Simplifying/Multiplying/Dividing Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both 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 does it mean to multiply rational expressions?

Back

Multiplying rational expressions involves multiplying the numerators together and the denominators together, then simplifying if possible.

Front

What is the process for dividing rational expressions?

Back

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

Front

What is the first step in simplifying the expression (x^2 - 1)/(x^2 + 2x + 1)?

Back

Factor both the numerator and the denominator.

Front

What is the result of (x + 2)/(x + 3) * (x + 5)/(x + 1)?

Back

(x + 2)(x + 5)/((x + 3)(x + 1)) after multiplying.

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.

Front

What is the simplified form of (x^2 - 4)/(x^2 - 2x)?

Back

The simplified form is (x + 2)/(x) after factoring.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors.

Front

What is the significance of canceling common factors in rational expressions?

Back

Canceling common factors simplifies the expression and helps in finding the final answer.