Question: Add and Subtract Rational Expressions
Simplify each expression.
1) $\frac{x + 3y}{25x^3y} - \frac{x + y}{25x^3y}$
2) $\frac{x + y}{16y} + \frac{x + 3y}{16y}$
3) $\frac{4}{4y^2x^2} + \frac{2}{4y^2x^2}$
4) $\frac{3}{15p + 6} - \frac{p - 3}{15p + 6}$
5) $\frac{5x - 4}{x^2 + x - 20} + \frac{x - 3}{x^2 + x - 20}$
6) $\frac{n + 4}{4n^2 + 17n + 4} - \frac{n + 3}{4n^2 + 17n + 4}$
7) $\frac{2b}{2a} - \frac{3}{6a}$
8) $\frac{4}{6y} + \frac{3x}{2y^3}$
9) $\frac{3}{4x^2} - \frac{5y}{6y}$
10) $\frac{4a}{4ab} - \frac{3b}{2b^2}$
11) $\frac{6v}{3} + \frac{4}{9v - 12}$
12) $\frac{2b}{2} + \frac{b - 1}{2b + 6}$
13) $\frac{6}{x + 6} - \frac{4}{x - 1}$
14) $\frac{3}{a - 1} + \frac{5}{a + 4}$
15) $\frac{6}{2} - \frac{6k - 2}{9k + 6}$
16) $\frac{4}{n + 3} - \frac{6n}{4n^3}$
1. **Problem:** Simplify $\frac{x + 3y}{25x^3y} - \frac{x + y}{25x^3y}$.
2. **Formula:** When subtracting rational expressions with the same denominator, subtract the numerators and keep the denominator.
3. **Work:**
$$\frac{x + 3y}{25x^3y} - \frac{x + y}{25x^3y} = \frac{(x + 3y) - (x + y)}{25x^3y} = \frac{x + 3y - x - y}{25x^3y} = \frac{2y}{25x^3y}$$
4. **Simplify:** Cancel $y$ in numerator and denominator:
$$\frac{\cancel{2y}}{25x^3\cancel{y}} = \frac{2}{25x^3}$$
5. **Answer:** $\boxed{\frac{2}{25x^3}}$