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How do you in partial fractions?:
3*x^2/(x-2)^2+x^3*(4-2*x)/(x-2)^4
((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))
1/(((58/125)*(((x+1)/(x-1))^2))+(0.421815322*((x+1)/(x-1)))+0.2588190452)
(t^2+22t+121)/(t+11+t+11)
Factor polynomial:
-x+2*x^2+2*x^3/3
x^2-x-12/x-4
x^2+x-12/x-3
x^2*t^2+4*x*t+1
Least common denominator:
log((2*x-sqrt(17)+3)/(3+sqrt(17)+2*x))/sqrt(17)
cos(pi-a)+cos(3*pi/2++a)/1+2*cos(-a)/sin(-a)
-cos(7*x-1)^4/((x+5)^2*log(10))-28*cos(7*x-1)^3*sin(7*x-1)/((x+5)*log(10))
cos(120*pi)/360-32*sin(pi)^(4150)/360+2*cos(356*pi)/360-2*tan(135*pi)/360
Factor squared:
-x^2+x*b+5*b^2
x^2+x*a-3*a^2
-x^2+x+15
x^2-9*x*y-15*y^2
Identical expressions
((three *n+ two)/(three *n- two))/(((eighteen *n)/(twenty-seven ^ three - eight))+((six *n)/(nine *n^ two + six *n+ four))-(one /(three *n- two)))-((six *n+ eight)/(three *n- two))
((3 multiply by n plus 2) divide by (3 multiply by n minus 2)) divide by (((18 multiply by n) divide by (27 cubed minus 8)) plus ((6 multiply by n) divide by (9 multiply by n squared plus 6 multiply by n plus 4)) minus (1 divide by (3 multiply by n minus 2))) minus ((6 multiply by n plus 8) divide by (3 multiply by n minus 2))
((three multiply by n plus two) divide by (three multiply by n minus two)) divide by (((eighteen multiply by n) divide by (twenty minus seven to the power of three minus eight)) plus ((six multiply by n) divide by (nine multiply by n to the power of two plus six multiply by n plus four)) minus (one divide by (three multiply by n minus two))) minus ((six multiply by n plus eight) divide by (three multiply by n minus two))
((3*n+2)/(3*n-2))/(((18*n)/(273-8))+((6*n)/(9*n2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))
3*n+2/3*n-2/18*n/273-8+6*n/9*n2+6*n+4-1/3*n-2-6*n+8/3*n-2
((3*n+2)/(3*n-2))/(((18*n)/(27³-8))+((6*n)/(9*n²+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))
((3*n+2)/(3*n-2))/(((18*n)/(27 to the power of 3-8))+((6*n)/(9*n to the power of 2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))
((3n+2)/(3n-2))/(((18n)/(27^3-8))+((6n)/(9n^2+6n+4))-(1/(3n-2)))-((6n+8)/(3n-2))
((3n+2)/(3n-2))/(((18n)/(273-8))+((6n)/(9n2+6n+4))-(1/(3n-2)))-((6n+8)/(3n-2))
3n+2/3n-2/18n/273-8+6n/9n2+6n+4-1/3n-2-6n+8/3n-2
3n+2/3n-2/18n/27^3-8+6n/9n^2+6n+4-1/3n-2-6n+8/3n-2
((3*n+2) divide by (3*n-2)) divide by (((18*n) divide by (27^3-8))+((6*n) divide by (9*n^2+6*n+4))-(1 divide by (3*n-2)))-((6*n+8) divide by (3*n-2))
Similar expressions
((3*n+2)/(3*n+2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))
((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n+2))
((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))+(1/(3*n-2)))-((6*n+8)/(3*n-2))
((3*n+2)/(3*n-2))/(((18*n)/(27^3+8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))
((3*n-2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))
((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))-((6*n-8)/(3*n-2))
((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n+2)))-((6*n+8)/(3*n-2))
((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))+((6*n+8)/(3*n-2))
((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2-6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))
((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n-4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))
((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))-((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))

Expression simplification/ Fraction Decomposition into the simple/ ((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2))

How do you ((3n+2)/(3n-2))/(((18n)/(27^3-8))+((6n)/(9n^2+6n+4))-(1/(3n-2)))-((6n+8)/(3*n-2)) in partial fractions?

The solution

You have entered [src]

           /3*n + 2\                      
           |-------|                      
           \3*n - 2/               6*n + 8
-------------------------------- - -------
 18*n        6*n            1      3*n - 2
----- + -------------- - -------          
19675      2             3*n - 2          
        9*n  + 6*n + 4

$$\frac{\frac{1}{3 n - 2} \left(3 n + 2\right)}{\left(\frac{6 n}{\left(9 n^{2} + 6 n\right) + 4} + \frac{18 n}{19675}\right) - \frac{1}{3 n - 2}} - \frac{6 n + 8}{3 n - 2}$$

((3*n + 2)/(3*n - 2))/((18*n)/19675 + (6*n)/(9*n^2 + 6*n + 4) - 1/(3*n - 2)) - (6*n + 8)/(3*n - 2)

General simplification [src]

                   5           2            4                
    314800 - 2916*n  + 709164*n  + 1589787*n  + 2834352*n    
-------------------------------------------------------------
                  2        4         5                      3
157400 - 1417032*n  - 972*n  + 1458*n  + 472488*n + 531225*n

$$\frac{- 2916 n^{5} + 1589787 n^{4} + 709164 n^{2} + 2834352 n + 314800}{1458 n^{5} - 972 n^{4} + 531225 n^{3} - 1417032 n^{2} + 472488 n + 157400}$$

(314800 - 2916*n^5 + 709164*n^2 + 1589787*n^4 + 2834352*n)/(157400 - 1417032*n^2 - 972*n^4 + 1458*n^5 + 472488*n + 531225*n^3)

Fraction decomposition [src]

-2 - 12/(-2 + 3*n) + 19675*(2 + 3*n)*(4 + 6*n + 9*n^2)/(-78700 - 354294*n + 486*n^4 + 177075*n^2)

$$\frac{19675 \left(3 n + 2\right) \left(9 n^{2} + 6 n + 4\right)}{486 n^{4} + 177075 n^{2} - 354294 n - 78700} - 2 - \frac{12}{3 n - 2}$$

                                   /             2\   
        12         19675*(2 + 3*n)*\4 + 6*n + 9*n /   
-2 - -------- + --------------------------------------
     -2 + 3*n                            4           2
                -78700 - 354294*n + 486*n  + 177075*n

Numerical answer [src]

-(8.0 + 6.0*n)/(-2.0 + 3.0*n) + (2.0 + 3.0*n)/((-2.0 + 3.0*n)*(-1/(-2.0 + 3.0*n) + 0.000914866581956798*n + 6.0*n/(4.0 + 6.0*n + 9.0*n^2)))

-(8.0 + 6.0*n)/(-2.0 + 3.0*n) + (2.0 + 3.0*n)/((-2.0 + 3.0*n)*(-1/(-2.0 + 3.0*n) + 0.000914866581956798*n + 6.0*n/(4.0 + 6.0*n + 9.0*n^2)))

Trigonometric part [src]

  8 + 6*n                        2 + 3*n                     
- -------- + ------------------------------------------------
  -2 + 3*n              /     1        18*n        6*n      \
             (-2 + 3*n)*|- -------- + ----- + --------------|
                        |  -2 + 3*n   19675                2|
                        \                     4 + 6*n + 9*n /

$$\frac{3 n + 2}{\left(3 n - 2\right) \left(\frac{18 n}{19675} + \frac{6 n}{9 n^{2} + 6 n + 4} - \frac{1}{3 n - 2}\right)} - \frac{6 n + 8}{3 n - 2}$$

-(8 + 6*n)/(-2 + 3*n) + (2 + 3*n)/((-2 + 3*n)*(-1/(-2 + 3*n) + 18*n/19675 + 6*n/(4 + 6*n + 9*n^2)))

Rational denominator [src]

                                4         6         5                    2            3            2                      2           3           2           2           2
-1259200 - 4724304*n - 3179574*n  - 8748*n  - 5832*n  + 157400*(-2 + 3*n)  + 4252392*n  + 8501328*n  + 472200*n*(-2 + 3*n)  + 531225*n *(-2 + 3*n)  + 708300*n *(-2 + 3*n) 
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                      2 /                         4           2\                                                           
                                                            (-2 + 3*n) *\-78700 - 354294*n + 486*n  + 177075*n /

$$\frac{- 8748 n^{6} - 5832 n^{5} - 3179574 n^{4} + 531225 n^{3} \left(3 n - 2\right)^{2} + 4252392 n^{3} + 708300 n^{2} \left(3 n - 2\right)^{2} + 8501328 n^{2} + 472200 n \left(3 n - 2\right)^{2} - 4724304 n + 157400 \left(3 n - 2\right)^{2} - 1259200}{\left(3 n - 2\right)^{2} \left(486 n^{4} + 177075 n^{2} - 354294 n - 78700\right)}$$

(-1259200 - 4724304*n - 3179574*n^4 - 8748*n^6 - 5832*n^5 + 157400*(-2 + 3*n)^2 + 4252392*n^3 + 8501328*n^2 + 472200*n*(-2 + 3*n)^2 + 531225*n^3*(-2 + 3*n)^2 + 708300*n^2*(-2 + 3*n)^2)/((-2 + 3*n)^2*(-78700 - 354294*n + 486*n^4 + 177075*n^2))

Assemble expression [src]

  8 + 6*n                        2 + 3*n                     
- -------- + ------------------------------------------------
  -2 + 3*n              /     1        18*n        6*n      \
             (-2 + 3*n)*|- -------- + ----- + --------------|
                        |  -2 + 3*n   19675                2|
                        \                     4 + 6*n + 9*n /

$$\frac{3 n + 2}{\left(3 n - 2\right) \left(\frac{18 n}{19675} + \frac{6 n}{9 n^{2} + 6 n + 4} - \frac{1}{3 n - 2}\right)} - \frac{6 n + 8}{3 n - 2}$$

-(8 + 6*n)/(-2 + 3*n) + (2 + 3*n)/((-2 + 3*n)*(-1/(-2 + 3*n) + 18*n/19675 + 6*n/(4 + 6*n + 9*n^2)))

Combinatorics [src]

 /                               4           2         5\ 
-\-314800 - 2834352*n - 1589787*n  - 709164*n  + 2916*n / 
----------------------------------------------------------
              /                         4           2\    
   (-2 + 3*n)*\-78700 - 354294*n + 486*n  + 177075*n /

$$- \frac{2916 n^{5} - 1589787 n^{4} - 709164 n^{2} - 2834352 n - 314800}{\left(3 n - 2\right) \left(486 n^{4} + 177075 n^{2} - 354294 n - 78700\right)}$$

-(-314800 - 2834352*n - 1589787*n^4 - 709164*n^2 + 2916*n^5)/((-2 + 3*n)*(-78700 - 354294*n + 486*n^4 + 177075*n^2))

Combining rational expressions [src]

-2*(4 + 3*n)*(-78700 - 59025*n*(2 + 3*n) + 6*n*(-2 + 3*n)*(19687 + 9*n*(2 + 3*n))) + 19675*(-2 + 3*n)*(2 + 3*n)*(4 + 3*n*(2 + 3*n))
-----------------------------------------------------------------------------------------------------------------------------------
                          (-2 + 3*n)*(-78700 - 59025*n*(2 + 3*n) + 6*n*(-2 + 3*n)*(19687 + 9*n*(2 + 3*n)))

$$\frac{19675 \left(3 n - 2\right) \left(3 n + 2\right) \left(3 n \left(3 n + 2\right) + 4\right) - 2 \left(3 n + 4\right) \left(6 n \left(3 n - 2\right) \left(9 n \left(3 n + 2\right) + 19687\right) - 59025 n \left(3 n + 2\right) - 78700\right)}{\left(3 n - 2\right) \left(6 n \left(3 n - 2\right) \left(9 n \left(3 n + 2\right) + 19687\right) - 59025 n \left(3 n + 2\right) - 78700\right)}$$

(-2*(4 + 3*n)*(-78700 - 59025*n*(2 + 3*n) + 6*n*(-2 + 3*n)*(19687 + 9*n*(2 + 3*n))) + 19675*(-2 + 3*n)*(2 + 3*n)*(4 + 3*n*(2 + 3*n)))/((-2 + 3*n)*(-78700 - 59025*n*(2 + 3*n) + 6*n*(-2 + 3*n)*(19687 + 9*n*(2 + 3*n))))

Powers [src]

-8 - 6*n                       2 + 3*n                     
-------- + ------------------------------------------------
-2 + 3*n              /     1        18*n        6*n      \
           (-2 + 3*n)*|- -------- + ----- + --------------|
                      |  -2 + 3*n   19675                2|
                      \                     4 + 6*n + 9*n /

$$\frac{- 6 n - 8}{3 n - 2} + \frac{3 n + 2}{\left(3 n - 2\right) \left(\frac{18 n}{19675} + \frac{6 n}{9 n^{2} + 6 n + 4} - \frac{1}{3 n - 2}\right)}$$

  8 + 6*n                        2 + 3*n                     
- -------- + ------------------------------------------------
  -2 + 3*n              /     1        18*n        6*n      \
             (-2 + 3*n)*|- -------- + ----- + --------------|
                        |  -2 + 3*n   19675                2|
                        \                     4 + 6*n + 9*n /

$$\frac{3 n + 2}{\left(3 n - 2\right) \left(\frac{18 n}{19675} + \frac{6 n}{9 n^{2} + 6 n + 4} - \frac{1}{3 n - 2}\right)} - \frac{6 n + 8}{3 n - 2}$$

-(8 + 6*n)/(-2 + 3*n) + (2 + 3*n)/((-2 + 3*n)*(-1/(-2 + 3*n) + 18*n/19675 + 6*n/(4 + 6*n + 9*n^2)))

Common denominator [src]

                         2            3            4              
       629600 - 2124900*n  + 1062450*n  + 1587843*n  + 3779328*n  
-2 + -------------------------------------------------------------
                       2        4         5                      3
     157400 - 1417032*n  - 972*n  + 1458*n  + 472488*n + 531225*n

$$\frac{1587843 n^{4} + 1062450 n^{3} - 2124900 n^{2} + 3779328 n + 629600}{1458 n^{5} - 972 n^{4} + 531225 n^{3} - 1417032 n^{2} + 472488 n + 157400} - 2$$

-2 + (629600 - 2124900*n^2 + 1062450*n^3 + 1587843*n^4 + 3779328*n)/(157400 - 1417032*n^2 - 972*n^4 + 1458*n^5 + 472488*n + 531225*n^3)

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Identical expressions

Similar expressions

How do you ((3*n+2)/(3*n-2))/(((18*n)/(27^3-8))+((6*n)/(9*n^2+6*n+4))-(1/(3*n-2)))-((6*n+8)/(3*n-2)) in partial fractions?

The solution

How do you ((3n+2)/(3n-2))/(((18n)/(27^3-8))+((6n)/(9n^2+6n+4))-(1/(3n-2)))-((6n+8)/(3*n-2)) in partial fractions?