Rational Expressions and Equations

Front

What is a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are 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 any common factors.

Front

What is the process for adding rational expressions?

Back

To add rational expressions, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

Front

What is the process for subtracting rational expressions?

Back

To subtract rational expressions, find a common denominator, rewrite each expression with that denominator, and then subtract the numerators.

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

How do you divide rational expressions?

Back

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

Front

What is a common denominator?

Back

A common denominator is a shared multiple of the denominators of two or more fractions, used to perform addition or subtraction.

Front

What are the restrictions on the variable in a rational expression?

Back

The restrictions are the values that make the denominator equal to zero, as these values are not allowed.

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, while an improper rational expression has a degree of the numerator greater than or equal to the degree of the denominator.

Front

What does it mean to solve a rational equation?

Back

To solve a rational equation means to find the values of the variable that make the equation true, often requiring finding a common denominator and clearing fractions.