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How do you in partial fractions?:
(x^3+1)/(x^3-5*x^2+6*x)
(c+2)/(2c-4)-(2-c)/(6+3c)+(5c^2+12)/(24-6c^2)
4/(8*p^3+14*p^2+7*p+9)
(x+5)/(x-5)*(5+x)/(125-x^3)
Least common denominator:
z/(x-z)+(x+z)/z
((x+5*y)/(x^2-5*x*y)-(x-5*y)/(x^2+5*x*y)*(25*y^2-x^2)/(5*y^2))
(x+2)/2*exp(-x)+|x+5|/2*cos(x)^(-1)
(x+2)/1*x/3*x+6
Identical expressions
ten /(x- three)^ four + seventy-five /(four *(x- three)^ six)-(twelve - four *x)/(four *(x- three)^ four)
10 divide by (x minus 3) to the power of 4 plus 75 divide by (4 multiply by (x minus 3) to the power of 6) minus (12 minus 4 multiply by x) divide by (4 multiply by (x minus 3) to the power of 4)
ten divide by (x minus three) to the power of four plus seventy minus five divide by (four multiply by (x minus three) to the power of six) minus (twelve minus four multiply by x) divide by (four multiply by (x minus three) to the power of four)
10/(x-3)4+75/(4*(x-3)6)-(12-4*x)/(4*(x-3)4)
10/x-34+75/4*x-36-12-4*x/4*x-34
10/(x-3)⁴+75/(4*(x-3)⁶)-(12-4*x)/(4*(x-3)⁴)
10/(x-3)^4+75/(4(x-3)^6)-(12-4x)/(4(x-3)^4)
10/(x-3)4+75/(4(x-3)6)-(12-4x)/(4(x-3)4)
10/x-34+75/4x-36-12-4x/4x-34
10/x-3^4+75/4x-3^6-12-4x/4x-3^4
10 divide by (x-3)^4+75 divide by (4*(x-3)^6)-(12-4*x) divide by (4*(x-3)^4)
Similar expressions
10/(x-3)^4+75/(4*(x-3)^6)+(12-4*x)/(4*(x-3)^4)
10/(x-3)^4+75/(4*(x-3)^6)-(12-4*x)/(4*(x+3)^4)
10/(x-3)^4+75/(4*(x-3)^6)-(12+4*x)/(4*(x-3)^4)
10/(x-3)^4+75/(4*(x+3)^6)-(12-4*x)/(4*(x-3)^4)
10/(x-3)^4-75/(4*(x-3)^6)-(12-4*x)/(4*(x-3)^4)
10/(x+3)^4+75/(4*(x-3)^6)-(12-4*x)/(4*(x-3)^4)

Expression simplification/ Fraction Decomposition into the simple/ 10/(x-3)^4+75/(4*(x-3)^6)-(12-4*x)/(4*(x-3)^4)

How do you 10/(x-3)^4+75/(4(x-3)^6)-(12-4x)/(4*(x-3)^4) in partial fractions?

The solution

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   10          75        12 - 4*x 
-------- + ---------- - ----------
       4            6            4
(x - 3)    4*(x - 3)    4*(x - 3)

$$- \frac{12 - 4 x}{4 \left(x - 3\right)^{4}} + \left(\frac{75}{4 \left(x - 3\right)^{6}} + \frac{10}{\left(x - 3\right)^{4}}\right)$$

10/(x - 3)^4 + 75/((4*(x - 3)^6)) - (12 - 4*x)/(4*(x - 3)^4)

General simplification [src]

               2        
75 + 4*(-3 + x) *(7 + x)
------------------------
                6       
      4*(-3 + x)

$$\frac{4 \left(x - 3\right)^{2} \left(x + 7\right) + 75}{4 \left(x - 3\right)^{6}}$$

(75 + 4*(-3 + x)^2*(7 + x))/(4*(-3 + x)^6)

Fraction decomposition [src]

(-3 + x)^(-3) + 10/(-3 + x)^4 + 75/(4*(-3 + x)^6)

$$\frac{1}{\left(x - 3\right)^{3}} + \frac{10}{\left(x - 3\right)^{4}} + \frac{75}{4 \left(x - 3\right)^{6}}$$

    1           10           75    
--------- + --------- + -----------
        3           4             6
(-3 + x)    (-3 + x)    4*(-3 + x)

Rational denominator [src]

          10                          4 /          6              4\
4*(-3 + x)  *(-12 + 4*x) + 20*(-3 + x) *\8*(-3 + x)  + 15*(-3 + x) /
--------------------------------------------------------------------
                                      14                            
                           16*(-3 + x)

$$\frac{4 \left(x - 3\right)^{10} \left(4 x - 12\right) + 20 \left(x - 3\right)^{4} \left(8 \left(x - 3\right)^{6} + 15 \left(x - 3\right)^{4}\right)}{16 \left(x - 3\right)^{14}}$$

(4*(-3 + x)^10*(-12 + 4*x) + 20*(-3 + x)^4*(8*(-3 + x)^6 + 15*(-3 + x)^4))/(16*(-3 + x)^14)

Assemble expression [src]

    10           75         12 - 4*x 
--------- + ----------- - -----------
        4             6             4
(-3 + x)    4*(-3 + x)    4*(-3 + x)

$$- \frac{12 - 4 x}{4 \left(x - 3\right)^{4}} + \frac{10}{\left(x - 3\right)^{4}} + \frac{75}{4 \left(x - 3\right)^{6}}$$

10/(-3 + x)^4 + 75/(4*(-3 + x)^6) - (12 - 4*x)/(4*(-3 + x)^4)

Expand expression [src]

   10          75        12 - 4*x 
-------- + ---------- - ----------
       4            6            4
(x - 3)    4*(x - 3)    4*(x - 3)

$$- \frac{12 - 4 x}{4 \left(x - 3\right)^{4}} + \frac{10}{\left(x - 3\right)^{4}} + \frac{75}{4 \left(x - 3\right)^{6}}$$

10/(x - 3)^4 + 75/(4*(x - 3)^6) - (12 - 4*x)/(4*(x - 3)^4)

Combining rational expressions [src]

                2             2        
75 + 40*(-3 + x)  - 4*(-3 + x) *(3 - x)
---------------------------------------
                        6              
              4*(-3 + x)

$$\frac{- 4 \left(3 - x\right) \left(x - 3\right)^{2} + 40 \left(x - 3\right)^{2} + 75}{4 \left(x - 3\right)^{6}}$$

(75 + 40*(-3 + x)^2 - 4*(-3 + x)^2*(3 - x))/(4*(-3 + x)^6)

Common denominator [src]

                                 2      3                
                327 - 132*x + 4*x  + 4*x                 
---------------------------------------------------------
                      3       5      6        4         2
2916 - 5832*x - 2160*x  - 72*x  + 4*x  + 540*x  + 4860*x

$$\frac{4 x^{3} + 4 x^{2} - 132 x + 327}{4 x^{6} - 72 x^{5} + 540 x^{4} - 2160 x^{3} + 4860 x^{2} - 5832 x + 2916}$$

(327 - 132*x + 4*x^2 + 4*x^3)/(2916 - 5832*x - 2160*x^3 - 72*x^5 + 4*x^6 + 540*x^4 + 4860*x^2)

Powers [src]

    10           75         12 - 4*x 
--------- + ----------- - -----------
        4             6             4
(-3 + x)    4*(-3 + x)    4*(-3 + x)

$$- \frac{12 - 4 x}{4 \left(x - 3\right)^{4}} + \frac{10}{\left(x - 3\right)^{4}} + \frac{75}{4 \left(x - 3\right)^{6}}$$

    1           10           75    
--------- + --------- + -----------
        3           4             6
(-3 + x)    (-3 + x)    4*(-3 + x)

$$\frac{1}{\left(x - 3\right)^{3}} + \frac{10}{\left(x - 3\right)^{4}} + \frac{75}{4 \left(x - 3\right)^{6}}$$

(-3 + x)^(-3) + 10/(-3 + x)^4 + 75/(4*(-3 + x)^6)

Trigonometric part [src]

    10           75         12 - 4*x 
--------- + ----------- - -----------
        4             6             4
(-3 + x)    4*(-3 + x)    4*(-3 + x)

$$- \frac{12 - 4 x}{4 \left(x - 3\right)^{4}} + \frac{10}{\left(x - 3\right)^{4}} + \frac{75}{4 \left(x - 3\right)^{6}}$$

10/(-3 + x)^4 + 75/(4*(-3 + x)^6) - (12 - 4*x)/(4*(-3 + x)^4)

Combinatorics [src]

                 2      3
327 - 132*x + 4*x  + 4*x 
-------------------------
                 6       
       4*(-3 + x)

$$\frac{4 x^{3} + 4 x^{2} - 132 x + 327}{4 \left(x - 3\right)^{6}}$$

(327 - 132*x + 4*x^2 + 4*x^3)/(4*(-3 + x)^6)

Numerical answer [src]

0.123456790123457/(-1 + 0.333333333333333*x)^4 + 0.0257201646090535/(-1 + 0.333333333333333*x)^6 - 0.00308641975308642*(12.0 - 4.0*x)/(-1 + 0.333333333333333*x)^4

0.123456790123457/(-1 + 0.333333333333333*x)^4 + 0.0257201646090535/(-1 + 0.333333333333333*x)^6 - 0.00308641975308642*(12.0 - 4.0*x)/(-1 + 0.333333333333333*x)^4

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How do you 10/(x-3)^4+75/(4*(x-3)^6)-(12-4*x)/(4*(x-3)^4) in partial fractions?

The solution

How do you 10/(x-3)^4+75/(4(x-3)^6)-(12-4x)/(4*(x-3)^4) in partial fractions?