Mister Exam

# How do you 3*x^2/(8-x^4)+4*x^6/(8-x^4)^2 in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
    2          6
3*x        4*x
------ + ---------
4           2
8 - x    /     4\
\8 - x / 
$$\frac{3 x^{2}}{8 - x^{4}} + \frac{4 x^{6}}{\left(8 - x^{4}\right)^{2}}$$
(3*x^2)/(8 - x^4) + (4*x^6)/(8 - x^4)^2
General simplification [src]
 2 /      4\
x *\24 + x /
------------
2
/      4\
\-8 + x /  
$$\frac{x^{2} \left(x^{4} + 24\right)}{\left(x^{4} - 8\right)^{2}}$$
x^2*(24 + x^4)/(-8 + x^4)^2
Fraction decomposition [src]
x^2/(-8 + x^4) + 32*x^2/(-8 + x^4)^2
$$\frac{x^{2}}{x^{4} - 8} + \frac{32 x^{2}}{\left(x^{4} - 8\right)^{2}}$$
    2           2
x        32*x
------- + ----------
4            2
-8 + x    /      4\
\-8 + x / 
0.0625*x^6/(1 - 0.125*x^4)^2 + 3.0*x^2/(8.0 - x^4)
0.0625*x^6/(1 - 0.125*x^4)^2 + 3.0*x^2/(8.0 - x^4)
Rational denominator [src]
             2
2 /     4\       6 /     4\
3*x *\8 - x /  + 4*x *\8 - x /
------------------------------
3
/     4\
\8 - x /            
$$\frac{4 x^{6} \left(8 - x^{4}\right) + 3 x^{2} \left(8 - x^{4}\right)^{2}}{\left(8 - x^{4}\right)^{3}}$$
(3*x^2*(8 - x^4)^2 + 4*x^6*(8 - x^4))/(8 - x^4)^3
Assemble expression [src]
    2          6
3*x        4*x
------ + ---------
4           2
8 - x    /     4\
\8 - x / 
$$\frac{4 x^{6}}{\left(8 - x^{4}\right)^{2}} + \frac{3 x^{2}}{8 - x^{4}}$$
3*x^2/(8 - x^4) + 4*x^6/(8 - x^4)^2
Powers [src]
    2          6
3*x        4*x
------ + ---------
4           2
8 - x    /     4\
\8 - x / 
$$\frac{4 x^{6}}{\left(8 - x^{4}\right)^{2}} + \frac{3 x^{2}}{8 - x^{4}}$$
3*x^2/(8 - x^4) + 4*x^6/(8 - x^4)^2
Common denominator [src]
    6       2
x  + 24*x
---------------
8       4
64 + x  - 16*x 
$$\frac{x^{6} + 24 x^{2}}{x^{8} - 16 x^{4} + 64}$$
(x^6 + 24*x^2)/(64 + x^8 - 16*x^4)
Trigonometric part [src]
    2          6
3*x        4*x
------ + ---------
4           2
8 - x    /     4\
\8 - x / 
$$\frac{4 x^{6}}{\left(8 - x^{4}\right)^{2}} + \frac{3 x^{2}}{8 - x^{4}}$$
3*x^2/(8 - x^4) + 4*x^6/(8 - x^4)^2
Combinatorics [src]
 2 /      4\
x *\24 + x /
------------
2
/      4\
\-8 + x /  
$$\frac{x^{2} \left(x^{4} + 24\right)}{\left(x^{4} - 8\right)^{2}}$$
x^2*(24 + x^4)/(-8 + x^4)^2
Combining rational expressions [src]
 2 /      4\
x *\24 + x /
------------
2
/     4\
\8 - x /   
$$\frac{x^{2} \left(x^{4} + 24\right)}{\left(8 - x^{4}\right)^{2}}$$
x^2*(24 + x^4)/(8 - x^4)^2
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