Mister Exam

Lang:

How to use it?
How do you in partial fractions?:
(a^-2-a/a^-1-1)/(a^2+1)
((2*x+10)/(3*x))/(2*x^2+20*x+50*x)
(u^2-4*u+16)/(16*u^2-1)*(4*u^2+u)/(u^3+64)
a^3-a^2-a-2/(a^3+1)*a^3-2*a^2+2*a-1/(a^3+a^2+a)*a^2+a/(a^2-3*a+2)
Factor polynomial:
m^2-a^2
y^5+y^3+y^2+1
u^2+2*u*v+v^2
x^7+x^5+1
Least common denominator:
cos(a)/2*sin(2)-1-sin(a)/2*cos(2)-1
x^2+25/x-5-10*x/x-5
(x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)^2))/(x+1)
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
Factor squared:
x^2-9*x+5
-y^2-10*y*p-2*p^2
x^2-x-2
x^2-x-5
Least common denominator:
(a^-2-a/a^-1-1)/(a^2+1)
Identical expressions
(a^- two -a/a^- one - one)/(a^ two + one)
(a to the power of minus 2 minus a divide by a to the power of minus 1 minus 1) divide by (a squared plus 1)
(a to the power of minus two minus a divide by a to the power of minus one minus one) divide by (a to the power of two plus one)
(a-2-a/a-1-1)/(a2+1)
a-2-a/a-1-1/a2+1
(a^-2-a/a^-1-1)/(a²+1)
(a to the power of -2-a/a to the power of -1-1)/(a to the power of 2+1)
a^-2-a/a^-1-1/a^2+1
(a^-2-a divide by a^-1-1) divide by (a^2+1)
Similar expressions
(a^-2-a/a^-1+1)/(a^2+1)
(a^-2-a/a^+1-1)/(a^2+1)
(a^+2-a/a^-1-1)/(a^2+1)
(a^-2+a/a^-1-1)/(a^2+1)
(a^-2-a/a^-1-1)/(a^2-1)

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

You have entered [src]

1     a     
-- - --- - 1
 2   /1\    
a    |-|    
     \a/    
------------
    2       
   a  + 1

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

(a^(-2) - a/1/a - 1)/(a^2 + 1)

Fraction decomposition [src]

-1 + a^(-2) - 1/(1 + a^2)

$$-1 - \frac{1}{a^{2} + 1} + \frac{1}{a^{2}}$$

     1      1   
-1 + -- - ------
      2        2
     a    1 + a

General simplification [src]

     2    4
1 - a  - a 
-----------
 2 /     2\
a *\1 + a /

$$\frac{- a^{4} - a^{2} + 1}{a^{2} \left(a^{2} + 1\right)}$$

(1 - a^2 - a^4)/(a^2*(1 + a^2))

Rational denominator [src]

     2    4
1 - a  - a 
-----------
 2 /     2\
a *\1 + a /

$$\frac{- a^{4} - a^{2} + 1}{a^{2} \left(a^{2} + 1\right)}$$

(1 - a^2 - a^4)/(a^2*(1 + a^2))

Numerical answer [src]

(-1.0 + a^(-2) - a^2)/(1.0 + a^2)

(-1.0 + a^(-2) - a^2)/(1.0 + a^2)

Combining rational expressions [src]

     2    4
1 - a  - a 
-----------
 2 /     2\
a *\1 + a /

$$\frac{- a^{4} - a^{2} + 1}{a^{2} \left(a^{2} + 1\right)}$$

(1 - a^2 - a^4)/(a^2*(1 + a^2))

Combinatorics [src]

 /      2    4\ 
-\-1 + a  + a / 
----------------
   2 /     2\   
  a *\1 + a /

$$- \frac{a^{4} + a^{2} - 1}{a^{2} \left(a^{2} + 1\right)}$$

-(-1 + a^2 + a^4)/(a^2*(1 + a^2))

Powers [src]

     1     2
-1 + -- - a 
      2     
     a      
------------
        2   
   1 + a

$$\frac{- a^{2} - 1 + \frac{1}{a^{2}}}{a^{2} + 1}$$

(-1 + a^(-2) - a^2)/(1 + a^2)

Common denominator [src]

        1   
-1 + -------
      2    4
     a  + a

$$-1 + \frac{1}{a^{4} + a^{2}}$$

-1 + 1/(a^2 + a^4)

Trigonometric part [src]

     1     2
-1 + -- - a 
      2     
     a      
------------
        2   
   1 + a

$$\frac{- a^{2} - 1 + \frac{1}{a^{2}}}{a^{2} + 1}$$

(-1 + a^(-2) - a^2)/(1 + a^2)

Assemble expression [src]

     1     2
-1 + -- - a 
      2     
     a      
------------
        2   
   1 + a

$$\frac{- a^{2} - 1 + \frac{1}{a^{2}}}{a^{2} + 1}$$

(-1 + a^(-2) - a^2)/(1 + a^2)