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Factors vs. Terms in Simplification
When simplifying fractions or rational expressions, only factors — quantities that are multiplied together to form a product — can be divided out (cancelled) from the numerator and denominator. A term — a quantity that is part of a sum or difference — cannot be cancelled.
For example, in , the binomial is a common factor of both the numerator and denominator because it is multiplied with other quantities. Since it is a factor of the product, it can be divided out, yielding .
However, in , the in the numerator is a term of the sum , not a factor of a product. It cannot be cancelled. Doing so would be the same error as cancelling the 's in , which would incorrectly give instead of the correct value .
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Ch.8 Rational Expressions and Equations - Elementary Algebra @ OpenStax
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Factors vs. Terms in Simplification
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Standardizing Procedure for Rational Expression Simplification
A corporate trainer is explaining the mathematical basis for simplifying rational expressions in a business modeling course. According to the standard procedure, this process is grounded in the same mathematical logic used for which of the following tasks?
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Simplifying
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When simplifying a fraction in a business spreadsheet, which of the following can be divided out (cancelled) from both the numerator and the denominator?
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When auditing a budget formula in a professional spreadsheet, you must ensure it is simplified correctly without introducing calculation errors. Arrange the following steps in the correct order to determine if a component can be safely cancelled from both the numerator and denominator.
When auditing a payroll spreadsheet, you encounter the formula: . In this expression, the component is being multiplied by other quantities in both the numerator and the denominator. What is the mathematical name for this type of component that allows it to be divided out (cancelled)?
A project manager is reviewing a cost-analysis formula: . To simplify this expression correctly, the manager must identify the mathematical role of 'ProjectCost' in the numerator. Based on the definitions of factors and terms, 'ProjectCost' in the numerator is a ________ and ________ be divided out (cancelled) with the denominator.