Mister Exam

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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
factorial(n)/factorial(n+1)-(n-1)/factorial(n)
((x*x-11*x+30)/(x*x-9*x+20))/((x*x-36)/(x*x-16))
((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
Factor polynomial:
x^4+16
3*p3+2*a^210-c^27
x^8-y^6
0.09-a^2
Factor squared:
-q^4-4*q^2+5
-9*p^2-5*p-4
-a^4-8*a^2-1
-5*b^2-2*b+1
How do you in partial fractions?:
(36x-6)/(36x^2-12x+1)
(x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
(6x^2+29x)/(x+5)
(t^4+9)/(t^4+9t^2)
Identical expressions
(-y*exp(one)/(exp(one)+ one)+(one -y)*exp(one)/((one - one /(exp(one)+ one))*(exp(one)+ one)^ two))/m
( minus y multiply by exponent of (1) divide by ( exponent of (1) plus 1) plus (1 minus y) multiply by exponent of (1) divide by ((1 minus 1 divide by ( exponent of (1) plus 1)) multiply by ( exponent of (1) plus 1) squared )) divide by m
( minus y multiply by exponent of (one) divide by ( exponent of (one) plus one) plus (one minus y) multiply by exponent of (one) divide by ((one minus one divide by ( exponent of (one) plus one)) multiply by ( exponent of (one) plus one) to the power of two)) divide by m
(-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)2))/m
-y*exp1/exp1+1+1-y*exp1/1-1/exp1+1*exp1+12/m
(-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)²))/m
(-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1) to the power of 2))/m
(-yexp(1)/(exp(1)+1)+(1-y)exp(1)/((1-1/(exp(1)+1))(exp(1)+1)^2))/m
(-yexp(1)/(exp(1)+1)+(1-y)exp(1)/((1-1/(exp(1)+1))(exp(1)+1)2))/m
-yexp1/exp1+1+1-yexp1/1-1/exp1+1exp1+12/m
-yexp1/exp1+1+1-yexp1/1-1/exp1+1exp1+1^2/m
(-y*exp(1) divide by (exp(1)+1)+(1-y)*exp(1) divide by ((1-1 divide by (exp(1)+1))*(exp(1)+1)^2)) divide by m
Similar expressions
(-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1+1/(exp(1)+1))*(exp(1)+1)^2))/m
(-y*exp(1)/(exp(1)+1)-(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
(y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
(-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)-1)^2))/m
(-y*exp(1)/(exp(1)-1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
(-y*exp(1)/(exp(1)+1)+(1+y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
(-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)-1))*(exp(1)+1)^2))/m

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

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

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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Identical expressions

Similar expressions

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

The solution

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