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ddrg
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math_formulas

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-4,555
\left(3 + x\right)*(x + 5*(-1)) = 15*(-1) + x^2 - 2*x
21,042
\pi*5/12 = \dfrac{5*\pi}{12}
2,179
1 \times 1 + 2^2 + ... + n^2 = n + ((-1) + n) \times 3 + 5 \times (2 \times (-1) + n) + ... + 2 \times (3 \times (-1) + 2 \times n) + n \times 2 + (-1)
-7,823
\left(36 - 54 \cdot i + 36 \cdot i + 54\right)/18 = (90 - 18 \cdot i)/18 = 5 - i
12,271
7875000 = {6 \choose 1}*5^6 {9 \choose 3}
1,560
6 = (-(-5)^{\frac{1}{2}} + 1) (1 + (-5)^{1 / 2})
10,459
-\frac14 + (1/2 + x)^2 = x * x + x
4,592
3 + 4\cdot n^2 + 7\cdot n = 4\cdot n^2 - n + n\cdot 8 + 3
-29,060
5^7 = 5^5\cdot 5^2
-7,760
\dfrac{1}{41} \cdot \left(-36 + 4 \cdot i - 45 \cdot i + 5 \cdot (-1)\right) = \dfrac{1}{41} \cdot (-41 - 41 \cdot i) = -1 - i
4,385
(y + 2 \cdot z)^2 = y \cdot y + z \cdot z \cdot 4 + y \cdot z \cdot 4
10,775
x^2 + x + 1 = \frac{1}{(-1) + x}\cdot (\left(-1\right) + x^3)
22,389
(x + \delta) \cdot (x + \delta) - x^2 = \delta^2 + x\delta \cdot 2
12,173
(-3 \cdot 3 + 4 \cdot 4)^{1 / 2} = 7^{\frac{1}{2}}
25,141
\left(C \cdot C\right)^X = (C\cdot C)^X = C^X\cdot C^X = (C^X)^2
7,945
x_n^{n + (-1)} = \frac{x_n^n}{x_n}
13,714
8! = 40320 = 2^7 \times 3^2 \times 5 \times 7
9,753
-12 x + 1 = 0 \Rightarrow x = \frac{1}{12}
1,015
( -x(t)*z(t), -y(t)*z\left(t\right), -z^2(t) + 1) = ( \frac{\mathrm{d}}{\mathrm{d}t} x(t), \frac{\mathrm{d}}{\mathrm{d}t} y(t), \frac{\mathrm{d}}{\mathrm{d}t} z(t))
-12,337
2 \sqrt{5} = \sqrt{20}
16,271
2^{a\cdot k} + (-1) = \left(2^a\right)^k + (-1) = (2^a + (-1))\cdot ((2^a)^{k + (-1)} + (2^a)^{k + (-1)} + ... + 1)
11,679
1/2 \cdot 4 \cdot a \cdot a \cdot 4 = a \cdot a \cdot 8
-7,148
\frac29 \cdot 4/10 = \frac{1}{45} \cdot 4
15,642
\dfrac{1}{1 + x^2}\cdot (1 + 2\cdot x) = \frac{1}{(1 + x^2)\cdot 2}\cdot (-x^2 + x\cdot 4 + 1) + 1/2
-20,424
\tfrac19(x + 5)*5/5 = \frac{1}{45}(x*5 + 25)
-9,177
-3\cdot 2\cdot 3 + 2\cdot 3\cdot 3\cdot 3\cdot z = 54\cdot z + 18\cdot (-1)
19,168
\frac{l\times ((-1) + j)}{(l - j + 1)^2} = \frac{1}{\left(l - j + 1\right)^2}\times l^2 - \frac{l}{l - j + 1}
4,656
3*\left(6*(-1) + 1006\right)/10 = 300
-10,826
\frac{136}{8} = 17
-11,990
\frac{2}{15} = s/(12 \pi)*12 \pi = s
9,147
x^5 = x^2 \cdot x \cdot x^2 = \tfrac{1}{3} \cdot x \cdot x \cdot x \cdot 3 \cdot x^2
37,239
3 \cdot (S + z) = 3 \cdot S + z \cdot 3
37,726
\frac1b\cdot h = \dfrac{1}{b}\cdot h
2,521
1 - y \gt 0 \Rightarrow y < 1
27,057
\frac{1}{e^{\left(-1\right)\cdot \left((-2)\cdot 1.0\cdot 10^{-10}\right)\cdot 1000}}\cdot 2 = 2\cdot 0.999999 = 1.99999
-11,884
0.002478 = 2.478\times 0.001
17,220
\tfrac{1}{1/U} = U
-8,974
50.4\% = \frac{1}{100}\cdot 50.4
9,754
s \cdot p^i \cdot p^x = p^i \cdot s \cdot p^x
2,126
\operatorname{E}\left[\tfrac{R}{R}\right] = \operatorname{E}\left[1\right] = 1 = \operatorname{E}\left[R\right]/\operatorname{E}\left[R\right]
38,950
-\pi/4 + 1 = -\frac{\pi}{4} + 1^{-1}
53,916
d/dx (e^x + e^{-x}) = \frac{dx}{dx} \cdot e^x + d/dx \left(-x\right) \cdot e^{-x} = e^x - e^{-x}
-856
734/10000 = \dfrac{4}{10000} + 0 + 0/10 + \frac{7}{100} + 3/1000
23,263
\tfrac{1}{12} = \tfrac{1}{3 \cdot 4}
-18,849
-4 = -\frac82
36,049
\frac{a}{d} = a/d
-1,587
-\frac{\pi}{2} = -\pi*5/4 + \pi*3/4
993
z \cdot y \cdot x = 1 rightarrow 1 = x, y = 1, z = 1
16,022
a\cdot d = 2\cdot (a + d)\cdot \ldots\cdot \ldots\cdot \ldots\cdot \ldots
16,770
287 = 1 + 2*\left(53 + 6 + 18 + 36\right) + 60
15,485
x*3 + x*3 = 6x
-23,348
\frac{1}{9}4*3/4 = \dfrac13
28,546
\sin{z} = \cos(z + \dfrac{1}{2}*3*\pi)
28,091
\sin{H_2} \cos{H_1} + \sin{H_1} \cos{H_2} = \sin(H_2 + H_1)
19,340
\tfrac{720}{3 \cdot 2}1 = \binom{10}{3}
25,843
5 \cdot \pi/3 = 2 \cdot \pi/3 + \frac{\pi}{2} + \pi/2
-560
e^{i \cdot \pi/12 \cdot 3} = e^{\frac{\pi}{12} \cdot i} \cdot (e^{\frac{\pi}{12} \cdot i})^2
-4,052
100/40 \frac{x}{x} = \dfrac{x*100}{x*40}
10,420
(5^n + (-1))\cdot (1 + 5^n) = 5^{2\cdot n} + (-1)
15,078
3/A + 2 \cdot (-1) = 3 \cdot (-1) + \frac{1}{A} \cdot (3 + A)
22,529
\operatorname{atan}(\tan(z - \pi)) = z - \pi = \operatorname{atan}\left(\tan(z)\right)
-15,317
\dfrac{\frac{1}{z^{25}}*f^{20}}{\tfrac{1}{f^8}*z^4}*1 = \frac{1}{\dfrac{1}{\dfrac{1}{z^4}*f^8}}*(\frac{f^4}{z^5})^5
-10,264
3/3*(-\frac{1}{5 + z}) = -\frac{3}{15 + 3*z}
24,483
\frac{1}{3}\times 2/9 + \frac{2}{9}\times 1/3 + \frac{1}{3}\times 2\times 0 = \frac{4}{27}
-27,489
2\cdot 2\cdot 7\cdot c\cdot c = c \cdot c\cdot 28
25,928
x^2 + 5 \cdot x + 6 = (3 + x) \cdot (x + 2)
6,051
-z^k + x^k = (x - z)\cdot (x^{\left(-1\right) + k} + z\cdot x^{2\cdot (-1) + k} + ... + z^{k + 2\cdot \left(-1\right)}\cdot x + z^{k + (-1)})
-19,421
2/5\cdot \frac{6}{1} = \dfrac{2}{1/6}\cdot 1/5
24,167
\frac{2\cdot \pi}{12} = \frac{\pi}{6} \approx 0.5236
-22,955
18/24 = \frac{6\cdot 3}{4\cdot 6}
-22,128
\dfrac{30}{35} = \frac67
6,738
x! - N! = N!\cdot (\frac{x!}{N!} + (-1))
22,476
8^3 - 5^3 - 3^3 = 512 + 125 \left(-1\right) + 27 (-1) = 360
28,623
\log_e(14623) = \tfrac{1}{0.434}4.176 = 9.616
-1,464
\frac{1}{1/4}*((-1)*\frac13) = -\frac{1}{3}*\dfrac41
28,280
4/3 x^{1/3} = x^{4/3} \cdot \frac{4}{3x}
9,329
\int 1/y\,dy = \left(\log_e(y)\right)! = \log_e(y)
11,816
\frac{1}{1 + (1 + x) \cdot 2} = \frac{1}{3 + 2 x}
47,056
-\left(\lambda+\frac{Y''}{Y}\right) = -k_x^2 \;\Rightarrow\; Y'' + (\lambda-k_x^2)Y = 0
1,194
(f - h) \cdot (f^{(-1) + l} + f^{2 \cdot (-1) + l} \cdot h + \dotsm + f \cdot h^{2 \cdot (-1) + l} + h^{l + (-1)}) = -h^l + f^l
-3,794
\frac{20}{12} x^4/x = \frac{x^4}{x} \frac{4 \cdot 5}{3 \cdot 4}
7,535
(a^2 + f^2) \cdot \left(d^2 + c^2\right) = (c \cdot a + d \cdot f)^2 + (a \cdot d - c \cdot f) \cdot (a \cdot d - c \cdot f)
23,007
B/c = \frac{c\cdot B/c}{c}
-8,074
\frac{1}{8} \times (20 + 4 \times i - 20 \times i + 4) = \tfrac{1}{8} \times \left(24 - 16 \times i\right) = 3 - 2 \times i
-24,117
\dfrac{1}{7 + 4} \cdot 99 = 99/11 = 99/11 = 9
31,936
2 \cdot \pi \cdot x \cdot x = \sqrt{2 \cdot \pi} \cdot x \cdot x \cdot \sqrt{2 \cdot \pi}
21,426
\frac{19}{20} = \frac{95}{100}
38,612
\infty*(0 + \left(-1\right)) = \infty*\left(-1\right) = -\infty
9,413
T - T*0 = T
7,122
t^2 + 2 \cdot h \cdot t + h^2 = (h + t)^2
27,610
\arctan{\infty} = \frac{\pi}{2}
-6,707
\frac{1}{10}3 + \frac{5}{100} = 30/100 + \dfrac{5}{100}
-8,328
-1 = \frac{8}{-8}
29,727
d/dz \sec(z) = \tan(z)\cdot \sec\left(z\right)
30,215
0 = \dfrac13*(a + 2) \Rightarrow a = -2
-2,629
3^{1 / 2}\times (5 + 2 + 4\times \left(-1\right)) = 3^{1 / 2}\times 3
6,894
\dfrac{1}{2^n\cdot \frac12} = \frac{2^1}{2^n} = \frac{2}{2^n}
-2,455
\sqrt{2}\cdot (3 + 5) = 8 \sqrt{2}
16,990
m = \left\{m, \ldots, 2, 1\right\}
50,156
4\times 5 + 880 + 2\times 85 + 3\times 30 = 1160