Подстановка условия
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x3 + 125/(x^2) - 12*x + 36*x^2 - 36/(x^2) - 5*x + 25 при x3 = 4
125 2 36
x3 + --- - 12*x + 36*x - -- - 5*x + 25
2 2
x x
$$36 x^{2} - 12 x - 5 x + x_{3} + 25 - \frac{36}{x^{2}} + \frac{125}{x^{2}}$$
2 89
25 + x3 - 17*x + 36*x + --
2
x
$$36 x^{2} - 17 x + x_{3} + 25 + \frac{89}{x^{2}}$$
$$x_{3} = 4$$
2 89
25 + (4) - 17*x + 36*x + --
2
x
$$36 x^{2} + (4) - 17 x + 25 + \frac{89}{x^{2}}$$
2 89
25 + 4 - 17*x + 36*x + --
2
x
$$36 x^{2} - 17 x + 4 + 25 + \frac{89}{x^{2}}$$
2 89
29 - 17*x + 36*x + --
2
x
$$36 x^{2} - 17 x + 29 + \frac{89}{x^{2}}$$
29 - 17*x + 36*x^2 + 89/x^2
Рациональный знаменатель
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2 89
25 + x3 - 17*x + 36*x + --
2
x
$$36 x^{2} - 17 x + x_{3} + 25 + \frac{89}{x^{2}}$$
2 / 2\
89 + x *\25 + x3 - 17*x + 36*x /
--------------------------------
2
x
$$\frac{x^{2} \cdot \left(36 x^{2} - 17 x + x_{3} + 25\right) + 89}{x^{2}}$$
(89 + x^2*(25 + x3 - 17*x + 36*x^2))/x^2
3 2 4 2
89 - 17*x + 25*x + 36*x + x3*x
----------------------------------
2
x
$$\frac{36 x^{4} - 17 x^{3} + x^{2} x_{3} + 25 x^{2} + 89}{x^{2}}$$
(89 - 17*x^3 + 25*x^2 + 36*x^4 + x3*x^2)/x^2
Объединение рациональных выражений
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3 2 4 2
89 - 17*x + 25*x + 36*x + x3*x
----------------------------------
2
x
$$\frac{36 x^{4} - 17 x^{3} + x^{2} x_{3} + 25 x^{2} + 89}{x^{2}}$$
(89 - 17*x^3 + 25*x^2 + 36*x^4 + x3*x^2)/x^2