Solve 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/or 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 multiply every term in the equation by the LCD to eliminate the denominators.

Front

What does cross-multiplying mean in solving rational equations?

Back

Cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction to create a new equation without fractions.

Front

Solve the equation: 1/(x - 2) = 3/x. What is x?

Back

x = 6.

Front

What is the solution to the equation: 2/(x + 1) = 4/(x - 1)?

Back

x = -10.

Front

If a rational equation has no solution, what does that imply about the denominators?

Back

It implies that the denominators lead to a contradiction, such as dividing by zero.

Front

What is the importance of checking for extraneous solutions in rational equations?

Back

Checking for extraneous solutions is important because some solutions may not satisfy the original equation due to restrictions from the denominators.

Front

Solve for x: 3/(x + 2) = 1/4. What is x?

Back

x = 10.