Rational Expressions and Equations

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 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 process for simplifying a rational expression?

Back

Factor both the numerator and the denominator, then cancel any common factors.

Front

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

Back

The least common denominator is the smallest expression that can be used to combine fractions; it is important for adding or subtracting rational expressions.

Front

How do you add two rational expressions?

Back

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

Front

What is the difference between adding and subtracting rational expressions?

Back

The process is similar, but when subtracting, you must subtract the numerators after finding a common denominator.

Front

What is a polynomial?

Back

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

Front

What are the steps to solve a rational equation?

Back

1. Find a common denominator. 2. Multiply both sides by the common denominator. 3. Simplify and solve the resulting equation.

Front

What is a vertical asymptote in relation to rational expressions?

Back

A vertical asymptote occurs at the values of x that make the denominator zero, indicating where the function approaches infinity.