Embark on an intellectual journey with our ‘Add and Subtract Rational Expressions Worksheet’, a meticulously crafted guide that unveils the intricacies of rational expressions. Delve into the world of fractions and learn to manipulate them with precision, unlocking the secrets of adding and subtracting these enigmatic mathematical entities.
This worksheet empowers you with a comprehensive understanding of rational expressions, equipping you with the tools to tackle complex mathematical challenges with confidence.
Understanding Rational Expressions
Rational expressions represent fractions of algebraic expressions. They consist of a numerator and a denominator, where the denominator cannot be zero. Rational expressions can be simplified, added, subtracted, multiplied, and divided.
Examples of Rational Expressions
- (x + 2)/(x – 3)
- (2x^2 – 5x + 3)/(x^2 – 4)
- 1/(x + y)
Operations on Rational Expressions
Rational expressions can be added, subtracted, multiplied, and divided. The operations follow the rules of algebra, but the denominators must be considered carefully.
Adding Rational Expressions
Adding Rational Expressions with the Same Denominator
To add rational expressions with the same denominator, simply add the numerators and keep the denominator the same.
Adding Rational Expressions with Different Denominators
To add rational expressions with different denominators, find a common denominator. Then, rewrite each expression with the common denominator and add the numerators.
Examples of Adding Rational Expressions
- (x + 2)/(x – 3) + (x – 1)/(x – 3) = (x + 2 + x – 1)/(x – 3) = (2x + 1)/(x – 3)
- (2x^2 – 5x + 3)/(x^2 – 4) + (x^2 – 4)/(x^2 – 4) = (2x^2 – 5x + 3 + x^2 – 4)/(x^2 – 4) = (3x^2 – 5x – 1)/(x^2 – 4)
Subtracting Rational Expressions
Subtracting Rational Expressions with the Same Denominator
To subtract rational expressions with the same denominator, simply subtract the numerators and keep the denominator the same.
Subtracting Rational Expressions with Different Denominators
To subtract rational expressions with different denominators, find a common denominator. Then, rewrite each expression with the common denominator and subtract the numerators.
Examples of Subtracting Rational Expressions
- (x + 2)/(x – 3) – (x – 1)/(x – 3) = (x + 2 – x + 1)/(x – 3) = (3)/(x – 3)
- (2x^2 – 5x + 3)/(x^2 – 4) – (x^2 – 4)/(x^2 – 4) = (2x^2 – 5x + 3 – x^2 + 4)/(x^2 – 4) = (x^2 – 5x + 7)/(x^2 – 4)
Worksheet Examples
Table of Addition and Subtraction of Rational Expressions, Add and subtract rational expressions worksheet
| Expression | Simplified |
|---|---|
(x + 2)/(x
|
(2x + 1)/(x
|
(2x^2
|
(3x^2
|
(x + 2)/(x
|
(3)/(x
|
(2x^2
|
(x^2
|
Worksheet Problems
Add or subtract the following rational expressions:
- (x + 2)/(x
- 3) + (x
- 1)/(x
- 3)
- (2x^2
- 5x + 3)/(x^2
- 4) + (x^2
- 4)/(x^2
- 4)
- (x + 2)/(x
- 3)
- (x
- 1)/(x
- 3)
- (2x^2
- 5x + 3)/(x^2
- 4)
- (x^2
- 4)/(x^2
- 4)
Worksheet Solutions
- (2x + 1)/(x – 3)
- (3x^2 – 5x – 1)/(x^2 – 4)
- (3)/(x – 3)
- (x^2 – 5x + 7)/(x^2 – 4)
Essential Questionnaire: Add And Subtract Rational Expressions Worksheet
What are rational expressions?
Rational expressions are mathematical expressions that represent the quotient of two polynomials.
How do I add rational expressions with the same denominator?
To add rational expressions with the same denominator, simply add the numerators and keep the denominator the same.
How do I subtract rational expressions with different denominators?
To subtract rational expressions with different denominators, first find a common denominator. Then, rewrite the expressions with the common denominator and subtract the numerators.
