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How do you in partial fractions?:
exp(-x)/(1+E^(-x))^2
4-4s-(s^2+s+1)*(4s^2-6)/((-s*(s^2+2*s+2)))
(2-i)^2-z/i+((4-i)*i^7)/(i-2)
1/(x-x^2)
Factor polynomial:
z^2+2*z+5
y*y/x-x^2+x*y/x-y^2
y*x-y^a+3*x-3*a
y^x*y^3-y-1+y^x*y
Least common denominator:
((x-x2+t)/2-x1+(abs((x-x2+t)/2-x1)))/2
(x/x^2-4+x/(x-2)^2)*(2-x)^2/2*x-x/x+2
(x-x^2/280)*(1-x/140)
x/x^2-25+5/5-x+1/x+5
Factor squared:
y^4+4*y^2+3
-y^4-4*y^2-2
-y^4+4*y^2-2
-y^4+4*y^2+2
Least common denominator:
((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)
Identical expressions
((x+ five)/(x^ two - eighty-one)+(x+ seven)/(x^ two - eighteen *x+ eighty-one))/((x+ three)^ two)/((x+ nine)^ two)+(seven +x)/(nine +x)
((x plus 5) divide by (x squared minus 81) plus (x plus 7) divide by (x squared minus 18 multiply by x plus 81)) divide by ((x plus 3) squared ) divide by ((x plus 9) squared ) plus (7 plus x) divide by (9 plus x)
((x plus five) divide by (x to the power of two minus eighty minus one) plus (x plus seven) divide by (x to the power of two minus eighteen multiply by x plus eighty minus one)) divide by ((x plus three) to the power of two) divide by ((x plus nine) to the power of two) plus (seven plus x) divide by (nine plus x)
((x+5)/(x2-81)+(x+7)/(x2-18*x+81))/((x+3)2)/((x+9)2)+(7+x)/(9+x)
x+5/x2-81+x+7/x2-18*x+81/x+32/x+92+7+x/9+x
((x+5)/(x²-81)+(x+7)/(x²-18*x+81))/((x+3)²)/((x+9)²)+(7+x)/(9+x)
((x+5)/(x to the power of 2-81)+(x+7)/(x to the power of 2-18*x+81))/((x+3) to the power of 2)/((x+9) to the power of 2)+(7+x)/(9+x)
((x+5)/(x^2-81)+(x+7)/(x^2-18x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)
((x+5)/(x2-81)+(x+7)/(x2-18x+81))/((x+3)2)/((x+9)2)+(7+x)/(9+x)
x+5/x2-81+x+7/x2-18x+81/x+32/x+92+7+x/9+x
x+5/x^2-81+x+7/x^2-18x+81/x+3^2/x+9^2+7+x/9+x
((x+5) divide by (x^2-81)+(x+7) divide by (x^2-18*x+81)) divide by ((x+3)^2) divide by ((x+9)^2)+(7+x) divide by (9+x)
Similar expressions
((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)-(7+x)/(9+x)
((x+5)/(x^2-81)+(x+7)/(x^2-18*x-81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)
((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7-x)/(9+x)
((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x-3)^2)/((x+9)^2)+(7+x)/(9+x)
((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9-x)
((x+5)/(x^2-81)+(x-7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)
((x-5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)
((x+5)/(x^2+81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)
((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x-9)^2)+(7+x)/(9+x)
((x+5)/(x^2-81)+(x+7)/(x^2+18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)
((x+5)/(x^2-81)-(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)

Expression simplification/ Fraction Decomposition into the simple/ ((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)

How do you ((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x) in partial fractions?

The solution

You have entered [src]

/ x + 5        x + 7     \        
|------- + --------------|        
| 2         2            |        
|x  - 81   x  - 18*x + 81|        
|------------------------|        
|               2        |        
\        (x + 3)         /   7 + x
-------------------------- + -----
                2            9 + x
         (x + 9)

$$\frac{\left(\frac{x + 5}{x^{2} - 81} + \frac{x + 7}{\left(x^{2} - 18 x\right) + 81}\right) \frac{1}{\left(x + 3\right)^{2}}}{\left(x + 9\right)^{2}} + \frac{x + 7}{x + 9}$$

(((x + 5)/(x^2 - 81) + (x + 7)/(x^2 - 18*x + 81))/(x + 3)^2)/(x + 9)^2 + (7 + x)/(9 + x)

Fraction decomposition [src]

1 - 34991/(17496*(9 + x)) - 1/(17496*(-9 + x)) + 1/(162*(9 + x)^3) + 1/(1458*(9 + x)^2) + 1/(2916*(-9 + x)^2)

$$1 - \frac{34991}{17496 \left(x + 9\right)} + \frac{1}{1458 \left(x + 9\right)^{2}} + \frac{1}{162 \left(x + 9\right)^{3}} - \frac{1}{17496 \left(x - 9\right)} + \frac{1}{2916 \left(x - 9\right)^{2}}$$

        34991             1               1               1               1       
1 - ------------- - -------------- + ------------ + ------------- + --------------
    17496*(9 + x)   17496*(-9 + x)              3               2                2
                                     162*(9 + x)    1458*(9 + x)    2916*(-9 + x)

General simplification [src]

         5         2        3      4         
45929 + x  - 1134*x  - 162*x  + 7*x  + 6561*x
---------------------------------------------
         5         2        3      4         
59049 + x  - 1458*x  - 162*x  + 9*x  + 6561*x

$$\frac{x^{5} + 7 x^{4} - 162 x^{3} - 1134 x^{2} + 6561 x + 45929}{x^{5} + 9 x^{4} - 162 x^{3} - 1458 x^{2} + 6561 x + 59049}$$

(45929 + x^5 - 1134*x^2 - 162*x^3 + 7*x^4 + 6561*x)/(59049 + x^5 - 1458*x^2 - 162*x^3 + 9*x^4 + 6561*x)

Numerical answer [src]

(7.0 + x)/(9.0 + x) + 0.00137174211248285*((5.0 + x)/(-81.0 + x^2) + (7.0 + x)/(81.0 + x^2 - 18.0*x))/((1 + 0.111111111111111*x)^2*(1 + 0.333333333333333*x)^2)

(7.0 + x)/(9.0 + x) + 0.00137174211248285*((5.0 + x)/(-81.0 + x^2) + (7.0 + x)/(81.0 + x^2 - 18.0*x))/((1 + 0.111111111111111*x)^2*(1 + 0.333333333333333*x)^2)

Combining rational expressions [src]

/       2\                                               2 /       2\                                   
\-81 + x /*(7 + x) + (5 + x)*(81 + x*(-18 + x)) + (3 + x) *\-81 + x /*(7 + x)*(9 + x)*(81 + x*(-18 + x))
--------------------------------------------------------------------------------------------------------
                            /       2\        2        2                                                
                            \-81 + x /*(3 + x) *(9 + x) *(81 + x*(-18 + x))

$$\frac{\left(x + 3\right)^{2} \left(x + 7\right) \left(x + 9\right) \left(x^{2} - 81\right) \left(x \left(x - 18\right) + 81\right) + \left(x + 5\right) \left(x \left(x - 18\right) + 81\right) + \left(x + 7\right) \left(x^{2} - 81\right)}{\left(x + 3\right)^{2} \left(x + 9\right)^{2} \left(x^{2} - 81\right) \left(x \left(x - 18\right) + 81\right)}$$

((-81 + x^2)*(7 + x) + (5 + x)*(81 + x*(-18 + x)) + (3 + x)^2*(-81 + x^2)*(7 + x)*(9 + x)*(81 + x*(-18 + x)))/((-81 + x^2)*(3 + x)^2*(9 + x)^2*(81 + x*(-18 + x)))

Trigonometric part [src]

         5 + x         7 + x     
        -------- + --------------
               2         2       
7 + x   -81 + x    81 + x  - 18*x
----- + -------------------------
9 + x              2        2    
            (3 + x) *(9 + x)

$$\frac{x + 7}{x + 9} + \frac{\frac{x + 5}{x^{2} - 81} + \frac{x + 7}{x^{2} - 18 x + 81}}{\left(x + 3\right)^{2} \left(x + 9\right)^{2}}$$

(7 + x)/(9 + x) + ((5 + x)/(-81 + x^2) + (7 + x)/(81 + x^2 - 18*x))/((3 + x)^2*(9 + x)^2)

Combinatorics [src]

         5         2        3      4         
45929 + x  - 1134*x  - 162*x  + 7*x  + 6561*x
---------------------------------------------
                      2        3             
              (-9 + x) *(9 + x)

$$\frac{x^{5} + 7 x^{4} - 162 x^{3} - 1134 x^{2} + 6561 x + 45929}{\left(x - 9\right)^{2} \left(x + 9\right)^{3}}$$

(45929 + x^5 - 1134*x^2 - 162*x^3 + 7*x^4 + 6561*x)/((-9 + x)^2*(9 + x)^3)

Assemble expression [src]

         5 + x         7 + x     
        -------- + --------------
               2         2       
7 + x   -81 + x    81 + x  - 18*x
----- + -------------------------
9 + x              2        2    
            (3 + x) *(9 + x)

$$\frac{x + 7}{x + 9} + \frac{\frac{x + 5}{x^{2} - 81} + \frac{x + 7}{x^{2} - 18 x + 81}}{\left(x + 3\right)^{2} \left(x + 9\right)^{2}}$$

(7 + x)/(9 + x) + ((5 + x)/(-81 + x^2) + (7 + x)/(81 + x^2 - 18*x))/((3 + x)^2*(9 + x)^2)

Rational denominator [src]

        //       2\                   /      2       \\          2        2 /       2\         /      2       \
(9 + x)*\\-81 + x /*(7 + x) + (5 + x)*\81 + x  - 18*x// + (3 + x) *(9 + x) *\-81 + x /*(7 + x)*\81 + x  - 18*x/
---------------------------------------------------------------------------------------------------------------
                                 /       2\        2        3 /      2       \                                 
                                 \-81 + x /*(3 + x) *(9 + x) *\81 + x  - 18*x/

$$\frac{\left(x + 3\right)^{2} \left(x + 7\right) \left(x + 9\right)^{2} \left(x^{2} - 81\right) \left(x^{2} - 18 x + 81\right) + \left(x + 9\right) \left(\left(x + 5\right) \left(x^{2} - 18 x + 81\right) + \left(x + 7\right) \left(x^{2} - 81\right)\right)}{\left(x + 3\right)^{2} \left(x + 9\right)^{3} \left(x^{2} - 81\right) \left(x^{2} - 18 x + 81\right)}$$

((9 + x)*((-81 + x^2)*(7 + x) + (5 + x)*(81 + x^2 - 18*x)) + (3 + x)^2*(9 + x)^2*(-81 + x^2)*(7 + x)*(81 + x^2 - 18*x))/((-81 + x^2)*(3 + x)^2*(9 + x)^3*(81 + x^2 - 18*x))

Powers [src]

         5 + x         7 + x     
        -------- + --------------
               2         2       
7 + x   -81 + x    81 + x  - 18*x
----- + -------------------------
9 + x              2        2    
            (3 + x) *(9 + x)

$$\frac{x + 7}{x + 9} + \frac{\frac{x + 5}{x^{2} - 81} + \frac{x + 7}{x^{2} - 18 x + 81}}{\left(x + 3\right)^{2} \left(x + 9\right)^{2}}$$

(7 + x)/(9 + x) + ((5 + x)/(-81 + x^2) + (7 + x)/(81 + x^2 - 18*x))/((3 + x)^2*(9 + x)^2)

Common denominator [src]

                             2      4            
                13120 - 324*x  + 2*x             
1 - ---------------------------------------------
             5         2        3      4         
    59049 + x  - 1458*x  - 162*x  + 9*x  + 6561*x

$$- \frac{2 x^{4} - 324 x^{2} + 13120}{x^{5} + 9 x^{4} - 162 x^{3} - 1458 x^{2} + 6561 x + 59049} + 1$$

1 - (13120 - 324*x^2 + 2*x^4)/(59049 + x^5 - 1458*x^2 - 162*x^3 + 9*x^4 + 6561*x)

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Identical expressions

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How do you ((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x) in partial fractions?

The solution