### Related

##### multthru-ratsimp-xthru

a: 1/(c-d)-c/(c^2-d^2...

xthru(a);

b:ratsimp(a);

Calculate

##### multthru

multthru (20*b / (a-3...

Calculate

##### multthru-ratsimp-xthru

a: 1/(c-d)-c/(c^2-d^2...

xthru(a);

b:ratsimp(a);

Calculate

##### multthru

eq1: (e1+e2+2*(e3+e4)...

multthru(eq1);

Calculate

? multthru;

Calculate

##### multthru-sqrt

expr:1/[1+sqrt(10)+sq...

multthru(expr);

Calculate

##### multthru-ratexpand

x/(x-y)^2 - 1/(x-y) -...

multthru ((x-y)^3, %);

ratexpand (%);

Calculate

##### multthru-ratsimp-xthru

a: 1/(c-d)-c/(c^2-d^2...

xthru(a);

b:ratsimp(a);

Calculate

##### multthru

f:(x1+x2)*(x2+x3)*(x3...

multthru(f);

Calculate

##### multthru-ratsimp-xthru

a: 1/(c-d)-c/(c^2-d^2...

xthru(a);

b:ratsimp(a);

Calculate

### multthru

Run Example
```(%i1)a: 1/(c-d)-c/(c^2-d^2)+1/(2*c+2*d);
c          1         1
(%o1)                    - ------- + --------- + -----
2    2   2 d + 2 c   c - d
c  - d
(%i2) xthru(a);
2    2
(d + 3 c) (c  - d ) - c (c - d) (2 d + 2 c)
(%o2)             -------------------------------------------
2    2
(c - d) (2 d + 2 c) (c  - d )
(%i3) b:ratsimp(a);
1
(%o3)                             - ---------
2 d - 2 c
(%i4) p: x/(x^2-y^2)-y/(x^2+2*x*y+y^2);
x             y
(%o4)                      ------- - ---------------
2    2    2            2
x  - y    y  + 2 x y + x
(%i5) q:ratsimp(p);
2    2
y  + x
(%o5)                       - ---------------------
3      2    2      3
y  + x y  - x  y - x
(%i6) multthru(e*c+e*d);
(%o6)                              d e + c e
(%i7) ```
Run Example
```globalsolve: true;
(%o1)                                true
(%i2) realonly: true;
(%o2)                                true
(%i3) /* Standard (x,y)->
(r,theta) coordinate translation */x(t) := r(t) * cos(theta(t));
(%o3)                     x(t) := r(t) cos(theta(t))
(%i4) y(t) := r(t) * sin(theta(t));
(%o4)                     y(t) := r(t) sin(theta(t))
(%i5) /* Constant course assumption */declare (slope,constant);
(%o5)                                done
(%i6) declare (slope,real);
(%o6)                                done
(%i7) declare (yintercept,constant);
(%o7)                                done
(%i8) declare (yintercept, real);
(%o8)                                done
(%i9) eq1: y(t)=slope * x(t) + yintercept;
(%o9)     r(t) sin(theta(t)) = slope r(t) cos(theta(t)) + yintercept
(%i10) eq1;
(%o10)    r(t) sin(theta(t)) = slope r(t) cos(theta(t)) + yintercept
(%i11) /* Constant velocity assumption */declare (velocityx,constant);
(%o11)                               done
(%i12) declare (velocityx,real);
(%o12)                               done
(%i13) declare (c0, constant);
(%o13)                               done
(%i14) declare (c0, real);
(%o14)                               done
(%i15) eq2: x(t) = velocityx * (t - c0);
(%o15)              r(t) cos(theta(t)) = velocityx (t - c0)
(%i16) eq2;
(%o16)              r(t) cos(theta(t)) = velocityx (t - c0)
(%i17) declare (A, constant);
(%o17)                               done
(%i18) declare (A, real);
(%o18)                               done
(%i19) eq3: y(t) = slope*velocityx* (t - c0) + A*velocityx;
(%o19)    r(t) sin(theta(t)) = slope velocityx (t - c0) + velocityx A
(%i20) eq3;
(%o20)    r(t) sin(theta(t)) = slope velocityx (t - c0) + velocityx A
(%i21) eq4: eq3/eq2;
sin(theta(t))   slope velocityx (t - c0) + velocityx A
(%o21)      ------------- = --------------------------------------
cos(theta(t))             velocityx (t - c0)
(%i22) trigreduce(lhs(eq4))=multthru(rhs(eq4));
A
(%o22)                  tan(theta(t)) = ------ + slope
t - c0
(%i23) ```
Run Example
```/* Umwandlung stern dreieck */Z10: R10+X10;
(%o1)                              X10 + R10
(%i2) kill;
(%o2)                                kill
(%i3) Z10:R10+X10;
(%o3)                              X10 + R10
(%i4) Z20:R20+X20;
(%o4)                              X20 + R20
(%i5) Z30:R30+X30;
(%o5)                              X30 + R30
(%i6) nZ0:1/Z10+1/Z20+1/Z30;
1           1           1
(%o6)                  --------- + --------- + ---------
X30 + R30   X20 + R20   X10 + R10
(%i7) Z0:1/nZ0;
1
(%o7)                  ---------------------------------
1           1           1
--------- + --------- + ---------
X30 + R30   X20 + R20   X10 + R10
(%i8) Z12:Z10*Z20/Z0;
1           1           1
(%o8)     (X10 + R10) (X20 + R20) (--------- + --------- + ---------)
X30 + R30   X20 + R20   X10 + R10
(%i9) R10:1000;
(%o9)                                1000
(%i10) R20:1000;
(%o10)                               1000
(%i11) R30:1000;
(%o11)                               1000
(%i12) X10:%i*2*%pi*f*L10;
(%o12)                          2 %i %pi f L10
(%i13) X20:%i*2*%pi*f*L20;
(%o13)                          2 %i %pi f L20
(%i14) X30:%i*2*%pi*f*L30;
(%o14)                          2 %i %pi f L30
(%i15) L10:0.022;
(%o15)                               0.022
(%i16) L20:0.022;
(%o16)                               0.022
(%i17) L30:0.022;
(%o17)                               0.022
(%i18) f:50;
(%o18)                                50
(%i19) X10,numer;
(%o19)                       6.911503837897545 %i
(%i20) X20,numer;
(%o20)                       6.911503837897545 %i
(%i21) X30,numer;
(%o21)                       6.911503837897545 %i
(%i22) ev (Z12),numer;
(%o22)                  3 (6.911503837897545 %i + 1000)
(%i23) ev (Z12, simp, numer, expand, f=60, L10=10);
2
39.47841760435743 f  L10 L20     2000 %i %pi f L20
(%o23) - ---------------------------- + ---------------------
2 %i %pi f L30 + 1000       2 %i %pi f L30 + 1000
2
2000 %i %pi f L10            1000000          39.47841760435743 f  L10 L20
+ --------------------- + --------------------- - ----------------------------
2 %i %pi f L30 + 1000   2 %i %pi f L30 + 1000      2 %i %pi f L20 + 1000
2000 %i %pi f L20       2000 %i %pi f L10            1000000
+ --------------------- + --------------------- + ---------------------
2 %i %pi f L20 + 1000   2 %i %pi f L20 + 1000   2 %i %pi f L20 + 1000
2
39.47841760435743 f  L10 L20     2000 %i %pi f L20       2000 %i %pi f L10
- ---------------------------- + --------------------- + ---------------------
2 %i %pi f L10 + 1000       2 %i %pi f L10 + 1000   2 %i %pi f L10 + 1000
1000000
+ ---------------------
2 %i %pi f L10 + 1000
(%i24) expand(Z12),numer;
2
39.47841760435743 f  L10 L20     2000 %i %pi f L20
(%o24) - ---------------------------- + ---------------------
2 %i %pi f L30 + 1000       2 %i %pi f L30 + 1000
2
2000 %i %pi f L10            1000000          39.47841760435743 f  L10 L20
+ --------------------- + --------------------- - ----------------------------
2 %i %pi f L30 + 1000   2 %i %pi f L30 + 1000      2 %i %pi f L20 + 1000
2000 %i %pi f L20       2000 %i %pi f L10            1000000
+ --------------------- + --------------------- + ---------------------
2 %i %pi f L20 + 1000   2 %i %pi f L20 + 1000   2 %i %pi f L20 + 1000
2
39.47841760435743 f  L10 L20     2000 %i %pi f L20       2000 %i %pi f L10
- ---------------------------- + --------------------- + ---------------------
2 %i %pi f L10 + 1000       2 %i %pi f L10 + 1000   2 %i %pi f L10 + 1000
1000000
+ ---------------------
2 %i %pi f L10 + 1000
(%i25) multthru(Z12);
(X10 + R10) (X20 + R20)
(%o25)          ----------------------- + X20 + X10 + R20 + R10
X30 + R30
(%i26) Z12,numer;
(%o26) (2 %i %pi f L10 + 1000) (2 %i %pi f L20 + 1000)
1                       1                       1
(--------------------- + --------------------- + ---------------------)
2 %i %pi f L30 + 1000   2 %i %pi f L20 + 1000   2 %i %pi f L10 + 1000
(%i27) ev(Z12);
(%o27) (2 %i %pi f L10 + 1000) (2 %i %pi f L20 + 1000)
1                       1                       1
(--------------------- + --------------------- + ---------------------)
2 %i %pi f L30 + 1000   2 %i %pi f L20 + 1000   2 %i %pi f L10 + 1000
(%i28) ev(Z12),numer;
(%o28)                  3 (6.911503837897545 %i + 1000)
(%i29) multthru(ev(Z12)),numer;
(%o29)                    20.73451151369264 %i + 3000
(%i30) Z12;
1           1           1
(%o30)    (X10 + R10) (X20 + R20) (--------- + --------- + ---------)
X30 + R30   X20 + R20   X10 + R10
(%i31) float(fullratsimp(Z12));
(%o31) ((X20 + X10 + R20 + R10) X30 + (X10 + R30 + R10) X20 + (R30 + R20) X10
+ (R20 + R10) R30 + R10 R20)/(X30 + R30)
(%i32) ```

### Related Help

Help for Multthru