# Mathematica the Simplify[] command

• Mentallic
In summary, the conversation is about simplifying a complicated expression involving fractions and square roots. The person asking for help has attempted to simplify it on their own but is unsure of how to proceed further. The expert provides a simplified solution using the Simplify command and suggests using a program like Mathematica or Wolfram Alpha for future simplification tasks.
Mentallic
Homework Helper

## Homework Statement

Simplify to a certain extent, as much as possible (factorized form would be best):

$$\frac{\sqrt{3}}{2}\left(\frac{md}{m-\sqrt{3}}\right)^2+\frac{\sqrt{3}}{2}\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2+\frac{1}{2}\left(s+\frac{md}{m-\sqrt{3}}-\frac{m(s+d)}{m+\sqrt{3}}\right)\left(\frac{\sqrt{3}md}{\sqrt{3}-m}+\frac{\sqrt{3}m(s+d)}{m+\sqrt{3}}\right)$$

## The Attempt at a Solution

This isn't an actual question but rather a part of a bigger picture. I need this simplified as much as possible before I can even think of manipulating it further.

I've tried quite a bit, but after expanding the last factored expression, it became pretty ugly. This route seems most promising:

$$\frac{\sqrt{3}}{2}\left(\left(\frac{md}{m-\sqrt{3}}\right)^2+\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2+\left(s+\frac{md}{m-\sqrt{3}}-\frac{m(s+d)}{m+\sqrt{3}}\right)\left(\frac{m(s+d)}{m+\sqrt{3}}-\frac{md}{m-\sqrt{3}}\right)\right)$$

$$\frac{\sqrt{3}}{2}\left(\left(\frac{md}{m-\sqrt{3}}\right)^2+\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2+s\left(\frac{m(s+d)}{m+\sqrt{3}}-\frac{md}{m-\sqrt{3}}\right)-\left(\frac{2\sqrt{3}md+\sqrt{3}ms-m^2s}{m^2-3}\right)^2\right)$$

$$\frac{\sqrt{3}}{2}\left(\left(\frac{md}{m-\sqrt{3}}\right)^2+\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2-s\left(\frac{2\sqrt{3}d+\sqrt{3}s-ms}{m^2-3}\right)-m^2\left(\frac{2\sqrt{3}d+\sqrt{3}s-ms}{m^2-3}\right)^2\right)$$

I'm unsure of what else to do without making a big mess. And this still isn't simple enough for what I need this for, so if you have the stomach to tackle this, please do so

#### Attachments

• factor.jpg
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Thanks for the response.

I don't quite understand what your final solution is. When it gets to the : and then it has just one entire fraction. That one fraction can't possibly be equal? It only has a second degree for m, while if you look at this part which is located on the last line in the last factor of my OP:

$$m^2\left(\frac{2\sqrt{3}d+\sqrt{3}s-ms}{m^2-3}\right)^2$$

it clearly suggests the denominator should be of a 4th degree in m, no?

#### Attachments

• sol.jpg
19 KB · Views: 391

Oh wow thanks a lot for that!

It still took me a while to understand what was happening, but it all sunk in and when I tested it for some values of s,d and m and they turned out equal, I was even more ecstatic!

you are most welcome(=

Did you simplify this yourself, or did you use a program of some sort?
Reason being because I'm going to need more simplifying of this type to be done.

I've checked with a program and indeed it is the simplest form.

If you have access to Mathematica the Simplify[] command would come in handy.

Come to think of it there might also be something similar you can use on Wolfram Alpha to simplify expressions.

## 1. What is the Simplify[] command in Mathematica?

The Simplify[] command is a built-in function in the Mathematica software that simplifies algebraic expressions, equations, and functions. It uses various mathematical techniques to reduce the complexity of an expression and provide a more concise form.

## 2. How do I use the Simplify[] command in Mathematica?

To use the Simplify[] command, you simply need to type "Simplify[]" followed by the expression or equation you want to simplify. You can also specify additional parameters to customize the simplification process, such as assumptions or variables to be treated as constants.

## 3. What types of expressions can be simplified with the Simplify[] command?

The Simplify[] command can simplify a wide range of expressions, including algebraic expressions, trigonometric expressions, logarithmic expressions, and more. It can also handle both single and multi-variable expressions.

## 4. Can the Simplify[] command handle complex expressions?

Yes, the Simplify[] command has the ability to handle complex expressions involving real and imaginary numbers. It also supports simplification of expressions with special functions, such as Bessel functions and Gamma functions.

## 5. Are there any limitations to using the Simplify[] command?

While the Simplify[] command is a powerful tool for simplifying expressions, it may not always provide the most simplified form of an expression. This is because it uses a set of predefined rules and may not take into account certain mathematical properties or specific simplification techniques. In such cases, it may be necessary to use other functions or techniques to further simplify an expression.

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