Simplifying/Multiplying/Dividing Rational Express w/asymptotes

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Front

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its simplest form by canceling common factors in the numerator and denominator.

Front

What is an asymptote in relation to rational expressions?

Back

An asymptote is a line that a graph approaches but never touches. For rational expressions, vertical asymptotes occur where the denominator is zero.

Front

How do you find vertical asymptotes of a rational expression?

Back

To find vertical asymptotes, set the denominator equal to zero and solve for the variable.

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 is the first step in simplifying a rational expression?

Back

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

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials.

Front

What is a common factor in the context of rational expressions?

Back

A common factor is a factor that appears in both the numerator and the denominator of a rational expression.

Front

How do you identify removable discontinuities in rational expressions?

Back

Removable discontinuities occur at values that make both the numerator and denominator zero; these can be canceled out.