Simplifying Rational Expressions

Front

What is the GCF of the expression 3x^2 + 18x + 15?

Back

The GCF is 3.

Front

What values of x must be excluded in the expression \( \frac{2x(x-2)}{(x-2)(x+5)} \) to prevent division by zero?

Back

The values to exclude are 2 and -5.

Front

Find the LCD of the rational expressions \( \frac{2x}{x+1} \) and \( \frac{1}{x^2-1} \).

Back

The LCD is (x+1)(x-1).

Front

What are the vertical asymptotes (VA) of the expression \( \frac{x^2+6x}{x^2+3x-18} \)?

Back

The VAs are -6 and 3.

Front

Which value of x makes the expression \( \frac{1}{x+2} \) undefined?

Back

The value that makes it undefined is -2.

Front

Define a rational expression.

Back

A rational expression is a fraction where the numerator and the denominator are polynomials.

Front

What is the process of simplifying a rational expression?

Back

To simplify a rational expression, factor the numerator and denominator and cancel out common factors.

Front

What does it mean for a rational expression to be undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

How do you find the GCF of two or more terms?

Back

The GCF is found by identifying the largest factor that divides all terms.

Front

What is the difference between a vertical asymptote and a hole in a rational function?

Back

A vertical asymptote occurs where the function approaches infinity, while a hole occurs where a factor cancels out.