4.2 Rational Expressions Operations

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 multiply two rational expressions?

Back

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

Front

What is the process for simplifying a rational expression?

Back

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

Front

What is a common denominator?

Back

A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be combined or compared.

Front

How do you find the least common denominator (LCD) of multiple fractions?

Back

To find the least common denominator, determine the least common multiple (LCM) of the denominators.

Front

What is the lowest common denominator of 9, 8, and 12?

Back

The lowest common denominator of 9, 8, and 12 is 72.

Front

How do you divide rational expressions?

Back

To divide rational expressions, multiply by the reciprocal of the divisor and simplify.

Front

What is the reciprocal of a fraction?

Back

The reciprocal of a fraction is obtained by swapping its numerator and denominator.

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to reduce it to its simplest form, removing any unnecessary factors or terms.

Front

What is the significance of factoring in rational expressions?

Back

Factoring is significant because it allows for the identification and cancellation of common factors in the numerator and denominator.