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

How do you divide rational expressions?

Back

To divide rational expressions, multiply the first expression by the reciprocal of the second expression.

Front

What is the reciprocal of a fraction?

Back

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

Front

Simplify the expression: (2x^2)/(4x) ÷ (x/3).

Back

(2x^2)/(4x) ÷ (x/3) = (2x^2)/(4x) * (3/x) = (6x)/(4) = (3/2) x.

Front

What is the first step in dividing rational expressions?

Back

The first step is to rewrite the division as multiplication by the reciprocal of the second expression.

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 in the numerator and denominator.

Front

What are common factors in polynomials?

Back

Common factors are terms that appear in both the numerator and denominator that can be canceled out.

Front

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

Back

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

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents.

Front

What is the importance of factoring in dividing rational expressions?

Back

Factoring is important because it allows you to identify and cancel common factors in the numerator and denominator.