Mister Exam

# How do you z/(z+4)^2-z/z^2-16 in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
   z       z
-------- - -- - 16
2    2
(z + 4)    z      
$$\left(\frac{z}{\left(z + 4\right)^{2}} - \frac{z}{z^{2}}\right) - 16$$
z/(z + 4)^2 - z/z^2 - 16
Fraction decomposition [src]
-16 + 1/(4 + z) - 1/z - 4/(4 + z)^2
$$-16 + \frac{1}{z + 4} - \frac{4}{\left(z + 4\right)^{2}} - \frac{1}{z}$$
        1     1      4
-16 + ----- - - - --------
4 + z   z          2
(4 + z) 
General simplification [src]
      1      z
-16 - - + --------
z          2
(4 + z) 
$$\frac{z}{\left(z + 4\right)^{2}} - 16 - \frac{1}{z}$$
-16 - 1/z + z/(4 + z)^2
Trigonometric part [src]
      1      z
-16 - - + --------
z          2
(4 + z) 
$$\frac{z}{\left(z + 4\right)^{2}} - 16 - \frac{1}{z}$$
-16 - 1/z + z/(4 + z)^2
Common denominator [src]
          16 + 8*z
-16 - ----------------
3      2
z  + 8*z  + 16*z
$$- \frac{8 z + 16}{z^{3} + 8 z^{2} + 16 z} - 16$$
-16 - (16 + 8*z)/(z^3 + 8*z^2 + 16*z)
Rational denominator [src]
 3            2       2        2
z  - z*(4 + z)  - 16*z *(4 + z)
--------------------------------
2        2
z *(4 + z)            
$$\frac{z^{3} - 16 z^{2} \left(z + 4\right)^{2} - z \left(z + 4\right)^{2}}{z^{2} \left(z + 4\right)^{2}}$$
(z^3 - z*(4 + z)^2 - 16*z^2*(4 + z)^2)/(z^2*(4 + z)^2)
Assemble expression [src]
      1      z
-16 - - + --------
z          2
(4 + z) 
$$\frac{z}{\left(z + 4\right)^{2}} - 16 - \frac{1}{z}$$
-16 - 1/z + z/(4 + z)^2
Combining rational expressions [src]
 2          2               2
z  - (4 + z)  - 16*z*(4 + z)
-----------------------------
2
z*(4 + z)          
$$\frac{z^{2} - 16 z \left(z + 4\right)^{2} - \left(z + 4\right)^{2}}{z \left(z + 4\right)^{2}}$$
(z^2 - (4 + z)^2 - 16*z*(4 + z)^2)/(z*(4 + z)^2)
Combinatorics [src]
   /       3       2       \
-8*\2 + 2*z  + 16*z  + 33*z/
----------------------------
2
z*(4 + z)          
$$- \frac{8 \left(2 z^{3} + 16 z^{2} + 33 z + 2\right)}{z \left(z + 4\right)^{2}}$$
-8*(2 + 2*z^3 + 16*z^2 + 33*z)/(z*(4 + z)^2)
Powers [src]
      1      z
-16 - - + --------
z          2
(4 + z) 
$$\frac{z}{\left(z + 4\right)^{2}} - 16 - \frac{1}{z}$$
-16 - 1/z + z/(4 + z)^2
-16.0 - 1/z + 0.0625*z/(1 + 0.25*z)^2
-16.0 - 1/z + 0.0625*z/(1 + 0.25*z)^2