Multiplying 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 multiply rational expressions?

Back

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

Front

What is the first step in simplifying a rational expression?

Back

The first step is to factor both the numerator and the denominator.

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its lowest terms by canceling common factors.

Front

What is a common factor in rational expressions?

Back

A common factor is a term that appears in both the numerator and the denominator that can be canceled out.

Front

What is the product of (x+2)/(x+3) and (x+4)/(x+5)?

Back

The product is (x+2)(x+4)/((x+3)(x+5)).

Front

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

Back

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

Front

What is the importance of factoring in multiplying rational expressions?

Back

Factoring helps to identify and cancel common factors, making the multiplication and simplification easier.

Front

What happens if you multiply by zero in a rational expression?

Back

Multiplying by zero results in zero, which can lead to an undefined expression if it occurs in the denominator.

Front

What is the result of multiplying (2x)/(3) by (3)/(4x)?

Back

The result is (2)/(4) or 1/2 after simplification.