# What is the simplified form of #(sqrt(2)-sqrt(10))/(sqrt(2)+sqrt(10))# ?

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The squares identity difference can be expressed as follows:

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To simplify ( \frac{\sqrt{2} - \sqrt{10}}{\sqrt{2} + \sqrt{10}} ), you can use the technique of rationalizing the denominator. Multiply both the numerator and the denominator by the conjugate of the denominator, which is ( \sqrt{2} - \sqrt{10} ).

[ \frac{\sqrt{2} - \sqrt{10}}{\sqrt{2} + \sqrt{10}} \times \frac{\sqrt{2} - \sqrt{10}}{\sqrt{2} - \sqrt{10}} ]

This results in:

[ \frac{(\sqrt{2} - \sqrt{10})^2}{(\sqrt{2} + \sqrt{10})(\sqrt{2} - \sqrt{10})} ]

Simplify the numerator:

[ \frac{(2 - 2\sqrt{20} + 10)}{2 - 10} ]

[ \frac{(12 - 2\sqrt{20})}{-8} ]

[ \frac{-6 + \sqrt{20}}{4} ]

[ \frac{-3 + \sqrt{5}}{2} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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