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 denominator are polynomials.

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What are the steps to solve a rational equation?

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1. Identify the domain restrictions. 2. Find a common denominator. 3. Multiply both sides by the common denominator to eliminate fractions. 4. Solve the resulting equation. 5. Check for extraneous solutions.

Front

What are domain restrictions in rational equations?

Back

Domain restrictions are values that make the denominator of a rational expression equal to zero, which are not allowed in the solution.

Front

How do you find the domain of a rational expression?

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To find the domain, set the denominator equal to zero and solve for the variable. The solutions are excluded from the domain.

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What is an extraneous solution?

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An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

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How can you check if a solution is extraneous?

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Substitute the solution back into the original equation. If it does not satisfy the equation, it is extraneous.

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What is the importance of checking solutions in rational equations?

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Checking solutions is crucial because it ensures that the solutions are valid and do not violate any domain restrictions.

Front

What is a common denominator?

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A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be combined or compared.

Front

How do you find a common denominator for two fractions?

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To find a common denominator, identify the least common multiple (LCM) of the denominators.

Front

What is the least common multiple (LCM)?

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The least common multiple is the smallest multiple that is exactly divisible by each of the numbers in a set.