Mister Exam

# 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
(0.268941421369995 - 1.0*y)/m
(0.268941421369995 - 1.0*y)/m
-(-1 + y + E*y)
m + E*m     
$$- \frac{y + e y - 1}{m + e m}$$
-(-1 + y + E*y)/(m + E*m)