Mister Exam

# 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
-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