Solving 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 the denominator are polynomials.

Front

What does it mean to solve a rational equation?

Back

To solve a rational equation means to find the values of the variable that make the equation true, often by eliminating the fractions.

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.

Front

How do you solve a rational equation using the LCD?

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To solve a rational equation using the LCD, multiply every term by the LCD to eliminate the fractions, then solve the resulting equation.

Front

What is the first step in solving a rational equation?

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

Front

What is the importance of simplifying rational expressions?

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Simplifying rational expressions makes it easier to solve equations and helps to identify any restrictions on the variable.

Front

What are restrictions in rational equations?

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Restrictions are values that the variable cannot take, usually because they would make a denominator equal to zero.

Front

How do you find the restrictions for a rational equation?

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To find restrictions, set each denominator equal to zero and solve for the variable.