# Adding and subtracting rational expressions

#### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

#### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

#### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/1
0/28
##### 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: $\frac{{{x^2} - 5x + 6}}{{{x^2} - 2x - 3}} - \frac{{{x^2} + 9x + 20}}{{{x^2} + 7x + 10}}$
###### Topic Notes
When adding and subtracting rational expressions, the denominators of the expressions will dictate how we solve the questions. Different denominators in the expressions, for example, common denominators, different monomial/binomial denominators, and denominators with factors in common, will require different treatments. In addition, we need to keep in mind the restrictions on variables.