac{2}{4}y$$
3. **Problem:** Subtract $\frac{2}{x} + 1$ from $\frac{6}{x} + 4$.
Group like terms:
$$\left(\frac{6}{x} - \frac{2}{x}\right) + (4 - 1)$$
Subtract fractions with common denominator $x$:
$$\frac{6-2}{x} + 3 = \frac{4}{x} + 3$$
4. **Problem:** Subtract $\frac{1}{x} - 5$ from $\frac{4}{x} - 2$.
Group like terms:
$$\left(\frac{4}{x} - \frac{1}{x}\right) + (-2 - (-5))$$
Simplify:
$$\frac{4-1}{x} + (-2 + 5) = \frac{3}{x} + 3$$
5. **Problem:** Subtract $\frac{3}{x} + 4$ from $\frac{7}{x^2} - 16$.
Group terms:
$$\frac{7}{x^2} - 16 - \frac{3}{x} - 4 = \frac{7}{x^2} - \frac{3}{x} - (16 + 4)$$
Simplify constants:
$$\frac{7}{x^2} - \frac{3}{x} - 20$$