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 a common denominator?

Back

A common denominator is a shared multiple of the denominators of two or more fractions.

Front

How do you find the least common denominator (LCD) of two rational expressions?

Back

The least common denominator (LCD) is the smallest multiple that is common to both denominators.

Front

What is the process of simplifying a rational expression?

Back

Simplifying a rational expression involves factoring the numerator and denominator and then canceling out 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

What is the formula for adding two rational expressions \( \frac{a}{b} + \frac{c}{d} \)?

Back

The formula is: \( \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \).

Front

What is the importance of checking for extraneous solutions when solving rational equations?

Back

Checking for extraneous solutions is important because some solutions may not satisfy the original equation due to restrictions in the denominators.