Adding and Subtracting 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

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

Back

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

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 least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest multiple that is common to the denominators of two or more rational expressions.

Front

How do you find the LCD of \( \frac{1}{x} \) and \( \frac{1}{x^2} \)?

Back

The LCD of \( \frac{1}{x} \) and \( \frac{1}{x^2} \) is \( x^2 \).

Front

What is the process for adding \( \frac{2}{x} + \frac{3}{x^2} \)?

Back

1. Find the LCD, which is \( x^2 \). 2. Rewrite \( \frac{2}{x} \) as \( \frac{2x}{x^2} \). 3. Add: \( \frac{2x + 3}{x^2} \).

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents.

Front

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its lowest terms by canceling common factors in the numerator and denominator.

Front

How do you simplify \( \frac{4x^2}{8x} \)?

Back

1. Factor out common terms: \( \frac{4x^2}{8x} = \frac{4}{8} \cdot \frac{x^2}{x} = \frac{1}{2} \cdot x = \frac{x}{2} \).