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#### Search: #### Ratsimp

Function: ratsimp (<expr>) Function: ratsimp (<expr>, <x_1>, ..., <x_n>) Simplifies the expression <expr> and all of its subexpressions, including the arguments to non-rational functions. The result is returned as the quotient of two polynomials in a recursive form, that is, the coefficients of the main variable are polynomials in the other variables. Variables may include non-rational functions (e.g., `sin (x^2 + 1)`) and the arguments to any such functions are also rationally simplified.

`ratsimp (<expr>, <x_1>, ..., <x_n>)` enables rational simplification with the specification of variable ordering as in `ratvars`.

When `ratsimpexpons` is `true`, `ratsimp` is applied to the exponents of expressions during simplification.

See also `ratexpand`. Note that `ratsimp` is affected by some of the flags which affect `ratexpand`.

Examples:

```          (%i1) sin (x/(x^2 + x)) = exp ((log(x) + 1)^2 - log(x)^2);
2      2
x         (log(x) + 1)  - log (x)
(%o1)        sin(------) = %e
2
x  + x
(%i2) ratsimp (%);
1          2
(%o2)                  sin(-----) = %e x
x + 1
(%i3) ((x - 1)^(3/2) - (x + 1)*sqrt(x - 1))/sqrt((x - 1)*(x + 1));
3/2
(x - 1)    - sqrt(x - 1) (x + 1)
(%o3)           --------------------------------
sqrt((x - 1) (x + 1))
(%i4) ratsimp (%);
2 sqrt(x - 1)
(%o4)                    - -------------
2
sqrt(x  - 1)
(%i5) x^(a + 1/a), ratsimpexpons: true;
2
a  + 1
------
a
(%o5)                        x```

There are also some inexact matches for `ratsimp`. Try `?? ratsimp` to see them.

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

### Related Examples

##### ratsimp

ratsimp((2*x+3)/6-x/2...

Calculate

A:[xA,yA];

B:[xB,yB];

C:[xC,yC];

Calculate

##### ratsimp

ratsimp((x^2+(y+2/3)^...

Calculate

##### ratsimp-sqrt-subst-sum

Rc1:N/(2*T)*(252/sqrt...

Rc1_2:subst(J,K(n+1),...

ratsimp(Rc1_2);

Calculate

##### ratsimp-subst

ratsimp(subst(1/z, z,...

Calculate

##### ratsimp

ratsimp((x-3)*(x+2)*(...

Calculate

##### ratsimp-sqrt-taylor

f(x):=(x^31-1)/(x-1);

f(0.99999);

t(x):=taylor(sqrt(f(x...

Calculate

##### ratsimp-second-solve

second(ratsimp(solve(...

Calculate

##### ratsimp

eq1:r3 =( l + (((l/2)...

ratsimp(eq1);

Calculate

##### ratsimp-sqrt

m:3/2;

Ax:0;

Ay:0;

Calculate 