Simplifying 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 cancel in a rational expression?

Back

Cancelling means removing common factors from the numerator and denominator.

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 - 9)/(x + 9).

Back

The expression is already in its simplest form.

Front

What is the simplified form of (2x^2 - 98)/(2x^2 + 18x + 28)?

Back

The simplified form is (x - 7)/(x + 2).

Front

What does it mean if a rational expression can't be simplified?

Back

It means there are no common factors in the numerator and denominator.

Front

What is the result of simplifying 1/(x + 9)?

Back

The expression is already in its simplest form.