Simplifying 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 cancel in rational expressions?

Back

Cancelling means removing common factors from the numerator and denominator to simplify the expression.

Front

What is the first step in simplifying (2x^2 - 98)/(2x^2 + 18x + 28)?

Back

The first step is to factor both the numerator and the denominator.

Front

What is the factored form of 2x^2 - 98?

Back

The factored form is 2(x^2 - 49) = 2(x - 7)(x + 7).

Front

What is the factored form of 2x^2 + 18x + 28?

Back

The factored form is 2(x^2 + 9x + 14) = 2(x + 2)(x + 7).

Front

Simplify (x^2 - 9)/(x^2 - 81). What is the answer?

Back

The answer is (x + 3)/(x - 9).

Front

What is the result of simplifying (x - 9)/(x + 9)?

Back

The result is (x - 9)/(x + 9) (no further simplification possible).

Front

What happens if there are no common factors in a rational expression?

Back

If there are no common factors, the expression is already in its simplest form.

Front

What is the simplified form of (x^2 - 4)/(x^2 - 1)?

Back

The simplified form is (x - 2)/(x - 1).