# Adding and Subtracting Rational Expressions: A Comprehensive Guide Unlock the secrets of rational expressions! Learn step-by-step methods for adding, subtracting, and simplifying complex fractions. Boost your algebra skills and conquer challenging math problems with confidence.

Examples

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**Adding and Subtracting with Common Denominators**

State any restrictions on the variables, then simplify:**Adding and Subtracting with Different Monomial Denominators**

State any restrictions on the variables, then simplify:**Adding and Subtracting with Different Monomial/Binomial Denominators**

State any restrictions on the variables, then simplify:- State any restrictions on the variables, then simplify: $\frac{1}{{x + 2}} - \frac{5}{{x - 1}} + \frac{3}{x}$
**Denominators with Factors in Common**

State any restrictions on the variables, then simplify:**Denominators with Factors in Common**

State any restrictions on the variables, then simplify: $\frac{5}{{\left( {x - 1} \right)\left( {x + 3} \right)}} + \frac{4}{{\left( {x + 2} \right)\left( {x - 1} \right)}}$- State any restrictions on the variables, then simplify: $\frac{x}{{{x^2} - 9}} + \frac{5}{{x - 3}}$
- State any restrictions on the variables, then simplify:
- State any restrictions on the variables, then simplify: $\frac{{{x^2} - 5x + 6}}{{{x^2} - 2x - 3}} - \frac{{{x^2} + 9x + 20}}{{{x^2} + 7x + 10}}$