Operations with Rational Expressions Flashcard

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 different denominators?

Back

To add rational expressions with different denominators, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest expression that can be used as a common denominator for a set of rational expressions.

Front

What is the process for subtracting rational expressions?

Back

Similar to addition, subtracting rational expressions involves finding a common denominator, rewriting each expression, and then subtracting the numerators.

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 does it mean to multiply rational expressions?

Back

Multiplying rational expressions involves multiplying the numerators together and the denominators together, then simplifying if possible.

Front

What is the formula for adding two rational expressions?

Back

For two rational expressions \( \frac{a}{b} + \frac{c}{d} \), the formula is \( \frac{ad + bc}{bd} \).

Front

What is the formula for subtracting two rational expressions?

Back

For two rational expressions \( \frac{a}{b} - \frac{c}{d} \), the formula is \( \frac{ad - bc}{bd} \).

Front

What is the formula for multiplying two rational expressions?

Back

For two rational expressions \( \frac{a}{b} \times \frac{c}{d} \), the formula is \( \frac{ac}{bd} \).

Front

What is the formula for dividing two rational expressions?

Back

For two rational expressions \( \frac{a}{b} \div \frac{c}{d} \), the formula is \( \frac{a}{b} \times \frac{d}{c} \).