LT 19 Rational Equation equations

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and the denominator are polynomials.

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest expression that can be used as a common denominator for a set of fractions.

Front

How do you find the LCD of the fractions \( \frac{1}{x} \) and \( \frac{1}{x-2} \)?

Back

The LCD is \( x(x-2) \).

Front

What happens when you multiply both sides of a rational equation by the LCD?

Back

Multiplying both sides by the LCD eliminates the fractions, making the equation easier to solve.

Front

What is a hole in the graph of a rational function?

Back

A hole occurs in the graph of a rational function at a point where a factor in the numerator and denominator cancels out.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line \( x = a \) where the function approaches infinity or negative infinity as it approaches \( a \).

Front

How do you identify vertical asymptotes in a rational function?

Back

Vertical asymptotes can be found by setting the denominator equal to zero and solving for \( x \).

Front

What is the difference between a hole and a vertical asymptote?

Back

A hole occurs when a factor cancels out, while a vertical asymptote occurs when the denominator is zero but the factor does not cancel.

Front

What is the general form of a rational function?

Back

The general form of a rational function is \( f(x) = \frac{P(x)}{Q(x)} \), where \( P(x) \) and \( Q(x) \) are polynomials.

Front

How do you solve a rational equation?

Back

To solve a rational equation, find the LCD, multiply both sides by the LCD, simplify, and then solve the resulting equation.