# Adding and subtracting rational expressions

##### Examples
###### Lessons
1. Simplify:
1. $\frac{3}{{13}} + \frac{8}{{13}}$
2. $\frac{3}{2} + \frac{4}{5}$
2. Simplify:
1. $\frac{x}{6} + \frac{{2x}}{3} - \frac{{5x}}{4}$
2. $\frac{{y - 3}}{3} + \frac{{2y + 3}}{6}$
3. $\frac{{3a - 5}}{3} - \frac{{2a - 1}}{2}$
3. Simplify:
1. $\frac{{5x - 3}}{9} + 6x - \frac{{3x - 2}}{3}$
2. $3 - \frac{{y - 1}}{4} - \frac{{4 - 3y}}{6}$
4. Adding and Subtracting with Common Denominators
State any restrictions on the variables, then simplify:
1. $\frac{3}{x} + \frac{{12}}{x} - \frac{5}{x}$
2. $\frac{{6a - 2}}{{3a}} + \frac{{ - 10a + 2}}{{3a}}$
3. $\frac{{6m}}{{6m - 5}} - \frac{5}{{6m - 5}}$
4. $\frac{{9x - 1}}{{2x - 3}} - \frac{{8 + 3x}}{{2x - 3}}$
5. Adding and Subtracting with Different Monomial Denominators
State any restrictions on the variables, then simplify:
1. $\frac{3}{{4m}} + \frac{2}{{5m}}$
2. $\frac{5}{{4x}} - \frac{7}{6}$
3. $\frac{{2x - 3}}{{10x}} - \frac{{3x - 2}}{{5x}}$
4. $\frac{{y - 1}}{{3y}} - \frac{2}{{2{y^2}}}$
6. Adding and Subtracting with Different Monomial/Binomial Denominators
State any restrictions on the variables, then simplify:
1. $\frac{{x - 4}}{{3x}} + \frac{{5x}}{{x - 2}}$
2. $\frac{5}{{3m + 2}} - \frac{1}{{4m - 7}}$
3. $\frac{6x-1}{2x+3}-\frac{1-x}{4x+5}$
7. State any restrictions on the variables, then simplify: $\frac{1}{{x + 2}} - \frac{5}{{x - 1}} + \frac{3}{x}$
1. Denominators with Factors in Common
State any restrictions on the variables, then simplify:
1. $\frac{5}{{4x}} - \frac{5}{{12x}}$
2. $\frac{4}{{3x + 9}} + \frac{5}{{2x + 6}}$
3. $\frac{3}{{{x^2} - 5x}} - \frac{8}{{{x^2}}}$
2. Denominators with Factors in Common
State any restrictions on the variables, then simplify: $\frac{5}{{\left( {x - 1} \right)\left( {x + 3} \right)}} + \frac{4}{{\left( {x + 2} \right)\left( {x - 1} \right)}}$
1. State any restrictions on the variables, then simplify: $\frac{x}{{{x^2} - 9}} + \frac{5}{{x - 3}}$
1. State any restrictions on the variables, then simplify:
1. $\frac{4}{{x - 3}} - \frac{{5 - x}}{{{x^2} - 2x - 3}}$
2. $\frac{3}{{{a^2} - a - 2}} + \frac{5}{{{a^2} + 3a + 2}}$
3. $\frac{1}{{{x^2} + 4x + 4}} - \frac{4}{{{x^2} + 5x + 6}}$
2. State any restrictions on the variables, then simplify: $\frac{{{x^2} - 5x + 6}}{{{x^2} - 2x - 3}} - \frac{{{x^2} + 9x + 20}}{{{x^2} + 7x + 10}}$