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Least common denominator:
(x/sqrt(x^2-y^2))^2+(-y/sqrt(x^2-y^2))^2
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))
x^cos(1/x)*(cos(1/x)/x+log(x)*sin(1/x)/x^2)
(((x-8)/(x+8))-((x+8)*(x-8)))/8*x/(x^2-64)
Factor polynomial:
y^3-9*y
y^3+64
y^3+49+7+y^2
y^3+4^3
Factor squared:
-y^4+5*y^2-11
y^4+4*y^2-13
y^4-3*y^2-2
y^4+3*y^2+2
How do you in partial fractions?:
sqrt(1-x^2)/(1-x^2)
(p^2+7p)/(p^2+14p+49)
c^6*u^6/(c^2)^3
acos((b3^2+b4^2-b2^2)/(2*b3*b4))
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 plus 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 plus 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/ 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)

Fraction decomposition [src]

1 - 209965/(104976*(9 + x)) - 31/(419904*(-9 + x)) - 5/(5832*(9 + x)^2) + 1/(720*(3 + x)^2) + 1/(2916*(-9 + x)^2) + 1/(4800*(3 + x)) - (459 + 7*x)/(656100*(81 + x^2))

$$- \frac{7 x + 459}{656100 \left(x^{2} + 81\right)} + 1 - \frac{209965}{104976 \left(x + 9\right)} - \frac{5}{5832 \left(x + 9\right)^{2}} + \frac{1}{4800 \left(x + 3\right)} + \frac{1}{720 \left(x + 3\right)^{2}} - \frac{31}{419904 \left(x - 9\right)} + \frac{1}{2916 \left(x - 9\right)^{2}}$$

        209965              31               5              1               1               1            459 + 7*x    
1 - -------------- - --------------- - ------------- + ------------ + -------------- + ------------ - ----------------
    104976*(9 + x)   419904*(-9 + x)               2              2                2   4800*(3 + x)          /      2\
                                       5832*(9 + x)    720*(3 + x)    2916*(-9 + x)                   656100*\81 + x /

General simplification [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)

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)

Common denominator [src]

                          3        4       5      6      7          2                
         1061910 - 13124*x  - 162*x  - 90*x  - 6*x  + 2*x  + 39372*x  + 590418*x     
1 - ---------------------------------------------------------------------------------
               8          3         4        5       6      7           2            
    4782969 + x  - 39366*x  - 7290*x  - 486*x  - 72*x  + 6*x  + 472392*x  + 3188646*x

$$- \frac{2 x^{7} - 6 x^{6} - 90 x^{5} - 162 x^{4} - 13124 x^{3} + 39372 x^{2} + 590418 x + 1061910}{x^{8} + 6 x^{7} - 72 x^{6} - 486 x^{5} - 7290 x^{4} - 39366 x^{3} + 472392 x^{2} + 3188646 x + 4782969} + 1$$

1 - (1061910 - 13124*x^3 - 162*x^4 - 90*x^5 - 6*x^6 + 2*x^7 + 39372*x^2 + 590418*x)/(4782969 + x^8 - 39366*x^3 - 7290*x^4 - 486*x^5 - 72*x^6 + 6*x^7 + 472392*x^2 + 3188646*x)

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)

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)

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)

Combining rational expressions [src]

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

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

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

Combinatorics [src]

           8          3         4        5       6      7           2            
3721059 + x  - 26242*x  - 7128*x  - 396*x  - 66*x  + 4*x  + 433020*x  + 2598228*x
---------------------------------------------------------------------------------
                              2        2        2 /      2\                      
                      (-9 + x) *(3 + x) *(9 + x) *\81 + x /

$$\frac{x^{8} + 4 x^{7} - 66 x^{6} - 396 x^{5} - 7128 x^{4} - 26242 x^{3} + 433020 x^{2} + 2598228 x + 3721059}{\left(x - 9\right)^{2} \left(x + 3\right)^{2} \left(x + 9\right)^{2} \left(x^{2} + 81\right)}$$

(3721059 + x^8 - 26242*x^3 - 7128*x^4 - 396*x^5 - 66*x^6 + 4*x^7 + 433020*x^2 + 2598228*x)/((-9 + x)^2*(3 + x)^2*(9 + x)^2*(81 + x^2))

Rational denominator [src]

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