Solving Rational Equations (Simple)

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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 does it mean to check for extraneous solutions?

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Checking for extraneous solutions means verifying if the solutions obtained from solving the equation are valid by substituting them back into the original equation.

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How do you solve a rational equation by cross-multiplying?

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To solve by cross-multiplying, multiply the numerator of one fraction by the denominator of the other fraction and set the two products equal to each other.

Front

What is the first step in solving a rational equation?

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The first step is to identify any restrictions on the variable that would make the denominator zero.

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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 the equation but does not satisfy the original equation.

Front

How can you eliminate fractions in a rational equation?

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You can eliminate fractions by multiplying both sides of the equation by the least common denominator (LCD) of all the fractions involved.

Front

What is the least common denominator (LCD)?

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The least common denominator is the smallest multiple that is common to the denominators of two or more fractions.

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What is the importance of simplifying rational expressions before solving?

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Simplifying rational expressions can make the equation easier to solve and help identify any restrictions on the variable.

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What does it mean for a rational equation to have no solution?

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A rational equation has no solution if the equation simplifies to a contradiction, such as 0 = 5.

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What is the process of solving a rational equation?

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The process includes identifying restrictions, eliminating fractions, solving the equation, and checking for extraneous solutions.