### The Maxima on-line user's manual

Algebra Calculator

#### Fullratsimp

Function: fullratsimp (<expr>) `fullratsimp` repeatedly applies `ratsimp` followed by non-rational simplification to an expression until no further change occurs, and returns the result.

When non-rational expressions are involved, one call to `ratsimp` followed as is usual by non-rational ("general") simplification may not be sufficient to return a simplified result. Sometimes, more than one such call may be necessary. `fullratsimp` makes this process convenient.

`fullratsimp (<expr>, <x_1>, ..., <x_n>)` takes one or more arguments similar to `ratsimp` and `rat`.

Example:

```          (%i1) expr: (x^(a/2) + 1)^2*(x^(a/2) - 1)^2/(x^a - 1);
a/2     2   a/2     2
(x    - 1)  (x    + 1)
(%o1)                -----------------------
a
x  - 1
(%i2) ratsimp (expr);
2 a      a
x    - 2 x  + 1
(%o2)                    ---------------
a
x  - 1
(%i3) fullratsimp (expr);
a
(%o3)                        x  - 1
(%i4) rat (expr);
a/2 4       a/2 2
(x   )  - 2 (x   )  + 1
(%o4)/R/             -----------------------
a
x  - 1```

```(%o1)                                true
(%i2) ```

### Related Examples

##### fullratsimp

eq1:(x+x^-1)/((x+x^-1...

fullratsimp(eq1);

Calculate

##### fullratsimp-linsolve-subst

eq1:K/(s*(s+1)*(s+2));

eq2:subst(%i*w, s, eq1);

eq3:fullratsimp(eq2);

Calculate

##### fullratsimp

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

fullratsimp(%);

Calculate

##### fullratsimp-solve-sqrt-subst

m: 4;

e0: ((m+1)*x+(m-1)*y)...

e1: ((m-1)*x+(m+1)*y)...

Calculate

##### fullratsimp

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

fullratsimp(p);

Calculate

##### fullratsimp-ratsimp

expr: ((243*x^(10))*(...

ratsimp (expr);

fullratsimp (expr);

Calculate

##### fullratsimp-linsolve

eqs:[2 *x1+x2+x3=1, 3...

linsolve(eqs, [x1,x2,...

a[2]:fullratsimp(eqs[...

Calculate

##### fullratsimp-integrate-log-ratsimp-sqrt

ratsimp(integrate(x*l...

F[x]:=2*(log(b/a/sqrt...

fullratsimp(F[b^2/a^2...

Calculate

##### fullratsimp-sqrt-subst

fullratsimp(subst((1-...

fullratsimp(subst((1-...

Calculate

##### fullratsimp

taxableAmtPerPeriod =...

shortfall = taxableAm...

fullratsimp(shortfall);

Calculate