Rational Equations Review

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 solve a rational equation by cross-multiplying?

Back

Cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction to eliminate the fractions and simplify the equation.

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 combine or compare fractions.

Front

How do you find the LCD of x and (x + 5)?

Back

The LCD is x(x + 5), which is the product of the two denominators.

Front

What is the solution to the equation 1/(x + 5) = 1/6?

Back

x = -10, found by cross-multiplying.

Front

What is the solution to the equation 2/(x - 2) = 1/3?

Back

x = 8, found by cross-multiplying.

Front

How do you solve a rational equation using the LCD?

Back

Multiply each term of the equation by the LCD to eliminate the fractions, then solve the resulting equation.

Front

What is the solution to the equation 3/(x + 5) + 2/(x + 5) = 1?

Back

x = 0, found by combining fractions and solving.

Front

What is the importance of checking for extraneous solutions in rational equations?

Back

Checking for extraneous solutions is important because some solutions may make the original equation undefined.

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.