Excluded Values in Rational Expressions

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What are excluded values in rational expressions?

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Excluded values are the values of the variable that make the denominator of a rational expression equal to zero, which are not allowed in the domain of the expression.

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CCSS.HSA.APR.D.7

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How do you find excluded values in a rational expression?

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To find excluded values, set the denominator equal to zero and solve for the variable.

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CCSS.HSF-IF.C.7D

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n = 0, because the denominator 24x equals zero when x = 0.

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x = -4 and x = 4, because the denominator factors to (x-4)(x+4) which equals zero at these values.

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11, because the denominator x-11 equals zero when x = 11.

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x = 8 and x = -10, because the denominator factors to (x-8)(x+10) which equals zero at these values.

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CCSS.HSF-IF.C.7D

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x = 1, because the denominator 10x-10 equals zero when x = 1.

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What happens if you substitute an excluded value into a rational expression?

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Substituting an excluded value into a rational expression results in an undefined expression, as it leads to division by zero.

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CCSS.6.EE.A.2C

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Can a rational expression have more than one excluded value?

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Yes, a rational expression can have multiple excluded values, depending on the factors of the denominator.

Tags

CCSS.HSA.APR.D.7

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What is the domain of a rational expression?

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The domain of a rational expression is the set of all real numbers except for the excluded values.