Operations with Rational Expressions

Front

What are rational expressions?

Back

Rational expressions are fractions where the numerator and the denominator are both polynomials.

Front

How do we find the restrictions of a rational expression?

Back

We set the denominator equal to zero and solve for the variable.

Front

What is a restriction in the context of rational expressions?

Back

A value of a variable that makes the expression mathematically illegal.

Front

What is the first step in simplifying a rational expression?

Back

Factor both the numerator and the denominator.

Front

What happens if you divide by zero in a rational expression?

Back

The expression is undefined.

Front

What is the difference between a hole and a vertical asymptote in a rational expression?

Back

A hole occurs when a factor cancels out, while a vertical asymptote occurs when the denominator approaches zero but does not cancel.

Front

How do you add two rational expressions?

Back

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

Front

What is the process for subtracting rational expressions?

Back

Similar to addition, find a common denominator, rewrite each expression, and subtract the numerators.

Front

How do you multiply two rational expressions?

Back

Multiply the numerators together and the denominators together, then simplify.

Front

What is the process for dividing rational expressions?

Back

Multiply by the reciprocal of the second expression.