Create and solve one-variable equations and inequalities from contexts using all studied expression types, including simple root functions.
Write and solve a one-variable rational equation from a context
Problem
\(\text{Two}\) workers complete a job individually in \(x~\text{hours}\) and \(x~+~2~\text{hours}\). Together they complete it in \(3~\text{hours}\). Write a rational equation and find the positive value of \(x\).
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What this problem is really about
In a work problem, completion times do not add; their reciprocals are the rates that combine. Write the rate equation while recording that time must be positive, then clear denominators and solve the resulting polynomial. The original rate model and its domain decide which algebraic candidate actually represents the situation.
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