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Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Find the value of
$\frac{1^4 + 2007^4 + 2008^4}{1^2 + 2007^2 + 2008^2}.$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; question papers published free at bmos.ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.