Solving 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 it mean to eliminate the denominators in a rational equation?

Back

Eliminating the denominators means multiplying both sides of the equation by the least common denominator (LCD) to remove the fractions.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify and eliminate the denominators by multiplying through by the least common denominator.

Front

What should you check for after solving a rational equation?

Back

You should check for extraneous solutions, which are solutions that do not satisfy the original equation.

Front

How do you find the least common denominator (LCD) of two fractions?

Back

The least common denominator is found by determining the least common multiple (LCM) of the denominators of the fractions.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving the equation but does not satisfy the original equation.

Front

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

Back

x = 1/2.

Front

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

Back

x = -2.

Front

What is the importance of checking your solutions in rational equations?

Back

Checking solutions ensures that they do not make any denominators zero, which would make the equation undefined.

Front

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

Back

Multiplying by zero is not valid as it eliminates the equation's meaning and can lead to incorrect solutions.