Try It 7.54: Simplifying by Writing it as Division
To simplify the complex rational expression by writing it as division, perform the following steps:
Step 1. Simplify the numerator and denominator. In the numerator, the common denominator is . Rewrite as . Subtracting yields . In the denominator, the common denominator is . Rewrite as . The complex fraction becomes: .
Step 2. Rewrite as fraction division. Replace the main fraction bar with division:
Step 3. Multiply by the reciprocal and simplify. Rewrite as multiplication by the reciprocal: Factor the denominator to . Divide out the common factors and . The final simplified expression is:
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Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax
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Simplifying
In professional data analysis, you may encounter complex rational expressions when comparing different performance metrics. To simplify these expressions by converting them into a division problem, arrange the following steps in the correct order.
A logistics coordinator is simplifying a complex rational expression that represents the ratio of two different shipping rate formulas. When using the method of writing the expression as division, which action must be completed first?
A healthcare administrator is simplifying a complex rational expression that represents the ratio of two different staffing efficiency formulas. When using the method of 'writing it as division,' the main fraction bar is rewritten as a(n) ________ sign.
Finalizing the Simplification Process
In a project management office, an analyst is using the 'writing as division' method to simplify a complex rational expression that represents a project's cost-to-benefit ratio. According to this specific method, the analyst must rewrite the main fraction bar as a division sign only after simplifying both the numerator and the denominator into single rational expressions.
A logistics coordinator is simplifying a complex rational expression that models the ratio of two different fuel efficiency standards. To correctly apply the 'writing as division' method, match each step of the process with its corresponding procedural action.
Quality Assurance Standards for Mathematical Modeling
Technical Training: Standardizing the 'Writing as Division' Method
A performance analyst is simplifying a complex rational expression that models the ratio between two different departmental efficiency formulas. After successfully rewriting the complex expression as a horizontal division problem, which specific mathematical component must the analyst multiply the numerator by to complete the simplification?
An operations analyst is simplifying a complex rational expression that represents the ratio of two different departmental efficiency formulas. When applying the 'writing as division' method, which component of the original complex expression must be used as the first term (the dividend) in the resulting horizontal division problem?
Example 7.27: Simplifying by Writing it as Division
Try It 7.53: Simplifying by Writing it as Division
Try It 7.54: Simplifying by Writing it as Division
Learn After
As a technical trainer explaining a legacy efficiency metric to new analysts, you need to document how the software engine simplifies the complex fraction . Based on standard algebraic procedures, arrange the computational steps the engine follows into the correct chronological order.
A supply chain analyst is auditing a performance ratio modeled by the complex rational expression . During the simplification process using the division method, the analyst has already simplified the numerator and denominator into single fractions as follows:
To continue the simplification by rewriting this as a multiplication problem, which of the following is the correct reciprocal of the divisor (the denominator) that must be used?
As a data analyst for a logistics firm, you are auditing an algorithm that uses the complex rational expression to calculate supply chain overhead. To ensure the algorithm's documentation is accurate, match each component of the expression with its correctly simplified single-fraction form as described in the standard procedure.
Numerator Simplification in Algorithm Optimization
As a quality assurance technician for an educational software company, you are verifying the simplification steps for the performance ratio . True or False: In the final stage of the division method, the factors and are divided out to obtain the simplified result of .