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How do you in partial fractions?:
(234/(((7/20)*p+1)*(p+1)*((111/10)*p+1)))*((3/10)+10/p)
(z-(5*z)/z+1)/(z-4)/(z+1)
1/(1+x^2/3)
(x^2-5*x+6)/(x-3)
Factor polynomial:
y^3+y^5
x^3-x
x1^2+x2^2
x^3+7*x^2+15*x+9
Least common denominator:
sqrt(4/x+1)*x+2*log(sqrt(4/x+1)+1)-2*log(sqrt(4/x+1)-1)
(a-3+18/a+3)/a^2+9/a^2+6*a+9/a-3
5*(2-2/x^2)*cos(2*x+2/x)
(2*a+b)/(a^2-b^2)+1/(a+b)
Factor squared:
y^4+y^2-3
y^4+y^2+4
y^4-12*y^2+7
y^2+4*y-3
Least common denominator:
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
Identical expressions
(z^ two - four *z+ sixteen)/(sixteen *z^ two - one)*(four *z^ two +z)/(z^ three + sixty-four)-(z+ four)/(four *z^ two -z)/ seven /(z^ two + four *z)-(twenty *z+ thirteen)/(seven - twenty-eight *z)
(z squared minus 4 multiply by z plus 16) divide by (16 multiply by z squared minus 1) multiply by (4 multiply by z squared plus z) divide by (z cubed plus 64) minus (z plus 4) divide by (4 multiply by z squared minus z) divide by 7 divide by (z squared plus 4 multiply by z) minus (20 multiply by z plus 13) divide by (7 minus 28 multiply by z)
(z to the power of two minus four multiply by z plus sixteen) divide by (sixteen multiply by z to the power of two minus one) multiply by (four multiply by z to the power of two plus z) divide by (z to the power of three plus sixty minus four) minus (z plus four) divide by (four multiply by z to the power of two minus z) divide by seven divide by (z to the power of two plus four multiply by z) minus (twenty multiply by z plus thirteen) divide by (seven minus twenty minus eight multiply by z)
(z2-4*z+16)/(16*z2-1)*(4*z2+z)/(z3+64)-(z+4)/(4*z2-z)/7/(z2+4*z)-(20*z+13)/(7-28*z)
z2-4*z+16/16*z2-1*4*z2+z/z3+64-z+4/4*z2-z/7/z2+4*z-20*z+13/7-28*z
(z²-4*z+16)/(16*z²-1)*(4*z²+z)/(z³+64)-(z+4)/(4*z²-z)/7/(z²+4*z)-(20*z+13)/(7-28*z)
(z to the power of 2-4*z+16)/(16*z to the power of 2-1)*(4*z to the power of 2+z)/(z to the power of 3+64)-(z+4)/(4*z to the power of 2-z)/7/(z to the power of 2+4*z)-(20*z+13)/(7-28*z)
(z^2-4z+16)/(16z^2-1)(4z^2+z)/(z^3+64)-(z+4)/(4z^2-z)/7/(z^2+4z)-(20z+13)/(7-28z)
(z2-4z+16)/(16z2-1)(4z2+z)/(z3+64)-(z+4)/(4z2-z)/7/(z2+4z)-(20z+13)/(7-28z)
z2-4z+16/16z2-14z2+z/z3+64-z+4/4z2-z/7/z2+4z-20z+13/7-28z
z^2-4z+16/16z^2-14z^2+z/z^3+64-z+4/4z^2-z/7/z^2+4z-20z+13/7-28z
(z^2-4*z+16) divide by (16*z^2-1)*(4*z^2+z) divide by (z^3+64)-(z+4) divide by (4*z^2-z) divide by 7 divide by (z^2+4*z)-(20*z+13) divide by (7-28*z)
Similar expressions
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)+(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2-4*z)-(20*z+13)/(7-28*z)
(z^2-4*z-16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3-64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2-z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2+z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)+(20*z+13)/(7-28*z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z-13)/(7-28*z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7+28*z)
(z^2-4*z+16)/(16*z^2+1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z-4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
(z^2+4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)

Expression simplification/ Fraction Decomposition into the simple/ (z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)

How do you (z^2-4z+16)/(16z^2-1)(4z^2+z)/(z^3+64)-(z+4)/(4z^2-z)/7/(z^2+4z)-(20z+13)/(7-28z) in partial fractions?

The solution

You have entered [src]

                           // z + 4  \\            
 2                         ||--------||            
z  - 4*z + 16 /   2    \   ||   2    ||            
-------------*\4*z  + z/   |\4*z  - z/|            
      2                    |----------|            
  16*z  - 1                \    7     /   20*z + 13
------------------------ - ------------ - ---------
         3                    2            7 - 28*z
        z  + 64              z  + 4*z

$$\left(- \frac{\frac{1}{7} \frac{z + 4}{4 z^{2} - z}}{z^{2} + 4 z} + \frac{\frac{\left(z^{2} - 4 z\right) + 16}{16 z^{2} - 1} \left(4 z^{2} + z\right)}{z^{3} + 64}\right) - \frac{20 z + 13}{7 - 28 z}$$

(((z^2 - 4*z + 16)/(16*z^2 - 1))*(4*z^2 + z))/(z^3 + 64) - ((z + 4)/(4*z^2 - z))/7/(z^2 + 4*z) - (20*z + 13)/(7 - 28*z)

Fraction decomposition [src]

5/7 + 1/(7*z^2) + 4/(7*z) + 4/(17*(4 + z)) + 41/(119*(-1 + 4*z))

$$\frac{5}{7} + \frac{41}{119 \left(4 z - 1\right)} + \frac{4}{17 \left(z + 4\right)} + \frac{4}{7 z} + \frac{1}{7 z^{2}}$$

5    1      4        4              41      
- + ---- + --- + ---------- + --------------
7      2   7*z   17*(4 + z)   119*(-1 + 4*z)
    7*z

General simplification [src]

             4       2        3
-4 - z + 20*z  + 52*z  + 100*z 
-------------------------------
       2 /        2       \    
    7*z *\-4 + 4*z  + 15*z/

$$\frac{20 z^{4} + 100 z^{3} + 52 z^{2} - z - 4}{7 z^{2} \left(4 z^{2} + 15 z - 4\right)}$$

(-4 - z + 20*z^4 + 52*z^2 + 100*z^3)/(7*z^2*(-4 + 4*z^2 + 15*z))

Trigonometric part [src]

                                         /       2\ /      2      \
  13 + 20*z            4 + z             \z + 4*z /*\16 + z  - 4*z/
- --------- - ------------------------ + --------------------------
   7 - 28*z     / 2      \ /        2\     /         2\ /      3\  
              7*\z  + 4*z/*\-z + 4*z /     \-1 + 16*z /*\64 + z /

$$- \frac{z + 4}{7 \left(z^{2} + 4 z\right) \left(4 z^{2} - z\right)} + \frac{\left(4 z^{2} + z\right) \left(z^{2} - 4 z + 16\right)}{\left(16 z^{2} - 1\right) \left(z^{3} + 64\right)} - \frac{20 z + 13}{7 - 28 z}$$

-(13 + 20*z)/(7 - 28*z) - (4 + z)/(7*(z^2 + 4*z)*(-z + 4*z^2)) + (z + 4*z^2)*(16 + z^2 - 4*z)/((-1 + 16*z^2)*(64 + z^3))

Assemble expression [src]

                                         /       2\ /      2      \
  13 + 20*z            4 + z             \z + 4*z /*\16 + z  - 4*z/
- --------- - ------------------------ + --------------------------
   7 - 28*z     / 2      \ /        2\     /         2\ /      3\  
              7*\z  + 4*z/*\-z + 4*z /     \-1 + 16*z /*\64 + z /

-(13 + 20*z)/(7 - 28*z) - (4 + z)/(7*(z^2 + 4*z)*(-z + 4*z^2)) + (z + 4*z^2)*(16 + z^2 - 4*z)/((-1 + 16*z^2)*(64 + z^3))

Rational denominator [src]

           //         2\          /      3\   /       2\ / 2      \ /           2\ /      2      \\   /         2\              /      3\ / 2      \ /           2\
(7 - 28*z)*\\-1 + 16*z /*(-4 - z)*\64 + z / + \z + 4*z /*\z  + 4*z/*\-7*z + 28*z /*\16 + z  - 4*z// + \-1 + 16*z /*(-13 - 20*z)*\64 + z /*\z  + 4*z/*\-7*z + 28*z /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                    /         2\            /      3\ / 2      \ /           2\                                                    
                                                    \-1 + 16*z /*(7 - 28*z)*\64 + z /*\z  + 4*z/*\-7*z + 28*z /

$$\frac{\left(7 - 28 z\right) \left(\left(- z - 4\right) \left(16 z^{2} - 1\right) \left(z^{3} + 64\right) + \left(z^{2} + 4 z\right) \left(4 z^{2} + z\right) \left(28 z^{2} - 7 z\right) \left(z^{2} - 4 z + 16\right)\right) + \left(- 20 z - 13\right) \left(z^{2} + 4 z\right) \left(16 z^{2} - 1\right) \left(28 z^{2} - 7 z\right) \left(z^{3} + 64\right)}{\left(7 - 28 z\right) \left(z^{2} + 4 z\right) \left(16 z^{2} - 1\right) \left(28 z^{2} - 7 z\right) \left(z^{3} + 64\right)}$$

((7 - 28*z)*((-1 + 16*z^2)*(-4 - z)*(64 + z^3) + (z + 4*z^2)*(z^2 + 4*z)*(-7*z + 28*z^2)*(16 + z^2 - 4*z)) + (-1 + 16*z^2)*(-13 - 20*z)*(64 + z^3)*(z^2 + 4*z)*(-7*z + 28*z^2))/((-1 + 16*z^2)*(7 - 28*z)*(64 + z^3)*(z^2 + 4*z)*(-7*z + 28*z^2))

Common denominator [src]

                  3       2 
5    -4 - z + 25*z  + 72*z  
- + ------------------------
7         2       4        3
    - 28*z  + 28*z  + 105*z

$$\frac{5}{7} + \frac{25 z^{3} + 72 z^{2} - z - 4}{28 z^{4} + 105 z^{3} - 28 z^{2}}$$

5/7 + (-4 - z + 25*z^3 + 72*z^2)/(-28*z^2 + 28*z^4 + 105*z^3)

Powers [src]

                                         /       2\ /      2      \
  13 + 20*z            4 + z             \z + 4*z /*\16 + z  - 4*z/
- --------- - ------------------------ + --------------------------
   7 - 28*z     / 2      \ /        2\     /         2\ /      3\  
              7*\z  + 4*z/*\-z + 4*z /     \-1 + 16*z /*\64 + z /

                      4   z                                     
                    - - - -           /       2\ /      2      \
-13 - 20*z            7   7           \z + 4*z /*\16 + z  - 4*z/
---------- + ---------------------- + --------------------------
 7 - 28*z    / 2      \ /        2\     /         2\ /      3\  
             \z  + 4*z/*\-z + 4*z /     \-1 + 16*z /*\64 + z /

$$\frac{- \frac{z}{7} - \frac{4}{7}}{\left(z^{2} + 4 z\right) \left(4 z^{2} - z\right)} + \frac{\left(4 z^{2} + z\right) \left(z^{2} - 4 z + 16\right)}{\left(16 z^{2} - 1\right) \left(z^{3} + 64\right)} + \frac{- 20 z - 13}{7 - 28 z}$$

(-13 - 20*z)/(7 - 28*z) + (-4/7 - z/7)/((z^2 + 4*z)*(-z + 4*z^2)) + (z + 4*z^2)*(16 + z^2 - 4*z)/((-1 + 16*z^2)*(64 + z^3))

Combinatorics [src]

             4       2        3
-4 - z + 20*z  + 52*z  + 100*z 
-------------------------------
       2                       
    7*z *(-1 + 4*z)*(4 + z)

$$\frac{20 z^{4} + 100 z^{3} + 52 z^{2} - z - 4}{7 z^{2} \left(z + 4\right) \left(4 z - 1\right)}$$

(-4 - z + 20*z^4 + 52*z^2 + 100*z^3)/(7*z^2*(-1 + 4*z)*(4 + z))

Combining rational expressions [src]

          /  /         2\ /      3\      3                                       \    2            /         2\             /      3\
(1 - 4*z)*\- \-1 + 16*z /*\64 + z / + 7*z *(1 + 4*z)*(-1 + 4*z)*(16 + z*(-4 + z))/ - z *(-1 + 4*z)*\-1 + 16*z /*(13 + 20*z)*\64 + z /
-------------------------------------------------------------------------------------------------------------------------------------
                                              2                      /         2\ /      3\                                          
                                           7*z *(1 - 4*z)*(-1 + 4*z)*\-1 + 16*z /*\64 + z /

$$\frac{- z^{2} \left(4 z - 1\right) \left(20 z + 13\right) \left(16 z^{2} - 1\right) \left(z^{3} + 64\right) + \left(1 - 4 z\right) \left(7 z^{3} \left(4 z - 1\right) \left(4 z + 1\right) \left(z \left(z - 4\right) + 16\right) - \left(16 z^{2} - 1\right) \left(z^{3} + 64\right)\right)}{7 z^{2} \left(1 - 4 z\right) \left(4 z - 1\right) \left(16 z^{2} - 1\right) \left(z^{3} + 64\right)}$$

((1 - 4*z)*(-(-1 + 16*z^2)*(64 + z^3) + 7*z^3*(1 + 4*z)*(-1 + 4*z)*(16 + z*(-4 + z))) - z^2*(-1 + 4*z)*(-1 + 16*z^2)*(13 + 20*z)*(64 + z^3))/(7*z^2*(1 - 4*z)*(-1 + 4*z)*(-1 + 16*z^2)*(64 + z^3))

Numerical answer [src]

-(13.0 + 20.0*z)/(7.0 - 28.0*z) - 0.142857142857143*(4.0 + z)/((z^2 + 4.0*z)*(-z + 4.0*z^2)) + (z + 4.0*z^2)*(16.0 + z^2 - 4.0*z)/((64.0 + z^3)*(-1.0 + 16.0*z^2))

-(13.0 + 20.0*z)/(7.0 - 28.0*z) - 0.142857142857143*(4.0 + z)/((z^2 + 4.0*z)*(-z + 4.0*z^2)) + (z + 4.0*z^2)*(16.0 + z^2 - 4.0*z)/((64.0 + z^3)*(-1.0 + 16.0*z^2))

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How to use it?

Identical expressions

Similar expressions

How do you (z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z) in partial fractions?

The solution

How do you (z^2-4z+16)/(16z^2-1)(4z^2+z)/(z^3+64)-(z+4)/(4z^2-z)/7/(z^2+4z)-(20z+13)/(7-28z) in partial fractions?