Simplify Rational Expressions

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 to reduce a fraction?

Back

To reduce a fraction means to simplify it to its lowest terms by dividing both the numerator and the denominator by their greatest common factor.

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor is the largest factor that two or more numbers share.

Front

Simplify the expression: (x^2 - 1)/(x - 1)

Back

x + 1 (after factoring the numerator as (x - 1)(x + 1) and canceling the common factor).

Front

What is the difference between a proper and improper fraction?

Back

A proper fraction has a numerator smaller than the denominator, while an improper fraction has a numerator larger than or equal to the denominator.

Front

What is the result of dividing two rational expressions?

Back

To divide two rational expressions, multiply the first expression by the reciprocal of the second expression.

Front

Simplify: (2x)/(4x^2)

Back

1/(2x) (after canceling the common factor of 2x).

Front

What is a polynomial?

Back

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

Front

What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors.