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 multiply 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 adding rational expressions with different denominators?

Back

Find a common denominator, rewrite each expression, then add the numerators and simplify.

Front

What does it mean for a rational expression to be undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

How do you find the values that make a rational expression undefined?

Back

Set the denominator equal to zero and solve for the variable.

Front

What is the first step in simplifying a rational expression?

Back

Factor both the numerator and the denominator.

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; an improper one has a degree of the numerator greater than or equal to the degree of the denominator.

Front

How do you simplify the expression (x^2 - 9)/(x^2 - 6x + 9)?

Back

Factor to get (x + 3)(x - 3)/((x - 3)(x - 3)), which simplifies to (x + 3)/(x - 3) for x ≠ 3.

Front

What is the least common denominator (LCD) of the expressions 1/(x-2) and 1/(x+3)?

Back

The LCD is (x - 2)(x + 3).

Front

How do you divide rational expressions?

Back

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