Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Model rate and work contexts with algebraic and physical domains
Problem
\(\text{Two}\) workers can complete \(\text{one}\) job individually in \(x~\text{hours}\) and \(x~+~2~\text{hours}\). Write their combined work-rate model and state the physical domain.
Big Picture
What this problem is really about
Convert each completion time to a rate before combining anything: one job completed in t hours corresponds to one over t jobs per hour. Rates add when workers operate together, whereas completion times do not. After simplifying the rational rate, intersect the algebraic domain with the physical requirement that every time quantity be positive.
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