How to simplify: ((sqrt3)/3)+1 /(1-(sqrt3)/3)

Thread starter TyErd
Start date Mar 13, 2010
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SUMMARY

The discussion focuses on simplifying the expression \(\frac{\sqrt{3}}{3} + \frac{1}{1 - \frac{\sqrt{3}}{3}}\). The correct approach involves rationalizing the denominator by multiplying the expression by \(\frac{1 + \frac{\sqrt{3}}{3}}{1 + \frac{\sqrt{3}}{3}}\), which is equivalent to multiplying by 1. This method maintains the value of the expression while facilitating simplification.

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Understanding of rational expressions
Knowledge of square roots and their properties
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Basic algebraic manipulation skills

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Mar 13, 2010

TyErd

ok, how do you simplify:

((sqrt3)/3)+1 /(1-(sqrt3)/3)

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Mar 13, 2010

vela

Staff Emeritus

Science Advisor

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Rationalize the denominator.

Mar 13, 2010

TyErd

sooo is it...((sqrt3)/3)+1 /(1-(sqrt3)/3) * (1+(sqrt3)/3)/(1+(sqrt3)/3) ?

Mar 14, 2010

Mark44

Mentor

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Yes. What you are doing is multiplying by 1 (in the form (1+(sqrt3)/3)/(1+(sqrt3)/3)). You can always multiply by 1 without changing the value of the expression being multiplied.