FOUNDATIONS 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 \( \frac{x^2 + 11x + 24}{x^2 + 4x - 32} \)?

Back

Factor both the numerator and the denominator.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

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

How do you identify common factors in rational expressions?

Back

Common factors can be identified by looking for the same polynomial factors in both the numerator and the denominator.

Front

What is the simplified form of \( \frac{(x + 3)(x + 8)}{(x + 8)(x - 4)} \)?

Back

The simplified form is \( \frac{x + 3}{x - 4} \).

Front

What is the importance of simplifying rational expressions?

Back

Simplifying rational expressions makes them easier to work with and helps in solving equations.

Front

What is the result of simplifying \( \frac{x^2 + 6x}{x^2 + 3x - 18} \)?

Back

The result is \( \frac{x}{x - 3} \).