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math_formulas

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10,818
6 \cdot (\frac{1}{216} + 1)^{1/3} = 217^{1/3}
-15,874
\frac{5}{10} = 7*\dfrac{1}{10}5 - 6*\frac{5}{10}
31,837
1 \cdot 2 \cdot 3 + 2 \cdot 4 + 3 + 5 + 6 = 6 + 8 + 3 + 5 + 6 = 28
20,386
a^2 \times b^2 = (a \times b)^2
34,010
\int (-c)\,\text{d}K = -\int c\,\text{d}K
5,077
\sin(\frac{y}{2}) = \cos(\dfrac{y}{2}) = \sin\left(\pi/2 - y/2\right)
-20,768
\frac{3 \cdot k + 9 \cdot (-1)}{3 \cdot k + 12 \cdot \left(-1\right)} = 3/3 \cdot \frac{3 \cdot (-1) + k}{k + 4 \cdot (-1)}
20,086
2 \cdot 770 + 653 = 2193
21,403
1 - 3 \times \frac{1}{21} \times 2 = 15/21 = 5/7
23,238
\left(a \cdot a - 2\cdot a\cdot g + g \cdot g = \left(a - g\right)^2 = 0 \implies 0 = -g + a\right) \implies g = a
36,609
z \cdot y + z + y + 1 = 20 = (z + 1) \cdot (y + 1)
12,536
H\cdot m = m\cdot H
-2,314
\frac{3}{18} = -\frac{6}{18} + \dfrac{1}{18}\cdot 9
19,713
0 = \cos{0} \sin{0}
16,250
|\dfrac{z^2}{z} + 0*(-1)| = |z + 0*\left(-1\right)|
34,341
\cos\left(1/z\right) = 1 - \frac{1}{(z^{22})!} + \frac{1}{(z^{44})!} - ...
7,607
s\cdot e = s\cdot e
33,935
7 + 2x = 0 + \frac1441 (x\cdot 8/41 + \frac{28}{41})
-10,742
-30 = 5 p + 1 + 21 (-1) = 5 p + 20 (-1)
7,459
3\times \frac{2\times \pi}{5} + 2\times 2\times \pi/5 = \pi\times 2
-5,072
8.7\cdot 10 = \dfrac{8.7}{100}\cdot 10 = \frac{8.7}{10}
930
g_{j,\phi} = g_{j,\phi}
30,564
2 \cdot \left(-1\right) + 6 = -2^5 + 6^2
21,761
(a^2 + b^2)\cdot (c^2 + d^2) = (a\cdot c + b\cdot d)^2 + (a\cdot d - b\cdot c) \cdot (a\cdot d - b\cdot c) = (a\cdot c - b\cdot d)^2 + (a\cdot d + b\cdot c)^2
37,796
\mathbb{E}(A_1*A_2) = \mathbb{E}(A_1)*\mathbb{E}(A_2)
10,798
6 (-1) + 2 k = 0 \Rightarrow 3 = k
19,529
-z_1 \cdot z_1 + z_2^2 = (-z_1 + z_2)\cdot (z_2 + z_1)
35,961
2\times \cos{R}\times \sin{R} = \sin{2\times R}
16,405
(x + 2\cdot (-1))\cdot \left(x + 1\right) = x^2 - x + 2\cdot (-1)
-23,426
\frac{\frac{1}{5}*4}{2} = 2/5
9,556
\mathbb{E}\left(|Y| + |Z|\right) = \mathbb{E}\left(|Y|\right) + \mathbb{E}\left(|Z|\right)
-25,049
5/13 \cdot 4/12 = \frac{20}{156} = 5/39
22,311
D_i \cdot D_x = D_i \cdot D_x
14,273
2 z \frac{dz}{dx} = \frac{d}{dx} z z
22,079
\tfrac16 = 2/12
18,286
E*X = X*E
-10,364
\dfrac{1}{2} \cdot 2 \cdot \dfrac{4}{y \cdot 10} = \dfrac{8}{20 \cdot y}
5,447
\frac{1}{6} + 1/6 + \frac16 = 3/6
-29,581
d/dy (-y \cdot 10 + y^4 - y^2 \cdot 4) = 10 \cdot \left(-1\right) + y^3 \cdot 4 - 8 \cdot y
13,206
-(-y + 1) + y = 2 \cdot y + (-1)
-1,458
\dfrac17*8*\left(-5/7\right) = 8*1/7/\left((-1)*7*\frac{1}{5}\right)
-18,418
\dfrac{l}{(4 \cdot (-1) + l) \cdot (9 \cdot (-1) + l)} \cdot (9 \cdot (-1) + l) = \frac{l^2 - 9 \cdot l}{l \cdot l - l \cdot 13 + 36}
23,142
\frac {6\cdot 5 \cdot 4 \cdot 3 \cdot 2}{5}=144
-6,007
\frac{4}{(y + 4) \cdot (10 + y)} = \frac{4}{y^2 + 14 \cdot y + 40}
36,238
K^c + S^c = K^c + S = K + S^c
27,213
3\zeta_{12}^6 = (\zeta_{12} \cdot 3^{1/6})^6
-6,625
\frac{1}{3 \cdot (s + 8)} \cdot 5 = \frac{5}{24 + s \cdot 3}
28,145
d = x^r\Longrightarrow d^{1/r} = x
6,606
9(-1) + ((5 + (2 + 1)*3*4)*6 + 7)*8 = 2015
624
(n!)! > \left(n^2\right)^{n! - n^2} = n^{2*n! - 2*n^2} > n^{n!}
7,917
\dfrac{1}{12} - \frac{1}{60} = \frac{1}{15} = 1/(3*5)
31,066
d/dx \tan^{-1}{x} = \frac{1}{1 + x^2}
10,095
-\frac{1}{5} + 1 - 1/5 = \frac{3}{5}
20,594
(\mu - \delta) (\mu + \delta) = \mu - \delta^2 = (\mu + \delta) \left(\mu - \delta\right)
2,999
(0 \cdot (-1) + x) \cdot 2 = y + (-1) \Rightarrow y = 1 + 2 \cdot x
15,375
1/64 + \frac{1}{64} \cdot 15 + 6/64 = 22/64
32,800
-9\cdot y^2 = -9\cdot y\cdot y
-6,076
\frac{1}{2\cdot m^2 + 12\cdot m + 54\cdot (-1)}\cdot (8\cdot \left(-1\right) + 3\cdot m + 27 - m\cdot 6 + 18) = \frac{1}{54\cdot (-1) + 2\cdot m \cdot m + 12\cdot m}\cdot (37 - 3\cdot m)
15,728
58 = \left\lfloor{\frac{1}{17} \times 1000}\right\rfloor
-9,367
-12\cdot m + 8\cdot m^2 = m\cdot 2\cdot 2\cdot 2\cdot m - m\cdot 2\cdot 2\cdot 3
11,435
\left(-d_1 + d_2\right)^2 = d_2^2 + d_1^2 - d_1 d_2*2
-9,425
t*3 + 3 = t*3 + 3
-2,581
\sqrt{6} = \left(2 + (-1)\right) \sqrt{6}
4,330
\left(n + 1\right)\cdot a = a + a\cdot n
-8,013
(50 - 150 \cdot i + 50 \cdot i + 150)/50 = \left(200 - 100 \cdot i\right)/50 = 4 - 2 \cdot i
7,018
f \approx a\Longrightarrow f \approx a
2,020
\|z\| * \|z\| = \left\{z\right\} = \|Wz\|^2 = ( Wz, Wz)
6,180
(\sin(x) + \cos(x))^2 = 1 + 2 \cdot \sin(x) \cdot \cos\left(x\right) = 1 + \sin(2 \cdot x) = 1^2 = 1 \Rightarrow 0 = \sin(2 \cdot x)
48,244
5^0\cdot 2^3 = 8
-22,280
x^2 + 12 x + 27 = (x + 3) \left(x + 9\right)
-3,470
\frac{5}{20 \cdot 5} \cdot 9 = 45/100
26,279
\frac{1}{x^{1/2}}3 = \tfrac{1}{x^{1/2}}3
31,724
E_R\cdot x\cdot D = x\cdot E_R\cdot D
3,164
(1 + n - k) (n - k)! = (n - k + 1)!
8,915
u_1^Y x_1 = u_1^Y x_1
-4,389
\frac{70 k^2}{k^4 \cdot 120} = \frac{1}{k^4}k^2 \cdot \frac{1}{120}70
25,428
1/2 \times 2 = 1
-11,031
\dfrac19*72 = 8
-2,540
\sqrt{6} \cdot (4 + 3 + 2) = \sqrt{6} \cdot 9
383
0 = \mathbb{E}[X^5] \Rightarrow \mathbb{E}[X X X] = 0
4,948
l\cdot m = l + l\cdot \left((-1) + m\right)
-1,743
-\pi/12 = -\pi/6 + \pi/12
19,803
-c_1 + c_2 = -(c_1 - c_2)
12,552
y^2 = (0*(-1) + y)*(y + 0*\left(-1\right))
28,131
1/6 + 1/6 + \dfrac16 + \frac16 = \frac{2}{3}
34,505
9 - \sqrt{3}*5 = 6 - 2*\sqrt{3} - 3*\sqrt{3} + 3
12,988
2 \cdot 2 + 2^4 \cdot 3 - 2^3 \cdot 3 = 28
26,710
|D/x| = |D|/|x|
28,100
\operatorname{atan}\left(3^{1 / 2}/3\right) = \dfrac{\pi}{6}
29,775
m_2*x*m_1 = x*m_2*m_1
-4,833
0.83*10^4 = 0.83*10^{2 - -2}
17,052
z^{w_2} z^{w_1} = z^{w_1 + w_2}
31,427
\frac{4577}{8} = 572.125
17,317
\pi \cdot 180 = 5 \cdot \pi \cdot 2 \cdot 18
28,041
\tan^{-1}(-\dfrac{1}{\sqrt{3}}) = -\pi/6
15,000
10\cdot \left(-1\right) + y^2 + 3\cdot y = (y + 2\cdot (-1))^2 + 7\cdot (y + 2\cdot (-1))
28,111
2^{-2/3} = 2^{\frac{1}{3}}/2
23,563
0 = \sin{\frac{π}{4}} \sin{0}\cdot 2
-9,146
32 + x \cdot 16 = x \cdot 2 \cdot 2 \cdot 2 \cdot 2 + 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2
2,547
\dfrac{1}{3}*(1 - 6*n) = \tfrac13 - 6*n/3 = 1/3 - 2*n