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/or 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?

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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)?

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

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Multiplying both sides of an equation by zero results in an undefined equation, as any number multiplied by zero is zero.

Front

What is a common mistake when solving rational equations?

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A common mistake is failing to check for extraneous solutions, which can lead to incorrect conclusions.

Front

What is the importance of checking solutions in rational equations?

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Checking solutions is important to ensure that the solutions are valid and do not make any denominators zero.