Related

fullratsimp

fullratsimp( (x^4-1)/...

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fullratsimp

eq1:1.0 - (1.0 + tuni...

fullratsimp(eq1);

partfraq(%);

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n: [x,y,z];

nn: n / sqrt(n.n);

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fullratsimp-solve

eq1:x*y=1;

eq2: x+y=1;

t:solve([eq1,eq2],[x,...

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fullratsimp-solve

z:(z^2-4*z+4-((3/4)*%...

fullratsimp(solve(z=0));

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fullratsimp

fullratsimp((a**3+2*a...

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fullratsimp

((a1*c1 + a2*c2) / (a...

fullratsimp(%);

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fullratsimp-integrate-plot2d-sqrt

t1: ((2/3)*(x^3-x^2)^...

t2: integrate(x*sqrt(...

fullratsimp(t1-t2);

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fullratsimp

zd1: fullratsimp(1/(s...

zdk: fullratsimp(zd1 ...

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fullratsimp

P:(1/(x+1)+1/(x-1))/(...

fullratsimp(P);

Calculate

fullratsimp

Run Example
```(%i1)num1: 2*a*x;
(%o1)                                2 a x
(%i2) num2: 2*y*sqrt(a*b*(a*x*x+b*y*y-1));
2      2
(%o2)                   2 y sqrt(a b (b y  + a x  - 1))
(%i3) den: 2*a*(a*x*x+b*y*y);
2      2
(%o3)                          2 a (b y  + a x )
(%i4) x1: (num1+num2)/den;
2      2
2 y sqrt(a b (b y  + a x  - 1)) + 2 a x
(%o4)               ---------------------------------------
2      2
2 a (b y  + a x )
(%i5) x2: (num1-num2)/den;
2      2
2 a x - 2 y sqrt(a b (b y  + a x  - 1))
(%o5)               ---------------------------------------
2      2
2 a (b y  + a x )
(%i6) y1: (1-a*x*x1)/(b*y);
2      2
x (2 y sqrt(a b (b y  + a x  - 1)) + 2 a x)
1 - -------------------------------------------
2      2
2 (b y  + a x )
(%o6)           -----------------------------------------------
b y
(%i7) y2: (1-a*x*x2)/(b*y);
2      2
x (2 a x - 2 y sqrt(a b (b y  + a x  - 1)))
1 - -------------------------------------------
2      2
2 (b y  + a x )
(%o7)           -----------------------------------------------
b y
(%i8) d1_2: fullratsimp(ratexpand((x-x1)^2+(y-y1)^2));
3  6          3      2  2   2    3        2   4
(%o8) - (- a b  y  + ((- a b  - 2 a  b ) x  - b  + 2 a b ) y
2      2            2             3
+ sqrt(a b (b y  + a x  - 1)) ((2 b  - 2 a b) x y
2   3
+ ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
2  2    3     4       2    2     2    2         2    3    6
+ ((- 2 a  b  - a  b) x  + (a b  + a  b) x  + b  - a b) y  - a  b x
2      3   4     2         2      3  4      2  2  2  2    3    4
+ (2 a  b - a ) x  + (a  - a b) x )/(a b  y  + 2 a  b  x  y  + a  b x )
(%i9) d2_2: fullratsimp((x-x2)^2+(y-y2)^2);
3  6        3      2  2   2    3        2   4
(%o9) (a b  y  + ((a b  + 2 a  b ) x  + b  - 2 a b ) y
2  2    2    2             2             3
+ sqrt(a b  y  + a  b x  - a b) ((2 b  - 2 a b) x y
2   3
+ ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
2  2    3     4         2    2     2    2         2    3    6
+ ((2 a  b  + a  b) x  + (- a b  - a  b) x  - b  + a b) y  + a  b x
3      2     4           2   2      3  4      2  2  2  2    3    4
+ (a  - 2 a  b) x  + (a b - a ) x )/(a b  y  + 2 a  b  x  y  + a  b x )
(%i10) d12_2: fullratsimp((x2-x1)^2+(y2-y1)^2);
3  4          2      2     2      2   2      3  4      2  2
4 b  y  + ((4 a b  + 4 a  b) x  - 4 b ) y  + 4 a  x  - 4 a  x
(%o10)  --------------------------------------------------------------
3  4      2  2  2  2    3    4
a b  y  + 2 a  b  x  y  + a  b x
(%i11) cosT: (d1_2+d2_2-d12_2)/(2*sqrt(d1_2*d2_2));
3  4          2      2     2      2   2      3  4      2  2
4 b  y  + ((4 a b  + 4 a  b) x  - 4 b ) y  + 4 a  x  - 4 a  x
(%o11) ((- --------------------------------------------------------------
3  4      2  2  2  2    3    4
a b  y  + 2 a  b  x  y  + a  b x
3  6        3      2  2   2    3        2   4
+ (a b  y  + ((a b  + 2 a  b ) x  + b  - 2 a b ) y
2  2    2    2             2             3
+ sqrt(a b  y  + a  b x  - a b) ((2 b  - 2 a b) x y
2   3
+ ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
2  2    3     4         2    2     2    2         2    3    6
+ ((2 a  b  + a  b) x  + (- a b  - a  b) x  - b  + a b) y  + a  b x
3      2     4           2   2      3  4      2  2  2  2    3    4
+ (a  - 2 a  b) x  + (a b - a ) x )/(a b  y  + 2 a  b  x  y  + a  b x )
3  6          3      2  2   2    3        2   4
- (- a b  y  + ((- a b  - 2 a  b ) x  - b  + 2 a b ) y
2      2            2             3
+ sqrt(a b (b y  + a x  - 1)) ((2 b  - 2 a b) x y
2   3
+ ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
2  2    3     4       2    2     2    2         2    3    6
+ ((- 2 a  b  - a  b) x  + (a b  + a  b) x  + b  - a b) y  - a  b x
2      3   4     2         2      3  4      2  2  2  2    3    4
+ (2 a  b - a ) x  + (a  - a b) x )/(a b  y  + 2 a  b  x  y  + a  b x ))
!   3  4      2  2  2  2    3    4!                  3  6          3      2  2   2    3        2   4                2      2            2             3                2   3                              2  2    3     4       2    2     2    2         2    3    6       2      3   4     2         2      3  6        3      2  2   2    3        2   4           2  2    2    2             2             3                2   3                            2  2    3     4         2    2     2    2         2    3    6     3      2     4           2
!a b  y  + 2 a  b  x  y  + a  b x !)/(2 sqrt(- (- a b  y  + ((- a b  - 2 a  b ) x  - b  + 2 a b ) y  + sqrt(a b (b y  + a x  - 1)) ((2 b  - 2 a b) x y  + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y) + ((- 2 a  b  - a  b) x  + (a b  + a  b) x  + b  - a b) y  - a  b x  + (2 a  b - a ) x  + (a  - a b) x ) (a b  y  + ((a b  + 2 a  b ) x  + b  - 2 a b ) y  + sqrt(a b  y  + a  b x  - a b) ((2 b  - 2 a b) x y  + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y) + ((2 a  b  + a  b) x  + (- a b  - a  b) x  - b  + a b) y  + a  b x  + (a  - 2 a  b) x  + (a b - a )
2
x )))
(%i12) fullratsimp(ratexpand(cosT));
3  6        3      2  2   2    3        2   4
(%o12) ((a b  y  + ((a b  + 2 a  b ) x  - b  - 2 a b ) y
2  2    2    2           2           3
+ sqrt(a b  y  + a  b x  - a b) ((b  - a b) x y
2   3                                2      2
+ ((a b - a ) x  + (a - b) x) y) + sqrt(a b (b y  + a x  - 1))
2     3      2         3
((a b - b ) x y  + ((a  - a b) x  + (b - a) x) y)
2  2    3     4           2      2     2    2         2    3    6
+ ((2 a  b  + a  b) x  + (- 3 a b  - 3 a  b) x  + b  + a b) y  + a  b x
2      3   4           2   2  !   3  4      2  2  2  2    3    4!
+ (- 2 a  b - a ) x  + (a b + a ) x ) !a b  y  + 2 a  b  x  y  + a  b x !)
3  4      2  2  2  2    3    4               3  6          3      2  2   2    3        2   4                2      2            2             3                2   3                              2  2    3     4       2    2     2    2         2    3    6       2      3   4     2         2      3  6        3      2  2   2    3        2   4           2  2    2    2             2             3                2   3
/((a b  y  + 2 a  b  x  y  + a  b x ) sqrt(- (- a b  y  + ((- a b  - 2 a  b ) x  - b  + 2 a b ) y  + sqrt(a b (b y  + a x  - 1)) ((2 b  - 2 a b) x y  + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y) + ((- 2 a  b  - a  b) x  + (a b  + a  b) x  + b  - a b) y  - a  b x  + (2 a  b - a ) x  + (a  - a b) x ) (a b  y  + ((a b  + 2 a  b ) x  + b  - 2 a b ) y  + sqrt(a b  y  + a  b x  - a b) ((2 b  - 2 a b) x y  + ((2 a b - 2 a ) x  + (2 a - 2 b) x) y)
2  2    3     4         2    2     2    2         2    3    6
+ ((2 a  b  + a  b) x  + (- a b  - a  b) x  - b  + a b) y  + a  b x
3      2     4           2
+ (a  - 2 a  b) x  + (a b - a )
2
x )))
(%i13) ```
Run Example
```m: 4;
(%o1)                                  4
(%i2) e0: ((m+1)*x+(m-1)*y)/(2*m);
3 y + 5 x
(%o2)                              ---------
8
(%i3) e1: ((m-1)*x+(m+1)*y)/(2*m);
5 y + 3 x
(%o3)                              ---------
8
(%i4) fullratsimp(subst(e0, y, e1));
15 y + 49 x
(%o4)                             -----------
64
(%i5)  solve((a-r)*(d-r)-b*c,r);
2                    2
sqrt(d  - 2 a d + 4 b c + a ) - d - a
(%o5) [r = - -------------------------------------,
2
2                    2
sqrt(d  - 2 a d + 4 b c + a ) + d + a
r = -------------------------------------]
2
(%i6) a0: 0;
(%o6)                                  0
(%i7) a1: 1;
(%o7)                                  1
(%i8) a: 49/64;
49
(%o8)                                 --
64
(%i9) b: 15/64;
15
(%o9)                                 --
64
(%i10) c: 3/8;
3
(%o10)                                 -
8
(%i11) d: 5/8;
5
(%o11)                                 -
8
(%i12) sqrt(a^2+d^2-2*a*d+4*b*c);
39
(%o12)                                --
64
(%i13) a1*b/sqrt(a^2+d^2-2*a*d+4*b*c);
5
(%o13)                                --
13
(%i14) ```
Run Example
```f: x/(1-x/a) = b/(1-b/a)*exp(r*t);
r t
x     b %e
(%o1)                           ----- = -------
x        b
1 - -    1 - -
a        a
(%i2) solve(f,x);
r t
a b %e
(%o2)                        [x = ---------------]
r t
b %e    - b + a
(%i3) fullratsimp(%o2);
(%o3)             fullratsimp(x/(1-x/a));
```

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