Mister Exam

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How do you in partial fractions?:
y/(b*y-2*b^2)-2/(y^2+y-2*b*y-2*b)*(1+(3*y+y^2)/(3+y))
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(4x^2-3x+1)/(x^4+x^2)
2/x+(3*x-2)/(x+1)
Factor polynomial:
y^5-32
y^n+3-y-1+y^n+1
x^4-5*x^3+6*x^2-10*x+8
t^4/4+4*t^3/3
Least common denominator:
(x*(x-1)^2)^(1/3)*((x-1)^2/3+x*(-2+2*x)/3)/(x*(x-1)^2)
((x^3+y^3)/(x+y))/(x^2-y^2)+(2*y)/(x+y)-(x*y)/(x^2-y^2)
(x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)^2))/(x+1)
((x*x^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3)
Factor squared:
y^4+y^2+9
-y^4-y^2+8
-y^2-4*y-3
x^2-x*a+4*a^2
Identical expressions
(((two s- two + two *s^ two)/(-s*(two +s^ two + two *s)))+((- two s^ two + two s- six))/((s*(s^ two +2*s+2))))* one /s-2/s
(((2s minus 2 plus 2 multiply by s squared ) divide by ( minus s multiply by (2 plus s squared plus 2 multiply by s))) plus (( minus 2s squared plus 2s minus 6)) divide by ((s multiply by (s squared plus 2 multiply by s plus 2)))) multiply by 1 divide by s minus 2 divide by s
(((two s minus two plus two multiply by s to the power of two) divide by ( minus s multiply by (two plus s to the power of two plus two multiply by s))) plus (( minus two s to the power of two plus two s minus six)) divide by ((s multiply by (s to the power of two plus 2 multiply by s plus 2)))) multiply by one divide by s minus 2 divide by s
(((2s-2+2*s2)/(-s*(2+s2+2*s)))+((-2s2+2s-6))/((s*(s2+2*s+2))))*1/s-2/s
2s-2+2*s2/-s*2+s2+2*s+-2s2+2s-6/s*s2+2*s+2*1/s-2/s
(((2s-2+2*s²)/(-s*(2+s²+2*s)))+((-2s²+2s-6))/((s*(s²+2*s+2))))*1/s-2/s
(((2s-2+2*s to the power of 2)/(-s*(2+s to the power of 2+2*s)))+((-2s to the power of 2+2s-6))/((s*(s to the power of 2+2*s+2))))*1/s-2/s
(((2s-2+2s^2)/(-s(2+s^2+2s)))+((-2s^2+2s-6))/((s(s^2+2s+2))))1/s-2/s
(((2s-2+2s2)/(-s(2+s2+2s)))+((-2s2+2s-6))/((s(s2+2s+2))))1/s-2/s
2s-2+2s2/-s2+s2+2s+-2s2+2s-6/ss2+2s+21/s-2/s
2s-2+2s^2/-s2+s^2+2s+-2s^2+2s-6/ss^2+2s+21/s-2/s
(((2s-2+2*s^2) divide by (-s*(2+s^2+2*s)))+((-2s^2+2s-6)) divide by ((s*(s^2+2*s+2))))*1 divide by s-2 divide by s
Similar expressions
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))-((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2-2*s+2))))*1/s-2/s
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s+2/s
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2-2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(((2s-2+2*s^2)/(s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(((2s-2+2*s^2)/(-s*(2+s^2-2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s+6))/((s*(s^2+2*s+2))))*1/s-2/s
(((2s-2+2*s^2)/(-s*(2-s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(((2s-2-2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(((2s+2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s-2))))*1/s-2/s

Expression simplification/ Fraction Decomposition into the simple/ (((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s

How do you (((2s-2+2s^2)/(-s(2+s^2+2s)))+((-2s^2+2s-6))/((s(s^2+2s+2))))1/s-2/s in partial fractions?

The solution

You have entered [src]

               2         2              
  2*s - 2 + 2*s     - 2*s  + 2*s - 6    
----------------- + ----------------    
   /     2      \     / 2          \    
-s*\2 + s  + 2*s/   s*\s  + 2*s + 2/   2
------------------------------------ - -
                 s                     s

$$\frac{\frac{\left(- 2 s^{2} + 2 s\right) - 6}{s \left(\left(s^{2} + 2 s\right) + 2\right)} + \frac{2 s^{2} + \left(2 s - 2\right)}{- s \left(2 s + \left(s^{2} + 2\right)\right)}}{s} - \frac{2}{s}$$

((2*s - 2 + 2*s^2)/(((-s)*(2 + s^2 + 2*s))) + (-2*s^2 + 2*s - 6)/((s*(s^2 + 2*s + 2))))/s - 2/s

Fraction decomposition [src]

-2/s^2 - 2*(3 + s)/(2 + s^2 + 2*s)

$$- \frac{2 \left(s + 3\right)}{s^{2} + 2 s + 2} - \frac{2}{s^{2}}$$

  2     2*(3 + s)  
- -- - ------------
   2        2      
  s    2 + s  + 2*s

General simplification [src]

 /       3            2\ 
-\4 + 2*s  + 4*s + 8*s / 
-------------------------
     2 /     2      \    
    s *\2 + s  + 2*s/

$$- \frac{2 s^{3} + 8 s^{2} + 4 s + 4}{s^{2} \left(s^{2} + 2 s + 2\right)}$$

-(4 + 2*s^3 + 4*s + 8*s^2)/(s^2*(2 + s^2 + 2*s))

Common denominator [src]

 /       3            2\ 
-\4 + 2*s  + 4*s + 8*s / 
-------------------------
      4      2      3    
     s  + 2*s  + 2*s

$$- \frac{2 s^{3} + 8 s^{2} + 4 s + 4}{s^{4} + 2 s^{3} + 2 s^{2}}$$

-(4 + 2*s^3 + 4*s + 8*s^2)/(s^4 + 2*s^2 + 2*s^3)

Expand expression [src]

           2                           2 
      - 2*s  + 2*s - 6    2*s - 2 + 2*s  
      ---------------- - ----------------
        / 2          \     /     2      \
  2   s*\s  + 2*s + 2/   s*\2 + s  + 2*s/
- - + -----------------------------------
  s                    s

$$\frac{\frac{\left(- 2 s^{2} + 2 s\right) - 6}{s \left(\left(s^{2} + 2 s\right) + 2\right)} - \frac{2 s^{2} + \left(2 s - 2\right)}{s \left(2 s + \left(s^{2} + 2\right)\right)}}{s} - \frac{2}{s}$$

-2/s + ((-2*s^2 + 2*s - 6)/(s*(s^2 + 2*s + 2)) - (2*s - 2 + 2*s^2)/(s*(2 + s^2 + 2*s)))/s

Trigonometric part [src]

              2                        2 
      -6 - 2*s  + 2*s    -2 + 2*s + 2*s  
      ---------------- - ----------------
        /     2      \     /     2      \
  2   s*\2 + s  + 2*s/   s*\2 + s  + 2*s/
- - + -----------------------------------
  s                    s

$$\frac{\frac{- 2 s^{2} + 2 s - 6}{s \left(s^{2} + 2 s + 2\right)} - \frac{2 s^{2} + 2 s - 2}{s \left(s^{2} + 2 s + 2\right)}}{s} - \frac{2}{s}$$

-2/s + ((-6 - 2*s^2 + 2*s)/(s*(2 + s^2 + 2*s)) - (-2 + 2*s + 2*s^2)/(s*(2 + s^2 + 2*s)))/s

Rational denominator [src]

                                                                                                   2
    /  /              2\ /     2      \     /        2      \ /     2      \\      3 /     2      \ 
- s*\s*\-2 + 2*s + 2*s /*\2 + s  + 2*s/ - s*\-6 - 2*s  + 2*s/*\2 + s  + 2*s// - 2*s *\2 + s  + 2*s/ 
----------------------------------------------------------------------------------------------------
                                                          2                                         
                                          4 /     2      \                                          
                                         s *\2 + s  + 2*s/

$$\frac{- 2 s^{3} \left(s^{2} + 2 s + 2\right)^{2} - s \left(- s \left(- 2 s^{2} + 2 s - 6\right) \left(s^{2} + 2 s + 2\right) + s \left(s^{2} + 2 s + 2\right) \left(2 s^{2} + 2 s - 2\right)\right)}{s^{4} \left(s^{2} + 2 s + 2\right)^{2}}$$

(-s*(s*(-2 + 2*s + 2*s^2)*(2 + s^2 + 2*s) - s*(-6 - 2*s^2 + 2*s)*(2 + s^2 + 2*s)) - 2*s^3*(2 + s^2 + 2*s)^2)/(s^4*(2 + s^2 + 2*s)^2)

Powers [src]

              2                        2 
      -6 - 2*s  + 2*s    -2 + 2*s + 2*s  
      ---------------- - ----------------
        /     2      \     /     2      \
  2   s*\2 + s  + 2*s/   s*\2 + s  + 2*s/
- - + -----------------------------------
  s                    s

$$\frac{\frac{- 2 s^{2} + 2 s - 6}{s \left(s^{2} + 2 s + 2\right)} - \frac{2 s^{2} + 2 s - 2}{s \left(s^{2} + 2 s + 2\right)}}{s} - \frac{2}{s}$$

              2                        2 
      -6 - 2*s  + 2*s     2 - 2*s - 2*s  
      ---------------- + ----------------
        /     2      \     /     2      \
  2   s*\2 + s  + 2*s/   s*\2 + s  + 2*s/
- - + -----------------------------------
  s                    s

$$\frac{\frac{- 2 s^{2} - 2 s + 2}{s \left(s^{2} + 2 s + 2\right)} + \frac{- 2 s^{2} + 2 s - 6}{s \left(s^{2} + 2 s + 2\right)}}{s} - \frac{2}{s}$$

-2/s + ((-6 - 2*s^2 + 2*s)/(s*(2 + s^2 + 2*s)) + (2 - 2*s - 2*s^2)/(s*(2 + s^2 + 2*s)))/s

Combining rational expressions [src]

  /                 /     2      \                   /          2\                     /     2      \\
2*\(-3 + s*(1 - s))*\2 + s  + 2*s/ - (2 + s*(2 + s))*\-1 + s + s / - s*(2 + s*(2 + s))*\2 + s  + 2*s//
------------------------------------------------------------------------------------------------------
                                   2                 /     2      \                                   
                                  s *(2 + s*(2 + s))*\2 + s  + 2*s/

$$\frac{2 \left(- s \left(s \left(s + 2\right) + 2\right) \left(s^{2} + 2 s + 2\right) + \left(s \left(1 - s\right) - 3\right) \left(s^{2} + 2 s + 2\right) - \left(s \left(s + 2\right) + 2\right) \left(s^{2} + s - 1\right)\right)}{s^{2} \left(s \left(s + 2\right) + 2\right) \left(s^{2} + 2 s + 2\right)}$$

2*((-3 + s*(1 - s))*(2 + s^2 + 2*s) - (2 + s*(2 + s))*(-1 + s + s^2) - s*(2 + s*(2 + s))*(2 + s^2 + 2*s))/(s^2*(2 + s*(2 + s))*(2 + s^2 + 2*s))

Combinatorics [src]

   /     3            2\
-2*\2 + s  + 2*s + 4*s /
------------------------
    2 /     2      \    
   s *\2 + s  + 2*s/

$$- \frac{2 \left(s^{3} + 4 s^{2} + 2 s + 2\right)}{s^{2} \left(s^{2} + 2 s + 2\right)}$$

-2*(2 + s^3 + 2*s + 4*s^2)/(s^2*(2 + s^2 + 2*s))

Assemble expression [src]

              2                        2 
      -6 - 2*s  + 2*s    -2 + 2*s + 2*s  
      ---------------- - ----------------
        /     2      \     /     2      \
  2   s*\2 + s  + 2*s/   s*\2 + s  + 2*s/
- - + -----------------------------------
  s                    s

$$\frac{\frac{- 2 s^{2} + 2 s - 6}{s \left(s^{2} + 2 s + 2\right)} - \frac{2 s^{2} + 2 s - 2}{s \left(s^{2} + 2 s + 2\right)}}{s} - \frac{2}{s}$$

-2/s + ((-6 - 2*s^2 + 2*s)/(s*(2 + s^2 + 2*s)) - (-2 + 2*s + 2*s^2)/(s*(2 + s^2 + 2*s)))/s

Numerical answer [src]

-2.0/s + ((-6.0 + 2.0*s - 2.0*s^2)/(s*(2.0 + s^2 + 2.0*s)) - (-2.0 + 2.0*s + 2.0*s^2)/(s*(2.0 + s^2 + 2.0*s)))/s

-2.0/s + ((-6.0 + 2.0*s - 2.0*s^2)/(s*(2.0 + s^2 + 2.0*s)) - (-2.0 + 2.0*s + 2.0*s^2)/(s*(2.0 + s^2 + 2.0*s)))/s

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Identical expressions

Similar expressions

How do you (((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s in partial fractions?

The solution

How do you (((2s-2+2s^2)/(-s(2+s^2+2s)))+((-2s^2+2s-6))/((s(s^2+2s+2))))1/s-2/s in partial fractions?