Add and Subtract Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are polynomials.

Front

How do you add rational expressions with the same denominator?

Back

To add rational expressions with the same denominator, combine the numerators and keep the denominator the same: \( \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} \).

Front

How do you subtract rational expressions with the same denominator?

Back

To subtract rational expressions with the same denominator, subtract the numerators and keep the denominator the same: \( \frac{a}{c} - \frac{b}{c} = \frac{a-b}{c} \).

Front

What is the first step in adding or subtracting rational expressions with different denominators?

Back

The first step is to find a common denominator for the rational expressions.

Front

How do you find a common denominator for two rational expressions?

Back

The common denominator is the least common multiple (LCM) of the denominators of the rational expressions.

Front

What is the process to add rational expressions with different denominators?

Back

1. Find the common denominator. 2. Rewrite each expression with the common denominator. 3. Add the numerators and simplify.

Front

What is the process to subtract rational expressions with different denominators?

Back

1. Find the common denominator. 2. Rewrite each expression with the common denominator. 3. Subtract the numerators and simplify.

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its lowest terms by factoring and canceling common factors.

Front

What is the importance of factoring in adding and subtracting rational expressions?

Back

Factoring helps to identify common factors and simplify expressions, making it easier to add or subtract them.

Front

What is an example of a rational expression?

Back

An example of a rational expression is \( \frac{x^2 - 1}{x + 1} \).