Rational 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 denominator are polynomials.

Front

What does LCD stand for in the context of rational equations?

Back

LCD stands for Least Common Denominator, which is the smallest multiple of the denominators of the rational expressions involved.

Front

How do you find the LCD of the expressions x and (x - 2)?

Back

The LCD is x(x - 2), which is the product of the two distinct factors.

Front

What is the first step in solving a rational equation using the LCD?

Back

The first step is to identify the LCD of all the denominators in the equation.

Front

Solve for x: 1/(x - 2) + 1/x = 1. What is x?

Back

x = 2.

Front

What is the importance of clearing denominators in rational equations?

Back

Clearing denominators simplifies the equation, making it easier to solve.

Front

Solve for x using the LCD: 1/x + 1/(x - 2) = 1. What is x?

Back

x = 5/2.

Front

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

Back

Multiplying by the LCD eliminates the denominators, resulting in a polynomial equation.

Front

Identify the LCD for the rational expressions 1/(x^2) and 1/(x - 2).

Back

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

Front

Solve for v: 1/(v + 1) = 3/5. What is v?

Back

v = 4/5.