Rewrite rational expressions using inspection, polynomial division, or technology.
Rewrite a rational expression to reveal its end behavior
Problem
Rewrite \((x^2~+~3x~+~5)/(x~+~1)\) in quotient-plus-remainder form and state its end behavior.
Big Picture
What this problem is really about
Rewrite the rational expression so its two roles are visible: the quotient gives the persistent trend, and the remainder over the divisor gives the temporary deviation from that trend. Verify the division identity and retain the original domain restriction. For large positive or negative inputs, the proper fraction fades toward zero, leaving the quotient to control end behavior.
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