## Re: [Maxima-discuss] How to simplify (sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x))

 Re: [Maxima-discuss] How to simplify (sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)) From: Jinsong Zhao - 2014-02-28 22:38:42 ```On 2014/2/28 14:24, Thomas D. Dean wrote: > On 02/28/14 13:49, Jinsong Zhao wrote: > > Look at the numerator and denominator: > eq:(sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)); > num(eq); > denom(eq); > > They are of the form (a+b)/(a-b) > (a+b)*(a-b) expands to a^2 - b^2 > multiplying the numerator and denominator by the denominator shows promise: > > num(eq)*denom(eq); > ratsimp(num(eq)*denom(eq)); > ratsimp(num(eq)*denom(eq))/(denom(eq)*denom(eq)); I thought Maxima could automatically do that... > > > The maxima documentaton online at > > http://maxima.sourceforge.net/documentation.html > > provides some help. > > Tom Dean > Thank you very much! Regards, Jinsong ```

 [Maxima-discuss] How to simplify (sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)) From: Jinsong Zhao - 2014-02-28 21:49:43 ```Hi there, Another expression, (sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)) that I hope to simplify to 1/(sqrt(x+1)+sqrt(x))^2 How to work out it? By the way, would you please to point me some documents that can guide me to use Maxima in a more effective way? Thank you very much! Regards, Jinsong ```
 Re: [Maxima-discuss] How to simplify (sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)) From: Thomas D. Dean - 2014-02-28 22:24:13 ```On 02/28/14 13:49, Jinsong Zhao wrote: Look at the numerator and denominator: eq:(sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)); num(eq); denom(eq); They are of the form (a+b)/(a-b) (a+b)*(a-b) expands to a^2 - b^2 multiplying the numerator and denominator by the denominator shows promise: num(eq)*denom(eq); ratsimp(num(eq)*denom(eq)); ratsimp(num(eq)*denom(eq))/(denom(eq)*denom(eq)); The maxima documentaton online at http://maxima.sourceforge.net/documentation.html provides some help. Tom Dean ```
 Re: [Maxima-discuss] How to simplify (sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)) From: Jinsong Zhao - 2014-02-28 22:38:42 ```On 2014/2/28 14:24, Thomas D. Dean wrote: > On 02/28/14 13:49, Jinsong Zhao wrote: > > Look at the numerator and denominator: > eq:(sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)); > num(eq); > denom(eq); > > They are of the form (a+b)/(a-b) > (a+b)*(a-b) expands to a^2 - b^2 > multiplying the numerator and denominator by the denominator shows promise: > > num(eq)*denom(eq); > ratsimp(num(eq)*denom(eq)); > ratsimp(num(eq)*denom(eq))/(denom(eq)*denom(eq)); I thought Maxima could automatically do that... > > > The maxima documentaton online at > > http://maxima.sourceforge.net/documentation.html > > provides some help. > > Tom Dean > Thank you very much! Regards, Jinsong ```
 Re: [Maxima-discuss] How to simplify (sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)) From: Raymond Toy - 2014-02-28 22:59:45 ```>>>>> "Jinsong" == Jinsong Zhao writes: Jinsong> On 2014/2/28 14:24, Thomas D. Dean wrote: >> On 02/28/14 13:49, Jinsong Zhao wrote: >> >> Look at the numerator and denominator: >> eq:(sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)); >> num(eq); >> denom(eq); >> >> They are of the form (a+b)/(a-b) >> (a+b)*(a-b) expands to a^2 - b^2 >> multiplying the numerator and denominator by the denominator shows promise: >> >> num(eq)*denom(eq); >> ratsimp(num(eq)*denom(eq)); >> ratsimp(num(eq)*denom(eq))/(denom(eq)*denom(eq)); Jinsong> I thought Maxima could automatically do that... There's ratsimp(eq),algebraic; but that gives something different (but equivalent). I think that in general if you want a specific form, you have to do it yourself. I don't see how maxima can read your mind and produce exactly what you want in general. Ray ```
 Re: [Maxima-discuss] How to simplify (sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)) From: Jinsong Zhao - 2014-02-28 23:10:59 ```On 2014/2/28 14:59, Raymond Toy wrote: >>>>>> "Jinsong" == Jinsong Zhao writes: > > Jinsong> On 2014/2/28 14:24, Thomas D. Dean wrote: > >> On 02/28/14 13:49, Jinsong Zhao wrote: > >> > >> Look at the numerator and denominator: > >> eq:(sqrt(x+1) - sqrt(x))/(sqrt(x+1)+sqrt(x)); > >> num(eq); > >> denom(eq); > >> > >> They are of the form (a+b)/(a-b) > >> (a+b)*(a-b) expands to a^2 - b^2 > >> multiplying the numerator and denominator by the denominator shows promise: > >> > >> num(eq)*denom(eq); > >> ratsimp(num(eq)*denom(eq)); > >> ratsimp(num(eq)*denom(eq))/(denom(eq)*denom(eq)); > > Jinsong> I thought Maxima could automatically do that... > > There's ratsimp(eq),algebraic; but that gives something different (but > equivalent). > > I think that in general if you want a specific form, you have to do it > yourself. I don't see how maxima can read your mind and produce > exactly what you want in general. > > Ray > yes, you are right. I will try to learn more about how to use to produce what I want. Regards, Jinsong ```