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)
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)
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))
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)
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))