11/21 Choice Day - 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?

Back

To subtract rational expressions, 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 least common denominator (LCD)?

Back

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

Front

How do you simplify a rational expression?

Back

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

Front

What is the process for finding 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 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 raised to the same power.

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 adding two rational expressions?

Back

Example: \( \frac{2}{3} + \frac{1}{3} = \frac{2 + 1}{3} = \frac{3}{3} = 1 \).