General simplification
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/ 2\ / 2 \
\-1 + x /*\6 - x + 7*x/
x + ------------------------
6
----------------------------
2
-1 + x
$$\frac{x + \frac{\left(x^{2} - 1\right) \left(- x^{2} + 7 x + 6\right)}{6}}{x^{2} - 1}$$
(x + (-1 + x^2)*(6 - x^2 + 7*x)/6)/(-1 + x^2)
Fraction decomposition
[src]
1 + 1/(2*(1 + x)) + 1/(2*(-1 + x)) - x^2/6 + 7*x/6
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + 1 + \frac{1}{2 \left(x + 1\right)} + \frac{1}{2 \left(x - 1\right)}$$
2
1 1 x 7*x
1 + --------- + ---------- - -- + ---
2*(1 + x) 2*(-1 + x) 6 6
1.0 + 1.16666666666667*x - 0.166666666666667*x^2 + x/(-1.0 + x^2)
1.0 + 1.16666666666667*x - 0.166666666666667*x^2 + x/(-1.0 + x^2)
2
x 7*x x
1 - -- + --- + -------
6 6 2
-1 + x
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + \frac{x}{x^{2} - 1} + 1$$
1 - x^2/6 + 7*x/6 + x/(-1 + x^2)
2
x 7*x x
1 - -- + --- + -------
6 6 2
-1 + x
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + \frac{x}{x^{2} - 1} + 1$$
1 - x^2/6 + 7*x/6 + x/(-1 + x^2)
Rational denominator
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/ 2\ / 2 \
6*x + \-1 + x /*\6 - x + 7*x/
------------------------------
2
-6 + 6*x
$$\frac{6 x + \left(x^{2} - 1\right) \left(- x^{2} + 7 x + 6\right)}{6 x^{2} - 6}$$
(6*x + (-1 + x^2)*(6 - x^2 + 7*x))/(-6 + 6*x^2)
/ 4 2 3\
-\6 + x + x - 7*x - 7*x /
----------------------------
6*(1 + x)*(-1 + x)
$$- \frac{x^{4} - 7 x^{3} - 7 x^{2} + x + 6}{6 \left(x - 1\right) \left(x + 1\right)}$$
-(6 + x + x^4 - 7*x^2 - 7*x^3)/(6*(1 + x)*(-1 + x))
Assemble expression
[src]
2
x 7*x x
1 - -- + --- + -------
6 6 2
-1 + x
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + \frac{x}{x^{2} - 1} + 1$$
1 - x^2/6 + 7*x/6 + x/(-1 + x^2)
Combining rational expressions
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/ 2\ / 2 \
6*x + \-1 + x /*\6 - x + 7*x/
------------------------------
/ 2\
6*\-1 + x /
$$\frac{6 x + \left(x^{2} - 1\right) \left(- x^{2} + 7 x + 6\right)}{6 \left(x^{2} - 1\right)}$$
(6*x + (-1 + x^2)*(6 - x^2 + 7*x))/(6*(-1 + x^2))
2
x 7*x x
1 - -- + --- + -------
6 6 2
-1 + x
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + \frac{x}{x^{2} - 1} + 1$$
1 - x^2/6 + 7*x/6 + x/(-1 + x^2)