I'm trying to solve this function.

 

[math] = \frac{1 + (\frac {2x + 3}{3x- 4})}{(\frac {4x + 6}{3x-4}) - 3} [/math]

 

[math] = \frac{\frac {2x + 3 + 3x -4}{3x- 4}}{\frac {4x + 6 - 9x +12}{3x-4}} [/math]

 

[math] = \frac {5x - 1}{3x- 4} / \frac {-5x + 18}{3x-4}[/math]

 

[math] = \frac {5x - 1}{3x- 4} * \frac {3x-4}{-5x + 18}[/math]

 

[math] = \frac {5x - 1}{1} * \frac {1}{-5x + 18}[/math]

 

[math] = \frac {5x - 1}{-5x + 18}[/math]

 

but how come mathematica got this?

 

mathematica 1

 

mathematica 2

 

where does the " -1 " came from???

they are the same. If you take

 

[math] = \frac {-1(5x - 1)}{-1(-5x + 18)} [/math]

 

ie multiply top and bottom by -1 you can get two different and slightly nicer ways of expressing same fraction

 

[math] = \frac {1-5x}{5x - 18} [/math] this is both upstairs and downstairs multiplied by -1

 

or

 

[math] = -1 * \frac {5x - 1}{5x - 18} [/math] this is with the minus 1 taken outside bracket and downstairs of fraction multiplied by -1

Edited June 8, 201114 yr by imatfaal

actually, the thing that I worried about is the value, however, when i see again in the mathematica, the value is same..

 

hmm... after do some random calculation... i think i found the 'secret' behind this, thnx anyway ^^