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Answer
The simplified form of
is
.
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Beyond the Answer
To rationalize the denominator of
, multiply both the numerator and the denominator by
:
Now, simplify the fraction:
So,
simplifies to
.
Rationalizing the denominator is a clever trick that helps avoid messy calculations or interpretations, especially in fields like engineering where precise measurements are vital. It ensures expressions are in a more standard form, making them easier to work with and compare.
When working on problems like this, a common mistake is to forget to multiply both the top and bottom by the same number, which can lead to incorrect results. Always remember to keep the fraction equivalent!