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, then cancel any common factors.

Front

What is the first step in simplifying the expression (x^2 - 49)/(x^2 + 9x + 14)?

Back

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

Front

What is the factored form of x^2 - 49?

Back

The factored form is (x - 7)(x + 7), which is a difference of squares.

Front

What is the factored form of x^2 + 9x + 14?

Back

The factored form is (x + 2)(x + 7).

Front

What does it mean to cancel common factors in a rational expression?

Back

Canceling common factors means removing the same factor from both the numerator and the denominator.

Front

Simplify the expression (x^2 + 11x + 24)/(x^2 + 4x - 32). What is the first step?

Back

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

Front

What is the factored form of x^2 + 11x + 24?

Back

The factored form is (x + 3)(x + 8).

Front

What is the factored form of x^2 + 4x - 32?

Back

The factored form is (x + 8)(x - 4).

Front

What is the simplified form of (x^2 + 6x + 8)/(x^2 - x - 6)?

Back

The simplified form is (x + 4)/(x - 3).