Solve Rational Equations Practice

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

How do you solve a rational equation?

Back

To solve a rational equation, find a common denominator, eliminate the fractions by multiplying both sides by that denominator, and then solve the resulting equation.

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

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 check for extraneous solutions?

Back

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

Front

What is cross-multiplication?

Back

Cross-multiplication is a method used to solve equations involving fractions by multiplying the numerator of one fraction by the denominator of the other.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify the denominators and find the least common denominator (LCD) to eliminate the fractions.

Front

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

Back

Multiplying both sides of an equation by zero results in an equation that is always true (0=0), which does not help in finding a solution.

Front

What is the importance of checking solutions in rational equations?

Back

Checking solutions is important to ensure that the solutions are valid and not extraneous, which can occur due to the manipulation of the equation.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents.