Operations and Solving 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 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 to find the least common denominator (LCD)?

Back

The least common denominator is the smallest multiple that is common to the denominators of two or more fractions.

Front

How do you add rational expressions with different denominators?

Back

To add rational expressions with different denominators, first find the least common denominator, rewrite each fraction with the LCD, and then combine the numerators.

Front

What is the process for dividing rational expressions?

Back

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

Front

What is the first step in solving a rational equation?

Back

The first step in solving a rational equation is to find a common denominator and eliminate the fractions.

Front

How do you solve for a variable in a rational expression?

Back

To solve for a variable in a rational expression, isolate the variable on one side of the equation, often by cross-multiplying.

Front

What is the significance of factoring in rational expressions?

Back

Factoring is crucial in rational expressions as it allows for simplification and solving equations by canceling common factors.

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 simplify a complex fraction?

Back

To simplify a complex fraction, find a common denominator for the fractions in the numerator and denominator, then simplify.