Mister Exam

# Least common denominator (a+4)*a/2+(4*a+16)/(4*a^2+a^3)

An expression to simplify:

### The solution

You have entered [src]
(a + 4)*a    4*a + 16
--------- + ---------
2          2    3
4*a  + a 
$$\frac{a \left(a + 4\right)}{2} + \frac{4 a + 16}{a^{3} + 4 a^{2}}$$
((a + 4)*a)/2 + (4*a + 16)/(4*a^2 + a^3)
General simplification [src]
 2
a          4
-- + 2*a + --
2           2
a 
$$\frac{a^{2}}{2} + 2 a + \frac{4}{a^{2}}$$
a^2/2 + 2*a + 4/a^2
Fraction decomposition [src]
a^2/2 + 2*a + 4/a^2
$$\frac{a^{2}}{2} + 2 a + \frac{4}{a^{2}}$$
 2
a          4
-- + 2*a + --
2           2
a 
Rational denominator [src]
                     / 3      2\
32 + 8*a + a*(4 + a)*\a  + 4*a /
--------------------------------
3      2
2*a  + 8*a            
$$\frac{a \left(a + 4\right) \left(a^{3} + 4 a^{2}\right) + 8 a + 32}{2 a^{3} + 8 a^{2}}$$
(32 + 8*a + a*(4 + a)*(a^3 + 4*a^2))/(2*a^3 + 8*a^2)
(16.0 + 4.0*a)/(a^3 + 4.0*a^2) + 0.5*a*(4.0 + a)
(16.0 + 4.0*a)/(a^3 + 4.0*a^2) + 0.5*a*(4.0 + a)
Combining rational expressions [src]
     3
8 + a *(4 + a)
--------------
2
2*a      
$$\frac{a^{3} \left(a + 4\right) + 8}{2 a^{2}}$$
(8 + a^3*(4 + a))/(2*a^2)
Common denominator [src]
 2
a          4
-- + 2*a + --
2           2
a 
$$\frac{a^{2}}{2} + 2 a + \frac{4}{a^{2}}$$
a^2/2 + 2*a + 4/a^2
Combinatorics [src]
     4      3
8 + a  + 4*a
-------------
2
2*a     
$$\frac{a^{4} + 4 a^{3} + 8}{2 a^{2}}$$
(8 + a^4 + 4*a^3)/(2*a^2)