How to Simplify a Rational Function

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To simplify the rational function u^2/(u^2 - 4), one approach is to recognize that u^2 can be expressed as (u^2 - 4) + 4, which leads to the equation being rewritten as 1 + 4/(u^2 - 4). Another method suggested is polynomial long division, which can also help in simplifying the expression. The discussion emphasizes the importance of using LaTeX for clarity in mathematical equations. Overall, both methods aim to clarify the relationship between the numerator and the denominator for easier simplification.
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Homework Statement



u^2
---------------
u^2 - 4

Homework Equations



I am told that this is equal to

1+ 4/u^2 - 4

The Attempt at a Solution



No clue how these two are related. Factor out a u^2/u^2? But that alters the denominator. My next that is partial fraction decomp. Am I on track?
 
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Use polynomial long division. Or, note that in the numerator,
u^2 = \left( u^2 - 4 \right) + 4.
 

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