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

How do you simplify a rational expression?

Back

To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.

Front

What is the first step in simplifying (x²+6x+8)/(x²-x-6)?

Back

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

Front

What are the factors of x²+6x+8?

Back

The factors are (x+2)(x+4).

Front

What are the factors of x²-x-6?

Back

The factors are (x-3)(x+2).

Front

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

Back

When you cancel common factors, you simplify the expression to its lowest terms.

Front

Simplify the expression (x²+11x+24)/(x²+4x-32). What is the first step?

Back

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

Front

What are the factors of x²+11x+24?

Back

The factors are (x+3)(x+8).

Front

What are the factors of x²+4x-32?

Back

The factors are (x+8)(x-4).