Flashcard-12: Rational Expressions & 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 does it mean for a rational expression to be undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

What is the process for solving rational equations?

Back

To solve rational equations, find a common denominator, eliminate the denominators, and solve the resulting equation.

Front

What is the importance of finding restrictions in rational expressions?

Back

Finding restrictions helps identify values that make the denominator zero, which are not allowed in the domain of the expression.

Front

How do you multiply rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together, then simplify.

Front

What is the formula 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 formula 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

What is a complex fraction?

Back

A complex fraction is a fraction where the numerator, the denominator, or both contain fractions.

Front

How do you solve for x in a rational equation?

Back

To solve for x, isolate x on one side of the equation after eliminating the denominators.