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 denominator are polynomials.

Front

What does it mean to solve by cross-multiplying?

Back

Cross-multiplying is a method used to eliminate fractions in a rational equation by multiplying the numerator of one fraction by the denominator of the other fraction.

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 identify the Least Common Denominator (LCD)?

Back

The LCD is the smallest expression that can be used as a common denominator for all fractions in an equation.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify and eliminate any fractions, often by finding the LCD and multiplying both sides of the equation by it.

Front

What is the solution to the equation 1/(x-2) = 3/4?

Back

x = 10/3.

Front

How do you check for extraneous solutions?

Back

Substitute the solution back into the original equation to see if it holds true.

Front

What is the process of solving for x in a rational equation?

Back

1. Clear fractions by multiplying by the LCD. 2. Simplify the equation. 3. Isolate x. 4. Check for extraneous solutions.

Front

What does it mean to solve using the LCD?

Back

It means to find a common denominator for all terms in the equation, allowing you to combine and simplify the equation.

Front

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

Back

x = 4/3.