Solving Rational Equations

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What is a rational equation?

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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.

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How do you solve a rational equation?

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To solve a rational equation, find a common denominator, eliminate the fractions by multiplying both sides by that denominator, and then solve the resulting polynomial equation.

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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, used to combine fractions.

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What does it mean if a rational equation has no solution?

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A rational equation has no solution if the variable leads to a contradiction, such as dividing by 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 an equation but does not satisfy the original equation.

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x = 1, x = 3.

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x = -3, x = 1.

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How do you check if a solution is valid in a rational equation?

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Substitute the solution back into the original equation to see if it holds true and does not result in division by zero.

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x = 3, x = 7.