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Least common denominator (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m

An expression to simplify:

The solution

You have entered [src]
    1                   1      
-y*e           (1 - y)*e       
------ + ----------------------
 1                            2
e  + 1   /      1   \ / 1    \ 
         |1 - ------|*\e  + 1/ 
         |     1    |          
         \    e  + 1/          
-------------------------------
               m               
$$\frac{\frac{- y e^{1}}{1 + e^{1}} + \frac{\left(1 - y\right) e^{1}}{\left(1 - \frac{1}{1 + e^{1}}\right) \left(1 + e^{1}\right)^{2}}}{m}$$
(((-y)*exp(1))/(exp(1) + 1) + ((1 - y)*exp(1))/(((1 - 1/(exp(1) + 1))*(exp(1) + 1)^2)))/m
General simplification [src]
1 - y - E*y
-----------
 m*(1 + E) 
$$\frac{- e y - y + 1}{m \left(1 + e\right)}$$
(1 - y - E*y)/(m*(1 + E))
Trigonometric part [src]
   E*y         E*(1 - y)      
- ----- + --------------------
  1 + E          2 /      1  \
          (1 + E) *|1 - -----|
                   \    1 + E/
------------------------------
              m               
$$\frac{- \frac{e y}{1 + e} + \frac{e \left(1 - y\right)}{\left(1 + e\right)^{2} \left(1 - \frac{1}{1 + e}\right)}}{m}$$
-(-1 + y + y*cosh(1) + y*sinh(1)) 
----------------------------------
    m*(1 + cosh(1) + sinh(1))     
$$- \frac{y + y \sinh{\left(1 \right)} + y \cosh{\left(1 \right)} - 1}{m \left(1 + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)}$$
  y*(cosh(1) + sinh(1))               (1 - y)*(cosh(1) + sinh(1))             
- --------------------- + ----------------------------------------------------
  1 + cosh(1) + sinh(1)   /              1          \                        2
                          |1 - ---------------------|*(1 + cosh(1) + sinh(1)) 
                          \    1 + cosh(1) + sinh(1)/                         
------------------------------------------------------------------------------
                                      m                                       
$$\frac{- \frac{y \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)}{1 + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}} + \frac{\left(1 - y\right) \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)}{\left(1 - \frac{1}{1 + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}}\right) \left(1 + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{2}}}{m}$$
(-y*(cosh(1) + sinh(1))/(1 + cosh(1) + sinh(1)) + (1 - y)*(cosh(1) + sinh(1))/((1 - 1/(1 + cosh(1) + sinh(1)))*(1 + cosh(1) + sinh(1))^2))/m
Combining rational expressions [src]
1 - y - E*y
-----------
 m*(1 + E) 
$$\frac{- e y - y + 1}{m \left(1 + e\right)}$$
(1 - y - E*y)/(m*(1 + E))
Powers [src]
   E*y         E*(1 - y)      
- ----- + --------------------
  1 + E          2 /      1  \
          (1 + E) *|1 - -----|
                   \    1 + E/
------------------------------
              m               
$$\frac{- \frac{e y}{1 + e} + \frac{e \left(1 - y\right)}{\left(1 + e\right)^{2} \left(1 - \frac{1}{1 + e}\right)}}{m}$$
(-E*y/(1 + E) + E*(1 - y)/((1 + E)^2*(1 - 1/(1 + E))))/m
Assemble expression [src]
   E*y           E*(1 - y)       
- ------ + ----------------------
       1                        2
  1 + e    /      1   \ /     1\ 
           |1 - ------|*\1 + e / 
           |         1|          
           \    1 + e /          
---------------------------------
                m                
$$\frac{- \frac{e y}{1 + e^{1}} + \frac{e \left(1 - y\right)}{\left(1 - \frac{1}{1 + e^{1}}\right) \left(1 + e^{1}\right)^{2}}}{m}$$
(-E*y/(1 + exp(1)) + E*(1 - y)/((1 - 1/(1 + exp(1)))*(1 + exp(1))^2))/m
Combinatorics [src]
-(-1 + y + E*y) 
----------------
   m*(1 + E)    
$$- \frac{y + e y - 1}{m \left(1 + e\right)}$$
-(-1 + y + E*y)/(m*(1 + E))
Rational denominator [src]
/         2              2            2  2\  -1
\E*(1 + E)  - E*y*(1 + E)  - y*(1 + E) *e /*e  
-----------------------------------------------
                            3                  
                    /     1\                   
                  m*\1 + e /                   
$$\frac{- y \left(1 + e\right)^{2} e^{2} - e y \left(1 + e\right)^{2} + e \left(1 + e\right)^{2}}{e m \left(1 + e^{1}\right)^{3}}$$
(E*(1 + E)^2 - E*y*(1 + E)^2 - y*(1 + E)^2*exp(2))*exp(-1)/(m*(1 + exp(1))^3)
Expand expression [src]
    1                          
-y*e           E*(1 - y)       
------ + ----------------------
 1                            2
e  + 1   /      1   \ / 1    \ 
         |1 - ------|*\e  + 1/ 
         |     1    |          
         \    e  + 1/          
-------------------------------
               m               
$$\frac{\frac{- y e^{1}}{1 + e^{1}} + \frac{e \left(1 - y\right)}{\left(1 - \frac{1}{1 + e^{1}}\right) \left(1 + e^{1}\right)^{2}}}{m}$$
(((-y)*exp(1))/(exp(1) + 1) + E*(1 - y)/((1 - 1/(exp(1) + 1))*(exp(1) + 1)^2))/m
Numerical answer [src]
(0.268941421369995 - 1.0*y)/m
(0.268941421369995 - 1.0*y)/m
Common denominator [src]
-(-1 + y + E*y) 
----------------
    m + E*m     
$$- \frac{y + e y - 1}{m + e m}$$
-(-1 + y + E*y)/(m + E*m)
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