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

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 (x^2 - 49)/(x^2 + 9x + 14)?

Back

Factor both the numerator and the denominator.

Front

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

Back

(x - 7)(x + 7) (Difference of squares)

Front

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

Back

(x + 2)(x + 7) (Sum of two numbers that multiply to 14)

Front

How do you identify common factors in rational expressions?

Back

Look for factors that appear in both the numerator and the denominator after factoring.

Front

What is the simplified form of (x^2 - 49)/(x^2 + 9x + 14)?

Back

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

Front

What is the significance of the expression (x^2 + 11x + 24)/(x^2 + 4x - 32)?

Back

It can be simplified to find the value of x in terms of its factors.

Front

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

Back

(x + 3)(x + 8) (Sum of two numbers that multiply to 24)

Front

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

Back

(x + 8)(x - 4) (Difference of squares)