Simplify 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 (8x + 32)/(x + 4)?

Back

Factor the numerator: 8(x + 4)/(x + 4).

Front

What happens when you cancel common factors in a rational expression?

Back

When you cancel common factors, you simplify the expression, making it easier to work with.

Front

Simplify the expression (x² + 11x + 24)/(x² + 4x - 32).

Back

(x + 3)/(x - 4).

Front

What is the result of simplifying (x² - 8x)/(x - 8)?

Back

x.

Front

How do you factor the polynomial x² + 11x + 24?

Back

It factors to (x + 3)(x + 8).

Front

What is the significance of identifying common factors in rational expressions?

Back

Identifying common factors allows for simplification, which can make solving equations easier.

Front

What is the simplified form of (4x³)/(x + 2)?

Back

4x³/(x + 2) is already in its simplest form.

Front

What is the process of factoring a polynomial?

Back

Factoring a polynomial involves rewriting it as a product of its factors.