# Rationalize the denominators problem

• Gughanath
In summary, the given expression is a fraction with a complex denominator, but it can be simplified by rationalizing the denominators and finding common denominators. The next step would be to factor out a common term and continue simplifying. The expression can be written using Latex code.
Gughanath

[2 (square root of 2)/[(square root of 3)-1] - [2(square root of 3)]/[(square root of 2)+1] in a simpler form. I am sorry if the expression looks completed, i didnt know how to write them properly on the forum, its bascailly a fraction (LHS) - another fraction (RHS). Please help

Gughanath said:

[2 (square root of 2)/[(square root of 3)-1] - [2(square root of 3)]/[(square root of 2)+1] in a simpler form. I am sorry if the expression looks completed, i didnt know how to write them properly on the forum, its bascailly a fraction (LHS) - another fraction (RHS). Please help

The usual thing is to rationalize the denominators, then find common denominators, then combine terms. To rationalize, you have to multiply numerator and denominator of each fraction by the conjugate of the denominator.

$$\frac{2\sqrt{2}}{\sqrt{3} -1} - \frac{2\sqrt{3}}{\sqrt{2}+1}$$

I would factor out a 2 and find a lowest common denominator, then go from there.

errmm...just before I continue...could you explain how you wrote that expression?

Click it, and on the bottom you should see Latex code reference.

## What does it mean to "rationalize the denominators" in a problem?

Rationalizing the denominators in a problem means to eliminate any radicals or irrational numbers from the denominator of a fraction. This is done by multiplying the fraction by a form of 1 that will result in a rational number in the denominator.

## Why is it important to rationalize denominators?

Rationalizing denominators is important because it allows for simpler, more standard forms of fractions. It also allows for easier computation and comparison of fractions.

## How do you rationalize a single-term denominator?

To rationalize a single-term denominator, you would multiply the fraction by the conjugate of the denominator. The conjugate is found by changing the sign between the two terms in the denominator. For example, if the denominator is √2, the conjugate would be -√2.

## Can you only rationalize denominators with radicals?

No, denominators can also be rationalized with other types of irrational numbers, such as pi or e. The same process of multiplying by a form of 1 can be used to eliminate these irrational numbers from the denominator.

## Are there any exceptions to the rule for rationalizing denominators?

Yes, there are certain cases where rationalizing the denominator may not be necessary or may not result in a simplified fraction. For example, when the denominator is already a perfect square or when the simplified fraction would contain a radical in the numerator.

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