/ 2 \
___ | / ___\ |
\/ m *\16 + \-4 + \/ m / - m/
------------------------------
2
/ ___\
(-16 + m)*\-4 + \/ m /
$$\frac{\sqrt{m} \left(\left(\sqrt{m} - 4\right)^{2} - m + 16\right)}{\left(\sqrt{m} - 4\right)^{2} \left(m - 16\right)}$$
sqrt(m)*(16 + (-4 + sqrt(m))^2 - m)/((-16 + m)*(-4 + sqrt(m))^2)
Подстановка условия
[src]
sqrt(m)/(m - 1*16) - sqrt(m)/((4 - sqrt(m))^2) при m = 1/3
___ ___
\/ m \/ m
------ - ------------
m - 16 2
/ ___\
\4 - \/ m /
$$\frac{\sqrt{m}}{m - 16} - \frac{\sqrt{m}}{\left(- \sqrt{m} + 4\right)^{2}}$$
/ 2 \
___ | / ___\ |
\/ m *\16 + \-4 + \/ m / - m/
------------------------------
2
/ ___\
(-16 + m)*\-4 + \/ m /
$$\frac{\sqrt{m} \left(\left(\sqrt{m} - 4\right)^{2} - m + 16\right)}{\left(\sqrt{m} - 4\right)^{2} \left(m - 16\right)}$$
$$m = \frac{1}{3}$$
/ 2 \
_______ | / _______\ |
\/ (1/3) *\16 + \-4 + \/ (1/3) / - (1/3)/
------------------------------------------
2
/ _______\
(-16 + (1/3))*\-4 + \/ (1/3) /
$$\frac{\sqrt{(1/3)} \left(\left(\sqrt{(1/3)} - 4\right)^{2} - (1/3) + 16\right)}{\left(\sqrt{(1/3)} - 4\right)^{2} \left((1/3) - 16\right)}$$
/ 2 \
1 | / 1 \ |
-----*|16 + |-4 + -----| - 1/3|
___ | | ___| |
\/ 3 \ \ \/ 3 / /
--------------------------------
2
/ 1 \
(-16 + 1/3)*|-4 + -----|
| ___|
\ \/ 3 /
$$\frac{\left(-1\right) \frac{1}{3} + \left(-4 + \sqrt{\frac{1}{3}}\right)^{2} + 16}{\sqrt{3} \left(-16 + \frac{1}{3}\right) \left(-4 + \sqrt{\frac{1}{3}}\right)^{2}}$$
/ 2\
| / ___\ |
___ |47 | \/ 3 | |
-\/ 3 *|-- + |-4 + -----| |
\3 \ 3 / /
----------------------------
2
/ ___\
| \/ 3 |
47*|-4 + -----|
\ 3 /
$$- \frac{\sqrt{3} \left(\left(-4 + \frac{\sqrt{3}}{3}\right)^{2} + \frac{47}{3}\right)}{47 \left(-4 + \frac{\sqrt{3}}{3}\right)^{2}}$$
-sqrt(3)*(47/3 + (-4 + sqrt(3)/3)^2)/(47*(-4 + sqrt(3)/3)^2)
Объединение рациональных выражений
[src]
/ 2 \
___ | / ___\ |
\/ m *\16 + \4 - \/ m / - m/
-----------------------------
2
/ ___\
(-16 + m)*\4 - \/ m /
$$\frac{\sqrt{m} \left(\left(- \sqrt{m} + 4\right)^{2} - m + 16\right)}{\left(- \sqrt{m} + 4\right)^{2} \left(m - 16\right)}$$
sqrt(m)*(16 + (4 - sqrt(m))^2 - m)/((-16 + m)*(4 - sqrt(m))^2)
Рациональный знаменатель
[src]
2 2 2 2
3/2 / ___\ ___ / ___\ ___ / ___\ / ___\
- m *\4 + \/ m / + 16*\/ m *\4 + \/ m / + \/ m *\-4 + \/ m / *\4 + \/ m /
------------------------------------------------------------------------------
3
(-16 + m)
$$\frac{- m^{\frac{3}{2}} \left(\sqrt{m} + 4\right)^{2} + \sqrt{m} \left(\sqrt{m} - 4\right)^{2} \left(\sqrt{m} + 4\right)^{2} + 16 \sqrt{m} \left(\sqrt{m} + 4\right)^{2}}{\left(m - 16\right)^{3}}$$
(-m^(3/2)*(4 + sqrt(m))^2 + 16*sqrt(m)*(4 + sqrt(m))^2 + sqrt(m)*(-4 + sqrt(m))^2*(4 + sqrt(m))^2)/(-16 + m)^3
___
-8*m + 32*\/ m
------------------------------
2 3/2 ___
-256 + m - 8*m + 128*\/ m
$$\frac{32 \sqrt{m} - 8 m}{- 8 m^{\frac{3}{2}} + m^{2} + 128 \sqrt{m} - 256}$$
(-8*m + 32*sqrt(m))/(-256 + m^2 - 8*m^(3/2) + 128*sqrt(m))