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 is a polynomial.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify any restrictions on the variable that would make the denominator zero, as these values are excluded from the solution.

Front

How do you find the least common denominator (LCD) in a rational equation?

Back

The least common denominator is found by determining the least common multiple of the denominators of all the rational expressions in the equation.

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

How do you check for extraneous solutions in rational equations?

Back

To check for extraneous solutions, substitute the solution back into the original equation to see if it holds true.

Front

What are excluded values in rational equations?

Back

Excluded values are the values of the variable that make any denominator in the equation equal to zero, which cannot be included in the solution set.

Front

What is the process for solving a rational equation?

Back

1. Identify excluded values. 2. Find the least common denominator. 3. Multiply through by the LCD to eliminate fractions. 4. Solve the resulting equation. 5. Check for extraneous solutions.

Front

What is the significance of factoring in solving rational equations?

Back

Factoring helps simplify rational expressions and can make it easier to identify common factors and excluded values.

Front

How do you handle rational equations with multiple fractions?

Back

Combine the fractions by finding a common denominator, or multiply through by the least common denominator to eliminate the fractions.

Front

What is the role of cross-multiplication in solving rational equations?

Back

Cross-multiplication can be used to eliminate fractions by multiplying the numerator of one side by the denominator of the other side.