Mister Exam

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How do you (a^3+a)/(a^4+a) in partial fractions?

You have entered [src]

 3    
a  + a
------
 4    
a  + a

$$\frac{a^{3} + a}{a^{4} + a}$$

(a^3 + a)/(a^4 + a)

Fraction decomposition [src]

2/(3*(1 + a)) + (1 + a)/(3*(1 + a^2 - a))

$$\frac{a + 1}{3 \left(a^{2} - a + 1\right)} + \frac{2}{3 \left(a + 1\right)}$$

    2           1 + a     
--------- + --------------
3*(1 + a)     /     2    \
            3*\1 + a  - a/

General simplification [src]

     2
1 + a 
------
     3
1 + a

$$\frac{a^{2} + 1}{a^{3} + 1}$$

(1 + a^2)/(1 + a^3)

Common denominator [src]

     2
1 + a 
------
     3
1 + a

$$\frac{a^{2} + 1}{a^{3} + 1}$$

(1 + a^2)/(1 + a^3)

Combinatorics [src]

            2       
       1 + a        
--------------------
        /     2    \
(1 + a)*\1 + a  - a/

$$\frac{a^{2} + 1}{\left(a + 1\right) \left(a^{2} - a + 1\right)}$$

(1 + a^2)/((1 + a)*(1 + a^2 - a))

Combining rational expressions [src]

     2
1 + a 
------
     3
1 + a

$$\frac{a^{2} + 1}{a^{3} + 1}$$

(1 + a^2)/(1 + a^3)

Numerical answer [src]

(a + a^3)/(a + a^4)

(a + a^3)/(a + a^4)