Mult. and Divide 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 does it mean to multiply rational expressions?

Back

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

Front

What does it mean to divide rational expressions?

Back

To divide rational expressions, multiply the first expression by the reciprocal of the second expression, then simplify if possible.

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 dividing rational expressions?

Back

The first step is to multiply by the reciprocal of the second rational expression.

Front

What is the significance of factoring in rational expressions?

Back

Factoring helps to identify and cancel common factors, making it easier to simplify the expression.

Front

What is the result of multiplying the rational expressions \( \frac{a}{b} \) and \( \frac{c}{d} \)?

Back

The result is \( \frac{ac}{bd} \).

Front

What is the result of dividing the rational expressions \( \frac{a}{b} \) by \( \frac{c}{d} \)?

Back

The result is \( \frac{a}{b} \cdot \frac{d}{c} = \frac{ad}{bc} \).

Front

What is the importance of identifying restrictions in rational expressions?

Back

Identifying restrictions is important to avoid division by zero, which is undefined.

Front

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

Back

The least common denominator is found by determining the least common multiple of the denominators of the rational expressions.