Simplify, Multiply, Divide 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 out any common factors.

Front

What is the first step in multiplying rational expressions?

Back

The first step is to factor all numerators and denominators.

Front

How do you multiply two rational expressions?

Back

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.

Front

What does it mean to find the least common denominator (LCD)?

Back

The least common denominator is the smallest expression that can be used as a common denominator for two or more rational expressions.

Front

How do you add rational expressions?

Back

To add rational expressions, first find a common denominator, then combine the numerators and simplify.

Front

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

Back

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

Front

What is a polynomial?

Back

A polynomial is an expression made up of variables, coefficients, and non-negative integer exponents.

Front

What is factoring in the context of rational expressions?

Back

Factoring is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.