Mister Exam

# How do you (4x^2-3x+1)/(x^4+x^2) in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
   2
4*x  - 3*x + 1
--------------
4    2
x  + x     
$$\frac{\left(4 x^{2} - 3 x\right) + 1}{x^{4} + x^{2}}$$
(4*x^2 - 3*x + 1)/(x^4 + x^2)
Fraction decomposition [src]
x^(-2) - 3/x + 3*(1 + x)/(1 + x^2)
$$\frac{3 \left(x + 1\right)}{x^{2} + 1} - \frac{3}{x} + \frac{1}{x^{2}}$$
1    3   3*(1 + x)
-- - - + ---------
2   x          2
x          1 + x  
General simplification [src]
             2
1 - 3*x + 4*x
--------------
2    4
x  + x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} + x^{2}}$$
(1 - 3*x + 4*x^2)/(x^2 + x^4)
(1.0 + 4.0*x^2 - 3.0*x)/(x^2 + x^4)
(1.0 + 4.0*x^2 - 3.0*x)/(x^2 + x^4)
Powers [src]
             2
1 - 3*x + 4*x
--------------
2    4
x  + x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} + x^{2}}$$
(1 - 3*x + 4*x^2)/(x^2 + x^4)
Common denominator [src]
             2
1 - 3*x + 4*x
--------------
2    4
x  + x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} + x^{2}}$$
(1 - 3*x + 4*x^2)/(x^2 + x^4)
Rational denominator [src]
             2
1 - 3*x + 4*x
--------------
2    4
x  + x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} + x^{2}}$$
(1 - 3*x + 4*x^2)/(x^2 + x^4)
Combining rational expressions [src]
1 + x*(-3 + 4*x)
----------------
2 /     2\
x *\1 + x /   
$$\frac{x \left(4 x - 3\right) + 1}{x^{2} \left(x^{2} + 1\right)}$$
(1 + x*(-3 + 4*x))/(x^2*(1 + x^2))
Trigonometric part [src]
             2
1 - 3*x + 4*x
--------------
2    4
x  + x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} + x^{2}}$$
(1 - 3*x + 4*x^2)/(x^2 + x^4)
Assemble expression [src]
             2
1 - 3*x + 4*x
--------------
2    4
x  + x     
$$\frac{4 x^{2} - 3 x + 1}{x^{4} + x^{2}}$$
(1 - 3*x + 4*x^2)/(x^2 + x^4)
Combinatorics [src]
             2
1 - 3*x + 4*x
--------------
2 /     2\
x *\1 + x /  
$$\frac{4 x^{2} - 3 x + 1}{x^{2} \left(x^{2} + 1\right)}$$
(1 - 3*x + 4*x^2)/(x^2*(1 + x^2))
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