simplify, multiply 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

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 process for multiplying rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together, then simplify 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 does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the least common denominator (LCD) and why is it important?

Back

The least common denominator is the smallest multiple of the denominators of two or more fractions, used to combine or compare fractions.

Front

What is the difference between a proper and improper rational expression?

Back

A proper rational expression has a degree of the numerator less than the degree of the denominator, while an improper rational expression has a degree of the numerator greater than or equal to the degree of the denominator.

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients.

Front

How do you find the domain of a rational expression?

Back

The domain of a rational expression is all real numbers except those that make the denominator equal to zero.

Front

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

Back

Canceling common factors simplifies the expression and can help in solving equations or inequalities.