Operations with 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

What is the first step when adding or subtracting rational expressions?

Back

Determine a Least Common Denominator (LCD).

Front

How do you find the Least Common Denominator (LCD) of two rational expressions?

Back

Factor the denominators and take the highest power of each factor.

Front

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its lowest terms by canceling common factors.

Front

What is the process for multiplying rational expressions?

Back

Multiply the numerators together and the denominators together, then simplify if possible.

Front

What is the process for dividing rational expressions?

Back

Multiply by the reciprocal of the divisor and then simplify.

Front

How do you add two rational expressions with different denominators?

Back

Find the LCD, rewrite each expression with the LCD, then add the numerators.

Front

What is a common mistake when adding rational expressions?

Back

A common mistake is to add the numerators directly without finding a common denominator.

Front

What is the result of simplifying (x^2 - 9)/(x + 3)?

Back

The result is (x - 3) after factoring the numerator.

Front

What is the result of simplifying 1/(x^2 - 9)?

Back

The result is 1/((x - 3)(x + 3)) after factoring the denominator.