Mister Exam

Lang:

How to use it?
How do you in partial fractions?:
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)
(z-2)/(6*z+(z-2)*(z-2))+(6/(z*z*z-8))
2*(-1+(-1+x)/(2+x))/(2+x)^2
((4*x)^3*x^-11)/((x^-12)*(5*x^5))
Factor polynomial:
x^3+27
p^9+64
x^2-y^2
x^6-x^4*y^2-x^3+x^2*y
Least common denominator:
(z+t)/(t-z)-(t-z)/(t+z)
(z/t-t/z)*5*t*z/z-t
(z/40+1/20)*(z/40+4/5)*z
y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)
Factor squared:
-y^4-y^2+1
-y^4+y^2+1
y^4+y^2+1
-y^4+y^2-10
Identical expressions
exp(-x)/(one +exp(-x))^ two
exponent of ( minus x) divide by (1 plus exponent of ( minus x)) squared
exponent of ( minus x) divide by (one plus exponent of ( minus x)) to the power of two
exp(-x)/(1+exp(-x))2
exp-x/1+exp-x2
exp(-x)/(1+exp(-x))²
exp(-x)/(1+exp(-x)) to the power of 2
exp-x/1+exp-x^2
exp(-x) divide by (1+exp(-x))^2
Similar expressions
exp(x)/(1+exp(-x))^2
exp(-x)/(1-exp(-x))^2
exp(-x)/(1+exp(x))^2

How do you exp(-x)/(1+exp(-x))^2 in partial fractions?

You have entered [src]

    -x    
   e      
----------
         2
/     -x\ 
\1 + e  /

$$\frac{e^{- x}}{\left(1 + e^{- x}\right)^{2}}$$

exp(-x)/(1 + exp(-x))^2

Fraction decomposition [src]

1/(1 + exp(x)) - 1/(1 + exp(x))^2

$$\frac{1}{e^{x} + 1} - \frac{1}{\left(e^{x} + 1\right)^{2}}$$

  1          1    
------ - ---------
     x           2
1 + e    /     x\ 
         \1 + e /

General simplification [src]

    1     
----------
      2/x\
4*cosh |-|
       \2/

$$\frac{1}{4 \cosh^{2}{\left(\frac{x}{2} \right)}}$$

1/(4*cosh(x/2)^2)

Numerical answer [src]

exp(-x)/(1.0 + exp(-x))^2

exp(-x)/(1.0 + exp(-x))^2

Combining rational expressions [src]

     x   
    e    
---------
        2
/     x\ 
\1 + e /

$$\frac{e^{x}}{\left(e^{x} + 1\right)^{2}}$$

exp(x)/(1 + exp(x))^2

Combinatorics [src]

     x   
    e    
---------
        2
/     x\ 
\1 + e /

$$\frac{e^{x}}{\left(e^{x} + 1\right)^{2}}$$

exp(x)/(1 + exp(x))^2

Rational denominator [src]

     x   
    e    
---------
        2
/     x\ 
\1 + e /

$$\frac{e^{x}}{\left(e^{x} + 1\right)^{2}}$$

exp(x)/(1 + exp(x))^2

Trigonometric part [src]

   -sinh(x) + cosh(x)   
------------------------
                       2
(1 - sinh(x) + cosh(x))

$$\frac{- \sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)} + 1\right)^{2}}$$

 -(-cosh(x) + sinh(x))  
------------------------
                       2
(1 - sinh(x) + cosh(x))

$$- \frac{\sinh{\left(x \right)} - \cosh{\left(x \right)}}{\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)} + 1\right)^{2}}$$

-(-cosh(x) + sinh(x))/(1 - sinh(x) + cosh(x))^2

Common denominator [src]

        x      
       e       
---------------
       x    2*x
1 + 2*e  + e

$$\frac{e^{x}}{e^{2 x} + 2 e^{x} + 1}$$

exp(x)/(1 + 2*exp(x) + exp(2*x))