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How do you in partial fractions?:
(c^4)^5*c^8/(c^7)^4
(x^2-6*x)/(x-5)-(10-3*x)/(x-5)
-tan(-1/2+x)/(-1+tan(-1/2+x)^2)
3/(x^3+5)-9*x^3/(x^3+5)^2
Factor polynomial:
z^3+11*z^2+36*z+26
z^3-1
z^2*x^2-9*y*y^2/100
z^2-6*z+5
Least common denominator:
(y/(x*y-x^2)+x/(x*y-y^2))/(x^2+2*x*y+y^2/(1/x+1/y))
y^(2*n-4)*y^n/(y^n+1-5*y)-(7*y^n-30)/(y^n+1-5*y)
x*y-y/x-x*y-x/y-x^2-y^2/x*y
((x/(y-x))^-2)*((x^2+x*y)/(((x+y)^2)-4*x*y))
Factor squared:
-y^4+8*y^2-1
-y^4+7*y^2-4
y^4+7*y^2-8
y^4-9*y^2+2
Identical expressions
((three *x+ two)^ four + twelve *(three *x+ two)^ three *(x- one))/(three *x- two)^ four - twelve *(three *x+ two)^ four *(x- one)/(three *x- two)^ five
((3 multiply by x plus 2) to the power of 4 plus 12 multiply by (3 multiply by x plus 2) cubed multiply by (x minus 1)) divide by (3 multiply by x minus 2) to the power of 4 minus 12 multiply by (3 multiply by x plus 2) to the power of 4 multiply by (x minus 1) divide by (3 multiply by x minus 2) to the power of 5
((three multiply by x plus two) to the power of four plus twelve multiply by (three multiply by x plus two) to the power of three multiply by (x minus one)) divide by (three multiply by x minus two) to the power of four minus twelve multiply by (three multiply by x plus two) to the power of four multiply by (x minus one) divide by (three multiply by x minus two) to the power of five
((3*x+2)4+12*(3*x+2)3*(x-1))/(3*x-2)4-12*(3*x+2)4*(x-1)/(3*x-2)5
3*x+24+12*3*x+23*x-1/3*x-24-12*3*x+24*x-1/3*x-25
((3*x+2)⁴+12*(3*x+2)³*(x-1))/(3*x-2)⁴-12*(3*x+2)⁴*(x-1)/(3*x-2)⁵
((3*x+2) to the power of 4+12*(3*x+2) to the power of 3*(x-1))/(3*x-2) to the power of 4-12*(3*x+2) to the power of 4*(x-1)/(3*x-2) to the power of 5
((3x+2)^4+12(3x+2)^3(x-1))/(3x-2)^4-12(3x+2)^4(x-1)/(3x-2)^5
((3x+2)4+12(3x+2)3(x-1))/(3x-2)4-12(3x+2)4(x-1)/(3x-2)5
3x+24+123x+23x-1/3x-24-123x+24x-1/3x-25
3x+2^4+123x+2^3x-1/3x-2^4-123x+2^4x-1/3x-2^5
((3*x+2)^4+12*(3*x+2)^3*(x-1)) divide by (3*x-2)^4-12*(3*x+2)^4*(x-1) divide by (3*x-2)^5
Similar expressions
((3*x-2)^4+12*(3*x+2)^3*(x-1))/(3*x-2)^4-12*(3*x+2)^4*(x-1)/(3*x-2)^5
((3*x+2)^4+12*(3*x+2)^3*(x-1))/(3*x+2)^4-12*(3*x+2)^4*(x-1)/(3*x-2)^5
((3*x+2)^4+12*(3*x+2)^3*(x-1))/(3*x-2)^4+12*(3*x+2)^4*(x-1)/(3*x-2)^5
((3*x+2)^4+12*(3*x+2)^3*(x+1))/(3*x-2)^4-12*(3*x+2)^4*(x-1)/(3*x-2)^5
((3*x+2)^4+12*(3*x+2)^3*(x-1))/(3*x-2)^4-12*(3*x-2)^4*(x-1)/(3*x-2)^5
((3*x+2)^4+12*(3*x+2)^3*(x-1))/(3*x-2)^4-12*(3*x+2)^4*(x-1)/(3*x+2)^5
((3*x+2)^4-12*(3*x+2)^3*(x-1))/(3*x-2)^4-12*(3*x+2)^4*(x-1)/(3*x-2)^5
((3*x+2)^4+12*(3*x+2)^3*(x-1))/(3*x-2)^4-12*(3*x+2)^4*(x+1)/(3*x-2)^5
((3*x+2)^4+12*(3*x-2)^3*(x-1))/(3*x-2)^4-12*(3*x+2)^4*(x-1)/(3*x-2)^5

Expression simplification/ Fraction Decomposition into the simple/ ((3*x+2)^4+12*(3*x+2)^3*(x-1))/(3*x-2)^4-12*(3*x+2)^4*(x-1)/(3*x-2)^5

How do you ((3x+2)^4+12(3x+2)^3(x-1))/(3x-2)^4-12(3x+2)^4(x-1)/(3*x-2)^5 in partial fractions?

The solution

You have entered [src]

         4               3                       4        
(3*x + 2)  + 12*(3*x + 2) *(x - 1)   12*(3*x + 2) *(x - 1)
---------------------------------- - ---------------------
                     4                              5     
            (3*x - 2)                      (3*x - 2)

$$- \frac{\left(x - 1\right) 12 \left(3 x + 2\right)^{4}}{\left(3 x - 2\right)^{5}} + \frac{\left(x - 1\right) 12 \left(3 x + 2\right)^{3} + \left(3 x + 2\right)^{4}}{\left(3 x - 2\right)^{4}}$$

((3*x + 2)^4 + (12*(3*x + 2)^3)*(x - 1))/(3*x - 2)^4 - (12*(3*x + 2)^4)*(x - 1)/(3*x - 2)^5

Fraction decomposition [src]

1 - 320/(-2 + 3*x)^3 - 80/(-2 + 3*x)^2 + 1024/(-2 + 3*x)^5

$$1 - \frac{80}{\left(3 x - 2\right)^{2}} - \frac{320}{\left(3 x - 2\right)^{3}} + \frac{1024}{\left(3 x - 2\right)^{5}}$$

        320            80           1024   
1 - ----------- - ----------- + -----------
              3             2             5
    (-2 + 3*x)    (-2 + 3*x)    (-2 + 3*x)

General simplification [src]

         3 /            2                       \
(2 + 3*x) *\5*(-2 + 3*x)  + 12*(1 - x)*(2 + 3*x)/
-------------------------------------------------
                             5                   
                   (-2 + 3*x)

$$\frac{\left(3 x + 2\right)^{3} \left(12 \left(1 - x\right) \left(3 x + 2\right) + 5 \left(3 x - 2\right)^{2}\right)}{\left(3 x - 2\right)^{5}}$$

(2 + 3*x)^3*(5*(-2 + 3*x)^2 + 12*(1 - x)*(2 + 3*x))/(-2 + 3*x)^5

Numerical answer [src]

0.0123456790123457*(81.0*(0.666666666666667 + x)^4 + 324.0*(0.666666666666667 + x)^3*(-1.0 + x))/(-0.666666666666667 + x)^4 - 4.0*(0.666666666666667 + x)^4*(-1.0 + x)/(-0.666666666666667 + x)^5

0.0123456790123457*(81.0*(0.666666666666667 + x)^4 + 324.0*(0.666666666666667 + x)^3*(-1.0 + x))/(-0.666666666666667 + x)^4 - 4.0*(0.666666666666667 + x)^4*(-1.0 + x)/(-0.666666666666667 + x)^5

Assemble expression [src]

         4               3                        4         
(2 + 3*x)  + 12*(2 + 3*x) *(-1 + x)   12*(2 + 3*x) *(-1 + x)
----------------------------------- - ----------------------
                      4                              5      
            (-2 + 3*x)                     (-2 + 3*x)

$$- \frac{12 \left(x - 1\right) \left(3 x + 2\right)^{4}}{\left(3 x - 2\right)^{5}} + \frac{12 \left(x - 1\right) \left(3 x + 2\right)^{3} + \left(3 x + 2\right)^{4}}{\left(3 x - 2\right)^{4}}$$

((2 + 3*x)^4 + 12*(2 + 3*x)^3*(-1 + x))/(-2 + 3*x)^4 - 12*(2 + 3*x)^4*(-1 + x)/(-2 + 3*x)^5

Trigonometric part [src]

         4               3                        4         
(2 + 3*x)  + 12*(2 + 3*x) *(-1 + x)   12*(2 + 3*x) *(-1 + x)
----------------------------------- - ----------------------
                      4                              5      
            (-2 + 3*x)                     (-2 + 3*x)

$$- \frac{12 \left(x - 1\right) \left(3 x + 2\right)^{4}}{\left(3 x - 2\right)^{5}} + \frac{12 \left(x - 1\right) \left(3 x + 2\right)^{3} + \left(3 x + 2\right)^{4}}{\left(3 x - 2\right)^{4}}$$

((2 + 3*x)^4 + 12*(2 + 3*x)^3*(-1 + x))/(-2 + 3*x)^4 - 12*(2 + 3*x)^4*(-1 + x)/(-2 + 3*x)^5

Combining rational expressions [src]

         3 /            2                        \
(2 + 3*x) *\5*(-2 + 3*x)  - 12*(-1 + x)*(2 + 3*x)/
--------------------------------------------------
                             5                    
                   (-2 + 3*x)

$$\frac{\left(3 x + 2\right)^{3} \left(- 12 \left(x - 1\right) \left(3 x + 2\right) + 5 \left(3 x - 2\right)^{2}\right)}{\left(3 x - 2\right)^{5}}$$

(2 + 3*x)^3*(5*(-2 + 3*x)^2 - 12*(-1 + x)*(2 + 3*x))/(-2 + 3*x)^5

Common denominator [src]

                         2                 3        
            -384 - 1440*x  - 960*x + 2160*x         
1 - ------------------------------------------------
               4        2                5         3
    -32 - 810*x  - 720*x  + 240*x + 243*x  + 1080*x

$$- \frac{2160 x^{3} - 1440 x^{2} - 960 x - 384}{243 x^{5} - 810 x^{4} + 1080 x^{3} - 720 x^{2} + 240 x - 32} + 1$$

1 - (-384 - 1440*x^2 - 960*x + 2160*x^3)/(-32 - 810*x^4 - 720*x^2 + 240*x + 243*x^5 + 1080*x^3)

Powers [src]

         4            3                         4            
(2 + 3*x)  + (2 + 3*x) *(-12 + 12*x)   (2 + 3*x) *(12 - 12*x)
------------------------------------ + ----------------------
                      4                               5      
            (-2 + 3*x)                      (-2 + 3*x)

$$\frac{\left(12 - 12 x\right) \left(3 x + 2\right)^{4}}{\left(3 x - 2\right)^{5}} + \frac{\left(3 x + 2\right)^{4} + \left(3 x + 2\right)^{3} \left(12 x - 12\right)}{\left(3 x - 2\right)^{4}}$$

         4               3                        4         
(2 + 3*x)  + 12*(2 + 3*x) *(-1 + x)   12*(2 + 3*x) *(-1 + x)
----------------------------------- - ----------------------
                      4                              5      
            (-2 + 3*x)                     (-2 + 3*x)

$$- \frac{12 \left(x - 1\right) \left(3 x + 2\right)^{4}}{\left(3 x - 2\right)^{5}} + \frac{12 \left(x - 1\right) \left(3 x + 2\right)^{3} + \left(3 x + 2\right)^{4}}{\left(3 x - 2\right)^{4}}$$

((2 + 3*x)^4 + 12*(2 + 3*x)^3*(-1 + x))/(-2 + 3*x)^4 - 12*(2 + 3*x)^4*(-1 + x)/(-2 + 3*x)^5

Rational denominator [src]

          5 /         4               3         \                4          4         
(-2 + 3*x) *\(2 + 3*x)  + 12*(2 + 3*x) *(-1 + x)/ - 12*(-2 + 3*x) *(2 + 3*x) *(-1 + x)
--------------------------------------------------------------------------------------
                                               9                                      
                                     (-2 + 3*x)

$$\frac{- 12 \left(x - 1\right) \left(3 x - 2\right)^{4} \left(3 x + 2\right)^{4} + \left(3 x - 2\right)^{5} \left(12 \left(x - 1\right) \left(3 x + 2\right)^{3} + \left(3 x + 2\right)^{4}\right)}{\left(3 x - 2\right)^{9}}$$

((-2 + 3*x)^5*((2 + 3*x)^4 + 12*(2 + 3*x)^3*(-1 + x)) - 12*(-2 + 3*x)^4*(2 + 3*x)^4*(-1 + x))/(-2 + 3*x)^9

Combinatorics [src]

         3 /               2\
(2 + 3*x) *\44 - 48*x + 9*x /
-----------------------------
                   5         
         (-2 + 3*x)

$$\frac{\left(3 x + 2\right)^{3} \left(9 x^{2} - 48 x + 44\right)}{\left(3 x - 2\right)^{5}}$$

(2 + 3*x)^3*(44 - 48*x + 9*x^2)/(-2 + 3*x)^5

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Identical expressions

Similar expressions

How do you ((3*x+2)^4+12*(3*x+2)^3*(x-1))/(3*x-2)^4-12*(3*x+2)^4*(x-1)/(3*x-2)^5 in partial fractions?

The solution

How do you ((3x+2)^4+12(3x+2)^3(x-1))/(3x-2)^4-12(3x+2)^4(x-1)/(3*x-2)^5 in partial fractions?