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Least common denominator:
((x*x^(1/2)-x)^3)/(((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3
x+(6-x^2/1+x)/6+x/(x^2-1)
((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x-9)^2)+(7+x)/(9+x)
(x/4+7/16)*(x^4-3*x^2+5*x-3)+(x^3+x-2)*((-x^2)/4-7*x/16+1)
Factor polynomial:
y^3-2*y^2*z-4*y*z+8*z^2
y^3+2*y^2*x^2-2*x^3
y^3-1/27
y^3+1000
Factor squared:
y^4-12*y^2+8
-y^4-10*y^2-2
y^4+2*y^2-3
-y^2+y*x-5*x^2
How do you in partial fractions?:
(4x^2-19x+12)/(x^3-64)
1/(x^4+x^2)
-540000000000*(1+300000*i)/(90000000000+x)^4
-2*x^3/(x^2-1)^2+2*x/(x^2-1)
How do you in partial fractions?:
((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 minus 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 minus 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/ 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)

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)

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)

General simplification [src]

          5                 4        3        2
 45929 + x  - 13851*x - 29*x  + 234*x  + 486*x 
-----------------------------------------------
         5                 4        3         2
59049 + x  - 19683*x - 27*x  + 162*x  + 1458*x

$$\frac{x^{5} - 29 x^{4} + 234 x^{3} + 486 x^{2} - 13851 x + 45929}{x^{5} - 27 x^{4} + 162 x^{3} + 1458 x^{2} - 19683 x + 59049}$$

(45929 + x^5 - 13851*x - 29*x^4 + 234*x^3 + 486*x^2)/(59049 + x^5 - 19683*x - 27*x^4 + 162*x^3 + 1458*x^2)

Fraction decomposition [src]

1 - 104975/(52488*(9 + x)) - 1/(162*(-9 + x)^3) - 1/(52488*(-9 + x)) + 1/(9*(-9 + x)^4) + 1/(2916*(-9 + x)^2)

$$1 - \frac{104975}{52488 \left(x + 9\right)} - \frac{1}{52488 \left(x - 9\right)} + \frac{1}{2916 \left(x - 9\right)^{2}} - \frac{1}{162 \left(x - 9\right)^{3}} + \frac{1}{9 \left(x - 9\right)^{4}}$$

        104975            1               1               1              1       
1 - ------------- - ------------- - -------------- + ----------- + --------------
    52488*(9 + x)               3   52488*(-9 + x)             4                2
                    162*(-9 + x)                     9*(-9 + x)    2916*(-9 + x)

Rational denominator [src]

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

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

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

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

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

Common denominator [src]

                              3      4        2    
         13120 - 5832*x - 72*x  + 2*x  + 972*x     
1 - -----------------------------------------------
             5                 4        3         2
    59049 + x  - 19683*x - 27*x  + 162*x  + 1458*x

$$- \frac{2 x^{4} - 72 x^{3} + 972 x^{2} - 5832 x + 13120}{x^{5} - 27 x^{4} + 162 x^{3} + 1458 x^{2} - 19683 x + 59049} + 1$$

1 - (13120 - 5832*x - 72*x^3 + 2*x^4 + 972*x^2)/(59049 + x^5 - 19683*x - 27*x^4 + 162*x^3 + 1458*x^2)

Assemble expression [src]

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

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

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

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 + 0.333333333333333*x)^2*(-1 + 0.111111111111111*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 + 0.333333333333333*x)^2*(-1 + 0.111111111111111*x)^2)

Trigonometric part [src]

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

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

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

Combining rational expressions [src]

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

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

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

Combinatorics [src]

         5                 4        3        2
45929 + x  - 13851*x - 29*x  + 234*x  + 486*x 
----------------------------------------------
                      4                       
              (-9 + x) *(9 + x)

$$\frac{x^{5} - 29 x^{4} + 234 x^{3} + 486 x^{2} - 13851 x + 45929}{\left(x - 9\right)^{4} \left(x + 9\right)}$$

(45929 + x^5 - 13851*x - 29*x^4 + 234*x^3 + 486*x^2)/((-9 + x)^4*(9 + x))

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Identical expressions

Similar expressions

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)

The solution