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

How do you find the least common denominator (LCD) of rational expressions?

Back

To find the LCD, factor each denominator into its prime factors, then take the highest power of each factor that appears in any of the denominators.

Front

Back

x = -3

Front

Back

r = 3

Front

What is an extraneous solution?

Back

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

Front

Back

x = 5.4

Front

Back

LCD = x(x-2)

Front

What is the first step in solving a rational equation?

Back

The first step is to find the least common denominator (LCD) and multiply both sides of the equation by it to eliminate the fractions.

Front

Back

x = 0

Front

What should you do after finding potential solutions to a rational equation?

Back

You should substitute the potential solutions back into the original equation to check for extraneous solutions.