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

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In summary, to simplify the expression ((sqrt3)/3)+1 /(1-(sqrt3)/3), we can combine the fractions by finding a common denominator of 3, resulting in (4+sqrt3) / (3-sqrt3). This expression can also be simplified by factoring and rationalizing the denominator. While a calculator can be used to simplify the expression, it is important to understand the steps involved. Whether or not it is necessary to simplify the expression depends on the context in which it is being used.
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TyErd
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ok, how do you simplify:

((sqrt3)/3)+1 /(1-(sqrt3)/3)
 
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Rationalize the denominator.
 
  • #3


sooo is it...((sqrt3)/3)+1 /(1-(sqrt3)/3) * (1+(sqrt3)/3)/(1+(sqrt3)/3) ?
 
  • #4


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.
 

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

How do I simplify the expression ((sqrt3)/3)+1 /(1-(sqrt3)/3)?

To simplify this expression, we can first rewrite it as (1/3)sqrt3 + 1 / ((3-sqrt3)/3). Then, we can combine the fractions by finding a common denominator of 3. This simplifies the expression to (4+sqrt3) / (3-sqrt3).

Can I simplify this expression by factoring?

Yes, you can simplify this expression by factoring. However, it may be easier to combine the fractions first and then factor the resulting expression.

3. Is there a simpler form for this expression?

Yes, the expression (4+sqrt3) / (3-sqrt3) can be further simplified by rationalizing the denominator. This results in (13+7sqrt3) / 6, which is a simpler form of the expression.

4. Can I use a calculator to simplify this expression?

Yes, you can use a calculator to simplify this expression. However, it is important to understand the steps involved in the simplification process in order to avoid any mistakes.

5. Is it necessary to simplify this expression?

It depends on the context in which the expression is being used. In some cases, simplifying the expression may make it easier to work with and understand. However, in other cases, the original expression may be more useful. It is always a good idea to simplify an expression if possible, but it is not always necessary.

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