Adding and Subtracting Rational Expressions Review

Front

What is a rational expression?

Back

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

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

Back

The first step is to find a common denominator, which is typically the least common multiple (LCM) of the denominators.

Front

How do you subtract rational expressions?

Back

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

Front

What is the formula for finding the least common denominator (LCD) of two fractions?

Back

The least common denominator (LCD) is the least common multiple (LCM) of the denominators of the fractions.

Front

What is the process for simplifying a rational expression?

Back

To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

Front

What does it mean to 'combine like terms' in rational expressions?

Back

Combining like terms means to add or subtract terms that have the same variable and exponent.

Front

How do you handle complex fractions?

Back

To simplify complex fractions, multiply the numerator and denominator by the least common denominator of the fractions within the complex fraction.

Front

What is an example of a rational expression?

Back

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

Front

What is the importance of checking for restrictions in rational expressions?

Back

Checking for restrictions is important because it identifies values that make the denominator zero, which are not allowed.