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/or denominator is a polynomial.

Front

What does it mean to solve by cross-multiplying?

Back

Cross-multiplying is a method used to solve equations of the form a/b = c/d by multiplying the numerator of one fraction by the denominator of the other, leading to ad = bc.

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

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 the Least Common Denominator (LCD)?

Back

The Least Common Denominator (LCD) is the smallest multiple that is common to the denominators of two or more fractions, used to eliminate fractions in equations.

Front

How do you solve a rational equation using the LCD?

Back

To solve using the LCD, multiply every term in the equation by the LCD to eliminate the denominators, then solve the resulting equation.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify the denominators and determine the LCD to eliminate fractions.

Front

What does it mean if a rational equation has no solution?

Back

If a rational equation has no solution, it means that there are no values for the variable that satisfy the equation, often due to contradictions.

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 the general form of a rational equation?

Back

The general form of a rational equation is P(x)/Q(x) = R(x)/S(x), where P, Q, R, and S are polynomials.