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Expression simplification/ Least common denominator/ (a-3+18/a+3)/a^2+9/a^2+6*a+9/a-3

Least common denominator (a-3+18/a+3)/a^2+9/a^2+6*a+9/a-3

An expression to simplify:

The solution

You have entered [src] 
        18                       
a - 3 + -- + 3                   
        a        9          9    
-------------- + -- + 6*a + - - 3
       2          2         a    
      a          a
$$\left(\left(6 a + \left(\frac{\left(\left(a - 3\right) + \frac{18}{a}\right) + 3}{a^{2}} + \frac{9}{a^{2}}\right)\right) + \frac{9}{a}\right) - 3$$ 
(a - 3 + 18/a + 3)/a^2 + 9/a^2 + 6*a + 9/a - 3
Fraction decomposition [src] 
-3 + 6*a + 9/a^2 + 10/a + 18/a^3
$$6 a - 3 + \frac{10}{a} + \frac{9}{a^{2}} + \frac{18}{a^{3}}$$ 
           9    10   18
-3 + 6*a + -- + -- + --
            2   a     3
           a         a
General simplification [src] 
           9    10   18
-3 + 6*a + -- + -- + --
            2   a     3
           a         a
$$6 a - 3 + \frac{10}{a} + \frac{9}{a^{2}} + \frac{18}{a^{3}}$$ 
-3 + 6*a + 9/a^2 + 10/a + 18/a^3
Common denominator [src] 
                          2
           18 + 9*a + 10*a 
-3 + 6*a + ----------------
                   3       
                  a
$$6 a - 3 + \frac{10 a^{2} + 9 a + 18}{a^{3}}$$ 
-3 + 6*a + (18 + 9*a + 10*a^2)/a^3
Trigonometric part [src] 
                        18
                    a + --
           9   9        a 
-3 + 6*a + - + -- + ------
           a    2      2  
               a      a
$$6 a - 3 + \frac{9}{a} + \frac{a + \frac{18}{a}}{a^{2}} + \frac{9}{a^{2}}$$ 
-3 + 6*a + 9/a + 9/a^2 + (a + 18/a)/a^2
Combining rational expressions [src] 
        3      4      2                    
18 - 3*a  + 6*a  + 9*a  + 12*a + a*(-3 + a)
-------------------------------------------
                      3                    
                     a
$$\frac{6 a^{4} - 3 a^{3} + 9 a^{2} + a \left(a - 3\right) + 12 a + 18}{a^{3}}$$ 
(18 - 3*a^3 + 6*a^4 + 9*a^2 + 12*a + a*(-3 + a))/a^3
Powers [src] 
                        18
                    a + --
           9   9        a 
-3 + 6*a + - + -- + ------
           a    2      2  
               a      a
$$6 a - 3 + \frac{9}{a} + \frac{a + \frac{18}{a}}{a^{2}} + \frac{9}{a^{2}}$$ 
-3 + 6*a + 9/a + 9/a^2 + (a + 18/a)/a^2
Combinatorics [src] 
        3      4             2
18 - 3*a  + 6*a  + 9*a + 10*a 
------------------------------
               3              
              a
$$\frac{6 a^{4} - 3 a^{3} + 10 a^{2} + 9 a + 18}{a^{3}}$$ 
(18 - 3*a^3 + 6*a^4 + 9*a + 10*a^2)/a^3
Assemble expression [src] 
                        18
                    a + --
           9   9        a 
-3 + 6*a + - + -- + ------
           a    2      2  
               a      a
$$6 a - 3 + \frac{9}{a} + \frac{a + \frac{18}{a}}{a^{2}} + \frac{9}{a^{2}}$$ 
-3 + 6*a + 9/a + 9/a^2 + (a + 18/a)/a^2
Rational denominator [src] 
     6      5     /   6      3    2                        \
- 3*a  + 9*a  + a*\6*a  + 9*a  + a *(18 + 3*a + a*(-3 + a))/
------------------------------------------------------------
                              6                             
                             a
$$\frac{- 3 a^{6} + 9 a^{5} + a \left(6 a^{6} + 9 a^{3} + a^{2} \left(a \left(a - 3\right) + 3 a + 18\right)\right)}{a^{6}}$$ 
(-3*a^6 + 9*a^5 + a*(6*a^6 + 9*a^3 + a^2*(18 + 3*a + a*(-3 + a))))/a^6
Numerical answer [src] 
-3.0 + 6.0*a + 9.0/a + 9.0/a^2 + (a + 18.0/a)/a^2
-3.0 + 6.0*a + 9.0/a + 9.0/a^2 + (a + 18.0/a)/a^2
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