Fraction decomposition
[src]
1/(-1 + x) - 1/x^2 - 4/(1 + x) + 3/x
$$- \frac{4}{x + 1} + \frac{1}{x - 1} + \frac{3}{x} - \frac{1}{x^{2}}$$
1 1 4 3
------ - -- - ----- + -
-1 + x 2 1 + x x
x
General simplification
[src]
2
1 - 3*x + 4*x
--------------
4 2
x - x
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
(1.0 + 4.0*x^2 - 3.0*x)/(x^4 - x^2)
(1.0 + 4.0*x^2 - 3.0*x)/(x^4 - x^2)
2
1 - 3*x + 4*x
--------------
4 2
x - x
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
2
1 - 3*x + 4*x
--------------
4 2
x - x
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
2
1 - 3*x + 4*x
--------------
4 2
x - x
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
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))
Assemble expression
[src]
2
1 - 3*x + 4*x
--------------
4 2
x - x
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)
2
1 - 3*x + 4*x
-------------------
2
x *(1 + x)*(-1 + x)
$$\frac{4 x^{2} - 3 x + 1}{x^{2} \left(x - 1\right) \left(x + 1\right)}$$
(1 - 3*x + 4*x^2)/(x^2*(1 + x)*(-1 + x))
Rational denominator
[src]
2
1 - 3*x + 4*x
--------------
4 2
x - x
$$\frac{4 x^{2} - 3 x + 1}{x^{4} - x^{2}}$$
(1 - 3*x + 4*x^2)/(x^4 - x^2)