Mister Exam

Other calculators

Expression simplification/ Fraction Decomposition into the simple/ (4s^2+4s-2)/((-s*(s^2+2*s+2)))-4/s

How do you (4s^2+4s-2)/((-s*(s^2+2*s+2)))-4/s in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
     2               
  4*s  + 4*s - 2    4
----------------- - -
   / 2          \   s
-s*\s  + 2*s + 2/
$$\frac{\left(4 s^{2} + 4 s\right) - 2}{- s \left(\left(s^{2} + 2 s\right) + 2\right)} - \frac{4}{s}$$ 
(4*s^2 + 4*s - 2)/(((-s)*(s^2 + 2*s + 2))) - 4/s
General simplification [src] 
 /       2       \ 
-\6 + 8*s  + 12*s/ 
-------------------
    /     2      \ 
  s*\2 + s  + 2*s/
$$- \frac{8 s^{2} + 12 s + 6}{s \left(s^{2} + 2 s + 2\right)}$$ 
-(6 + 8*s^2 + 12*s)/(s*(2 + s^2 + 2*s))
Fraction decomposition [src] 
-3/s - (6 + 5*s)/(2 + s^2 + 2*s)
$$- \frac{5 s + 6}{s^{2} + 2 s + 2} - \frac{3}{s}$$ 
  3     6 + 5*s   
- - - ------------
  s        2      
      2 + s  + 2*s
Numerical answer [src] 
-4.0/s - (-2.0 + 4.0*s + 4.0*s^2)/(s*(2.0 + s^2 + 2.0*s))
-4.0/s - (-2.0 + 4.0*s + 4.0*s^2)/(s*(2.0 + s^2 + 2.0*s))
Rational denominator [src] 
    /              2\       /     2      \
- s*\-2 + 4*s + 4*s / - 4*s*\2 + s  + 2*s/
------------------------------------------
             2 /     2      \             
            s *\2 + s  + 2*s/
$$\frac{- 4 s \left(s^{2} + 2 s + 2\right) - s \left(4 s^{2} + 4 s - 2\right)}{s^{2} \left(s^{2} + 2 s + 2\right)}$$ 
(-s*(-2 + 4*s + 4*s^2) - 4*s*(2 + s^2 + 2*s))/(s^2*(2 + s^2 + 2*s))
Combining rational expressions [src] 
2*(-3 - 2*s*(1 + s) - 2*s*(2 + s))
----------------------------------
        s*(2 + s*(2 + s))
$$\frac{2 \left(- 2 s \left(s + 1\right) - 2 s \left(s + 2\right) - 3\right)}{s \left(s \left(s + 2\right) + 2\right)}$$ 
2*(-3 - 2*s*(1 + s) - 2*s*(2 + s))/(s*(2 + s*(2 + s)))
Assemble expression [src] 
                    2 
  4   -2 + 4*s + 4*s  
- - - ----------------
  s     /     2      \
      s*\2 + s  + 2*s/
$$- \frac{4}{s} - \frac{4 s^{2} + 4 s - 2}{s \left(s^{2} + 2 s + 2\right)}$$ 
-4/s - (-2 + 4*s + 4*s^2)/(s*(2 + s^2 + 2*s))
Expand expression [src] 
          2           
  4    4*s  + 4*s - 2 
- - - ----------------
  s     / 2          \
      s*\s  + 2*s + 2/
$$- \frac{4}{s} - \frac{\left(4 s^{2} + 4 s\right) - 2}{s \left(\left(s^{2} + 2 s\right) + 2\right)}$$ 
-4/s - (4*s^2 + 4*s - 2)/(s*(s^2 + 2*s + 2))
Common denominator [src] 
 /       2       \ 
-\6 + 8*s  + 12*s/ 
-------------------
   3            2  
  s  + 2*s + 2*s
$$- \frac{8 s^{2} + 12 s + 6}{s^{3} + 2 s^{2} + 2 s}$$ 
-(6 + 8*s^2 + 12*s)/(s^3 + 2*s + 2*s^2)
Combinatorics [src] 
   /       2      \
-2*\3 + 4*s  + 6*s/
-------------------
    /     2      \ 
  s*\2 + s  + 2*s/
$$- \frac{2 \left(4 s^{2} + 6 s + 3\right)}{s \left(s^{2} + 2 s + 2\right)}$$ 
-2*(3 + 4*s^2 + 6*s)/(s*(2 + s^2 + 2*s))
Powers [src] 
                    2 
  4   -2 + 4*s + 4*s  
- - - ----------------
  s     /     2      \
      s*\2 + s  + 2*s/
$$- \frac{4}{s} - \frac{4 s^{2} + 4 s - 2}{s \left(s^{2} + 2 s + 2\right)}$$ 
                    2 
  4    2 - 4*s - 4*s  
- - + ----------------
  s     /     2      \
      s*\2 + s  + 2*s/
$$\frac{- 4 s^{2} - 4 s + 2}{s \left(s^{2} + 2 s + 2\right)} - \frac{4}{s}$$ 
-4/s + (2 - 4*s - 4*s^2)/(s*(2 + s^2 + 2*s))
Trigonometric part [src] 
                    2 
  4   -2 + 4*s + 4*s  
- - - ----------------
  s     /     2      \
      s*\2 + s  + 2*s/
$$- \frac{4}{s} - \frac{4 s^{2} + 4 s - 2}{s \left(s^{2} + 2 s + 2\right)}$$ 
-4/s - (-2 + 4*s + 4*s^2)/(s*(2 + s^2 + 2*s))
    © Mister Exam – Calculator