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

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its simplest form by canceling common factors in the numerator and denominator.

Front

What is the first step in simplifying the expression (2x² - 98)/(2x² + 18x + 28)?

Back

Factor both the numerator and the denominator.

Front

What is the factored form of the numerator 2x² - 98?

Back

2(x² - 49) = 2(x - 7)(x + 7).

Front

What is the factored form of the denominator 2x² + 18x + 28?

Back

2(x² + 9x + 14) = 2(x + 2)(x + 7).

Front

How do you find excluded values in a rational expression?

Back

Excluded values are found by setting the denominator equal to zero and solving for x.

Front

What is the excluded value for the expression 7/(x - 3)?

Back

The excluded value is 3.

Front

Simplify the expression (5x² + 21x + 4)/(25x + 100). What is the result?

Back

(5x + 1)/25.

Front

What is the simplified form of (x² - 49)/(x² + 9x + 14)?

Back

(x - 7)/(x + 2).

Front

What is the factored form of the expression x² + 11x + 24?

Back

(x + 3)(x + 8).