Rational Expressions and Equations

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 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 multiplying rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together, then simplify if possible.

Front

What is the process for adding rational expressions with different denominators?

Back

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

Front

What is the difference between a proper and improper rational expression?

Back

A proper rational expression has a degree of the numerator less than the degree of the denominator, while an improper rational expression has a degree of the numerator greater than or equal to the degree of the denominator.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which can be numbers, variables, or other polynomials.

Front

What is the least common denominator (LCD)?

Back

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

Front

How do you find the LCD of two rational expressions?

Back

To find the LCD, factor each denominator and take the highest power of each factor that appears.

Front

What is a complex fraction?

Back

A complex fraction is a fraction where the numerator, the denominator, or both contain fractions.

Front

How do you simplify a complex fraction?

Back

To simplify a complex fraction, find a common denominator for the fractions in the numerator and denominator, then rewrite and simplify.