8.6B Solving Rational Equations Worksheet

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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/or denominator are polynomials.

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How do you solve a rational equation?

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To solve a rational equation, first 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 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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The first step is to find a common denominator and eliminate the fractions.

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The solutions are x = 5/7 and x = 3.

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How do you check the solution of a rational equation?

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To check the solution, substitute the value back into the original equation to see if both sides are equal.

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What is the significance of finding extraneous solutions in rational equations?

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Extraneous solutions are values that do not satisfy the original equation, often introduced when multiplying by a variable expression that could be zero.

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The solution is x = 8.

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The value of x is 2.

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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.