Mister Exam

# How do you (2x-1)/(x*(x+2)^2*(x-4)) in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
     2*x - 1
------------------
2
x*(x + 2) *(x - 4)
$$\frac{2 x - 1}{x \left(x + 2\right)^{2} \left(x - 4\right)}$$
(2*x - 1)/(((x*(x + 2)^2)*(x - 4)))
Fraction decomposition [src]
-5/(12*(2 + x)^2) - 1/(9*(2 + x)) + 1/(16*x) + 7/(144*(-4 + x))
$$- \frac{1}{9 \left(x + 2\right)} - \frac{5}{12 \left(x + 2\right)^{2}} + \frac{7}{144 \left(x - 4\right)} + \frac{1}{16 x}$$
       5            1        1          7
- ----------- - --------- + ---- + ------------
2   9*(2 + x)   16*x   144*(-4 + x)
12*(2 + x)                                   
General simplification [src]
      -1 + 2*x
-------------------
2
x*(-4 + x)*(2 + x) 
$$\frac{2 x - 1}{x \left(x - 4\right) \left(x + 2\right)^{2}}$$
(-1 + 2*x)/(x*(-4 + x)*(2 + x)^2)
Rational denominator [src]
      -1 + 2*x
-------------------
2
x*(-4 + x)*(2 + x) 
$$\frac{2 x - 1}{x \left(x - 4\right) \left(x + 2\right)^{2}}$$
(-1 + 2*x)/(x*(-4 + x)*(2 + x)^2)
Common denominator [src]
     -1 + 2*x
-----------------
4              2
x  - 16*x - 12*x 
$$\frac{2 x - 1}{x^{4} - 12 x^{2} - 16 x}$$
(-1 + 2*x)/(x^4 - 16*x - 12*x^2)
Trigonometric part [src]
      -1 + 2*x
-------------------
2
x*(-4 + x)*(2 + x) 
$$\frac{2 x - 1}{x \left(x - 4\right) \left(x + 2\right)^{2}}$$
(-1 + 2*x)/(x*(-4 + x)*(2 + x)^2)
Combinatorics [src]
      -1 + 2*x
-------------------
2
x*(-4 + x)*(2 + x) 
$$\frac{2 x - 1}{x \left(x - 4\right) \left(x + 2\right)^{2}}$$
(-1 + 2*x)/(x*(-4 + x)*(2 + x)^2)
Powers [src]
      -1 + 2*x
-------------------
2
x*(-4 + x)*(2 + x) 
$$\frac{2 x - 1}{x \left(x - 4\right) \left(x + 2\right)^{2}}$$
(-1 + 2*x)/(x*(-4 + x)*(2 + x)^2)
Assemble expression [src]
      -1 + 2*x
-------------------
2
x*(-4 + x)*(2 + x) 
$$\frac{2 x - 1}{x \left(x - 4\right) \left(x + 2\right)^{2}}$$
(-1 + 2*x)/(x*(-4 + x)*(2 + x)^2)
Combining rational expressions [src]
      -1 + 2*x
-------------------
2
x*(-4 + x)*(2 + x) 
$$\frac{2 x - 1}{x \left(x - 4\right) \left(x + 2\right)^{2}}$$
(-1 + 2*x)/(x*(-4 + x)*(2 + x)^2)
0.25*(-1.0 + 2.0*x)/(x*(1 + 0.5*x)^2*(-4.0 + x))
0.25*(-1.0 + 2.0*x)/(x*(1 + 0.5*x)^2*(-4.0 + x))
     2*x - 1
x*(x - 4)*(x + 2) 
$$\frac{2 x - 1}{x \left(x - 4\right) \left(x + 2\right)^{2}}$$
(2*x - 1)/(x*(x - 4)*(x + 2)^2)