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Общий знаменатель sqrt((w*x-w*x^2+1-x)/p)*(-1+w-2*w*x)/(2*(w*x-w*x^2+1-x))
Решение
Вы ввели
[src]
____________________
/ 2
/ w*x - w*x + 1 - x
/ ------------------ *(-1 + w - 2*w*x)
\/ p
------------------------------------------
/ 2 \
2*\w*x - w*x + 1 - x/
$$\frac{\sqrt{\frac{- w x^{2} + w x - x + 1}{p}} \left(- 2 w x + w - 1\right)}{2 \left(- w x^{2} + w x - x + 1\right)}$$
sqrt((w*x - w*x^2 + 1 - x)/p)*(-1 + w - 2*w*x)/((2*(w*x - w*x^2 + 1 - x)))
Общее упрощение
[src]
____________________
/ 2
/ 1 - x + w*x - w*x /1 w \
/ ------------------ *|- - - + w*x|
\/ p \2 2 /
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2
-1 + x + w*x - w*x
$$\frac{\sqrt{\frac{- w x^{2} + w x - x + 1}{p}} \left(w x - \frac{w}{2} + \frac{1}{2}\right)}{w x^{2} - w x + x - 1}$$
sqrt((1 - x + w*x - w*x^2)/p)*(1/2 - w/2 + w*x)/(-1 + x + w*x^2 - w*x)
Численный ответ
[src]
((1.0 - x + w*x - w*x^2)/p)^0.5*(-1.0 + w - 2.0*w*x)/(2.0 - 2.0*x + 2.0*w*x - 2.0*w*x^2)
((1.0 - x + w*x - w*x^2)/p)^0.5*(-1.0 + w - 2.0*w*x)/(2.0 - 2.0*x + 2.0*w*x - 2.0*w*x^2)
Собрать выражение
[src]
____________________
/ 2
/ 1 - x + w*x - w*x
/ ------------------ *(-1 + w - 2*w*x)
\/ p
------------------------------------------
2
2 - 2*x - 2*w*x + 2*w*x
$$\frac{\sqrt{\frac{- w x^{2} + w x - x + 1}{p}} \left(- 2 w x + w - 1\right)}{- 2 w x^{2} + 2 w x - 2 x + 2}$$
_______________________
/ 2
/ 1 + x*(-1 + w) - w*x
/ --------------------- *(-1 + w - 2*w*x)
\/ p
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2
2 - 2*w*x + 2*x*(-1 + w)
$$\frac{\sqrt{\frac{- w x^{2} + x \left(w - 1\right) + 1}{p}} \left(- 2 w x + w - 1\right)}{- 2 w x^{2} + 2 x \left(w - 1\right) + 2}$$
____________________
/ / 2\
/ 1 - x + w*\x - x /
/ ------------------ *(-1 + w*(1 - 2*x))
\/ p
--------------------------------------------
/ 2\
2 - 2*x + 2*w*\x - x /
$$\frac{\sqrt{\frac{w \left(- x^{2} + x\right) - x + 1}{p}} \left(w \left(- 2 x + 1\right) - 1\right)}{2 w \left(- x^{2} + x\right) - 2 x + 2}$$
sqrt((1 - x + w*(x - x^2))/p)*(-1 + w*(1 - 2*x))/(2 - 2*x + 2*w*(x - x^2))
Комбинаторика
[src]
______________________
/ -(1 + w*x)*(-1 + x)
/ -------------------- *(1 - w + 2*w*x)
\/ p
------------------------------------------
2*(1 + w*x)*(-1 + x)
$$\frac{\sqrt{- \frac{\left(x - 1\right) \left(w x + 1\right)}{p}} \left(2 w x - w + 1\right)}{2 \left(x - 1\right) \left(w x + 1\right)}$$
sqrt(-(1 + w*x)*(-1 + x)/p)*(1 - w + 2*w*x)/(2*(1 + w*x)*(-1 + x))
Общий знаменатель
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____________________ ____________________ ____________________
/ 2 / 2 / 2
/ 1 x w*x w*x / 1 x w*x w*x / 1 x w*x w*x
/ - - - + --- - ---- - w* / - - - + --- - ---- + 2*w*x* / - - - + --- - ----
\/ p p p p \/ p p p p \/ p p p p
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2
-2 + 2*x - 2*w*x + 2*w*x
$$\frac{2 w x \sqrt{- \frac{w x^{2}}{p} + \frac{w x}{p} - \frac{x}{p} + \frac{1}{p}} - w \sqrt{- \frac{w x^{2}}{p} + \frac{w x}{p} - \frac{x}{p} + \frac{1}{p}} + \sqrt{- \frac{w x^{2}}{p} + \frac{w x}{p} - \frac{x}{p} + \frac{1}{p}}}{2 w x^{2} - 2 w x + 2 x - 2}$$
(sqrt(1/p - x/p + w*x/p - w*x^2/p) - w*sqrt(1/p - x/p + w*x/p - w*x^2/p) + 2*w*x*sqrt(1/p - x/p + w*x/p - w*x^2/p))/(-2 + 2*x - 2*w*x + 2*w*x^2)
Объединение рациональных выражений
[src]
____________________
/ 2
/ 1 - x + w*x - w*x
/ ------------------ *(-1 + w - 2*w*x)
\/ p
------------------------------------------
2
2 - 2*x - 2*w*x + 2*w*x
$$\frac{\sqrt{\frac{- w x^{2} + w x - x + 1}{p}} \left(- 2 w x + w - 1\right)}{- 2 w x^{2} + 2 w x - 2 x + 2}$$
sqrt((1 - x + w*x - w*x^2)/p)*(-1 + w - 2*w*x)/(2 - 2*x - 2*w*x^2 + 2*w*x)
Степени
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1 w
- - + - - w*x
2 2
-----------------------------
____________________
___ / 2
\/ p *\/ 1 - x + w*x - w*x
$$\frac{- w x + \frac{w}{2} - \frac{1}{2}}{\sqrt{p} \sqrt{- w x^{2} + w x - x + 1}}$$
____________________
/ 2
/ 1 - x + w*x - w*x
/ ------------------ *(-1 + w - 2*w*x)
\/ p
------------------------------------------
2
2 - 2*x - 2*w*x + 2*w*x
$$\frac{\sqrt{\frac{- w x^{2} + w x - x + 1}{p}} \left(- 2 w x + w - 1\right)}{- 2 w x^{2} + 2 w x - 2 x + 2}$$
____________________
/ 2
/ w*x - w*x + 1 - x / 1 w \
/ ------------------ *|- - + - - w*x|
\/ p \ 2 2 /
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2
w*x - w*x + 1 - x
$$\frac{\sqrt{\frac{- w x^{2} + w x - x + 1}{p}} \left(- w x + \frac{w}{2} - \frac{1}{2}\right)}{- w x^{2} + w x - x + 1}$$
sqrt((w*x - w*x^2 + 1 - x)/p)*(-1/2 + w/2 - w*x)/(w*x - w*x^2 + 1 - x)
Рациональный знаменатель
[src]
____________________
/ 2
/ 1 x w*x w*x
/ - - - + --- - ---- *(1 - w + 2*w*x)
\/ p p p p
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2
-2 + 2*x - 2*w*x + 2*w*x
$$\frac{\left(2 w x - w + 1\right) \sqrt{- \frac{w x^{2}}{p} + \frac{w x}{p} - \frac{x}{p} + \frac{1}{p}}}{2 w x^{2} - 2 w x + 2 x - 2}$$
____________________ ____________________ ____________________
/ 2 / 2 / 2
/ 1 x w*x w*x / 1 x w*x w*x / 1 x w*x w*x
/ - - - + --- - ---- w* / - - - + --- - ---- 2*w*x* / - - - + --- - ----
\/ p p p p \/ p p p p \/ p p p p
- ------------------------- + --------------------------- - -------------------------------
2 2 2
2 - 2*x - 2*w*x + 2*w*x 2 - 2*x - 2*w*x + 2*w*x 2 - 2*x - 2*w*x + 2*w*x
$$- \frac{2 w x \sqrt{- \frac{w x^{2}}{p} + \frac{w x}{p} - \frac{x}{p} + \frac{1}{p}}}{- 2 w x^{2} + 2 w x - 2 x + 2} + \frac{w \sqrt{- \frac{w x^{2}}{p} + \frac{w x}{p} - \frac{x}{p} + \frac{1}{p}}}{- 2 w x^{2} + 2 w x - 2 x + 2} - \frac{\sqrt{- \frac{w x^{2}}{p} + \frac{w x}{p} - \frac{x}{p} + \frac{1}{p}}}{- 2 w x^{2} + 2 w x - 2 x + 2}$$
-sqrt(1/p - x/p + w*x/p - w*x^2/p)/(2 - 2*x - 2*w*x^2 + 2*w*x) + w*sqrt(1/p - x/p + w*x/p - w*x^2/p)/(2 - 2*x - 2*w*x^2 + 2*w*x) - 2*w*x*sqrt(1/p - x/p + w*x/p - w*x^2/p)/(2 - 2*x - 2*w*x^2 + 2*w*x)