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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)
(5x^2+9x-2)/(x^2-5x-14)
y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)
1/(2*sqrt(x))
Factor polynomial:
x^2+3
x^4-x
x*y^3-x^3*y^2
x^2-1
Least common denominator:
4*x^(3/2)/3+2*sqrt(x)+x^5/5+e^(5*x^3+1)/15
z*((-z)*log(x)/c+z*log(y)/c)
(z*z-1/2*z)/(z*z-z+1)*z/(z-1/2)
-x^2/(x-2)^2+2*x/(x-2)
Factor squared:
y^4+y^2+2
y^4+y^2-15
y^4-y^2-5
-y^4+8*y^2-8
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)
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)
(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)
(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)
(z2-4*z+16)/(16*z2-1)*(4*z2+z)/(z3+64)-(z+4)/(4*z2-z)
z2-4*z+16/16*z2-1*4*z2+z/z3+64-z+4/4*z2-z
(z²-4*z+16)/(16*z²-1)*(4*z²+z)/(z³+64)-(z+4)/(4*z²-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)
(z^2-4z+16)/(16z^2-1)(4z^2+z)/(z^3+64)-(z+4)/(4z^2-z)
(z2-4z+16)/(16z2-1)(4z2+z)/(z3+64)-(z+4)/(4z2-z)
z2-4z+16/16z2-14z2+z/z3+64-z+4/4z2-z
z^2-4z+16/16z^2-14z^2+z/z^3+64-z+4/4z^2-z
(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)
Similar expressions
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2+z)
(z^2-4*z-16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z-4)/(4*z^2-z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)+(z+4)/(4*z^2-z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3-64)-(z+4)/(4*z^2-z)
(z^2+4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)
(z^2-4*z+16)/(16*z^2-1)*(4*z^2-z)/(z^3+64)-(z+4)/(4*z^2-z)
(z^2-4*z+16)/(16*z^2+1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-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)

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

The solution

You have entered [src]

 2                                 
z  - 4*z + 16 /   2    \           
-------------*\4*z  + z/           
      2                            
  16*z  - 1                 z + 4  
------------------------ - --------
         3                    2    
        z  + 64            4*z  - z

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

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

Fraction decomposition [src]

4/z - 288/(17*(-1 + 4*z)) + 4/(17*(4 + z))

$$- \frac{288}{17 \left(4 z - 1\right)} + \frac{4}{17 \left(z + 4\right)} + \frac{4}{z}$$

4        288            4     
- - ------------- + ----------
z   17*(-1 + 4*z)   17*(4 + z)

General simplification [src]

    -(16 + 8*z)     
--------------------
  /        2       \
z*\-4 + 4*z  + 15*z/

$$- \frac{8 z + 16}{z \left(4 z^{2} + 15 z - 4\right)}$$

-(16 + 8*z)/(z*(-4 + 4*z^2 + 15*z))

Numerical answer [src]

-(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))

-(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))

Common denominator [src]

    -(16 + 8*z)    
-------------------
          3       2
-4*z + 4*z  + 15*z

$$- \frac{8 z + 16}{4 z^{3} + 15 z^{2} - 4 z}$$

-(16 + 8*z)/(-4*z + 4*z^3 + 15*z^2)

Rational denominator [src]

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

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

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

Assemble expression [src]

              /       2\ /      2      \
    4 + z     \z + 4*z /*\16 + z  - 4*z/
- --------- + --------------------------
          2     /         2\ /      3\  
  -z + 4*z      \-1 + 16*z /*\64 + z /

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

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

Combinatorics [src]

     -8*(2 + z)     
--------------------
z*(-1 + 4*z)*(4 + z)

$$- \frac{8 \left(z + 2\right)}{z \left(z + 4\right) \left(4 z - 1\right)}$$

-8*(2 + z)/(z*(-1 + 4*z)*(4 + z))

Powers [src]

              /       2\ /      2      \
    4 + z     \z + 4*z /*\16 + z  - 4*z/
- --------- + --------------------------
          2     /         2\ /      3\  
  -z + 4*z      \-1 + 16*z /*\64 + z /

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

            /       2\ /      2      \
  -4 - z    \z + 4*z /*\16 + z  - 4*z/
--------- + --------------------------
        2     /         2\ /      3\  
-z + 4*z      \-1 + 16*z /*\64 + z /

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

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

Combining rational expressions [src]

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

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

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

Trigonometric part [src]

              /       2\ /      2      \
    4 + z     \z + 4*z /*\16 + z  - 4*z/
- --------- + --------------------------
          2     /         2\ /      3\  
  -z + 4*z      \-1 + 16*z /*\64 + z /

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

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

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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) in partial fractions?

The solution

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