Multiplying and Dividing 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 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 first step in adding rational expressions?

Back

The first step is to find a common denominator.

Front

What is the formula for multiplying two rational expressions?

Back

To multiply two rational expressions, multiply the numerators together and the denominators together.

Front

What is the process for dividing rational expressions?

Back

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

Front

What does GCF stand for and why is it important in simplifying expressions?

Back

GCF stands for Greatest Common Factor; it is important because factoring out the GCF can simplify the expression.

Front

What is the result of dividing the rational expression \( \frac{x^2-4x-5}{x^2-3x+2} \) by \( \frac{x^2-3x-10}{x^2-4} \)?

Back

The result is \( \frac{x+1}{x-1} \).

Front

What is the significance of factoring in simplifying rational expressions?

Back

Factoring allows you to identify and cancel common factors, which simplifies the expression.

Front

What is a common mistake when adding rational expressions?

Back

A common mistake is failing to find a common denominator before adding.

Front

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

Back

The LCD is found by determining the least common multiple of the denominators.