id
int64
-30,985
55.9k
text
stringlengths
5
437k
28,922
G \times G = \left(-G\right) \times \left(-G\right)
6,071
-(n + (-1)) + 2*n + 2*(-1) = n + (-1)
15,938
\cos{2 \cdot \theta} = -2 \cdot \sin^2{\theta} + 1
24,807
(1 + y y + y) \left(y + (-1)\right) = (-1) + y^3
-1,138
\frac{1}{6 \cdot 1/5} \cdot ((-8) \cdot \dfrac{1}{7}) = 5/6 \cdot (-\frac{8}{7})
15,832
g^3 + (-1) = \left(g^2 + g + 1\right)*((-1) + g)
10,489
|g_x + 0\cdot (-1)| = |g_x|
27,624
(-(x - z)^2 + (z + x)^2)/4 = xz
10,591
\dfrac{1}{g\cdot 2^{1 / 2} + a} = \tfrac{1}{a^2 - g^2\cdot 2}\cdot a + \dfrac{\left(-1\right)\cdot g}{a^2 - g \cdot g\cdot 2}\cdot 2^{1 / 2}
14,212
\lim_{y \to \infty} y*2 = \lim_{y \to \infty} y
54,206
3\cdot 11 = 33 = 4\cdot 8 + 1
23,705
\left(3*(-1) + z\right)^2 = 9 + z^2 - z*6
6,614
\frac{1}{\sin(A \cdot 2)} \cdot (\cos(A \cdot 2) + 1) = \cot(A)
-6,019
\tfrac{z}{(z + 8*(-1))*(7 + z)} = \frac{1}{56*(-1) + z * z - z}*z
16,169
(5 - \frac92)^2 = (-9/2 + 4)^2
18,197
x^6 - x^4 \cdot 3 + x^2 \cdot 3 + (-1) = ((-1) + x^2) \cdot \left(x^2 + (-1)\right)^2
-20,246
\frac{8}{8 + 6p}p*5/5 = \dfrac{40 p}{p*30 + 40}
-1,169
7/1 \cdot \frac56 = \frac16 \cdot 5/\left(1/7\right)
5,710
\frac{1}{1 + m^2 + m} = \dfrac{1}{(m + 1)^2 - 1 + m + 1}
-22,383
2(-1) + 6 = 4
21,497
d + g \cdot y = 0\Longrightarrow y = \frac1g \cdot (d \cdot (-1))
47,111
\binom{12 + 2}{12} = \binom{14}{12}
-20,860
4/1\cdot \dfrac{y + 9}{9 + y} = \frac{1}{9 + y}\cdot (36 + y\cdot 4)
31,052
(1 + z^2) \cdot (1 - z^2 + z^4) = 1 + z^6
-1,832
7/12 \cdot \pi = \frac{3}{4} \cdot \pi - \pi/6
43,795
\overline{x} + \overline{n} = \overline{n + x}
13,202
\frac{1}{-2} \cdot ((-1) \cdot y) = \frac{(-1) \cdot (-y)}{(-1) \cdot (-2)} = \frac12 \cdot y
19,153
5957\cdot 11 + 9 = 65536
26,394
\operatorname{atan}(x) = \tfrac{1}{x \cdot x + 1}
29,362
n + 3 = \frac{1}{3 \cdot \left(-1\right) + n} \cdot (n^2 + 9 \cdot \left(-1\right))
16,182
\sin(1 + n) = \sin{1}\cdot \cos{n} + \cos{1}\cdot \sin{n}
3,657
3\cdot l + \epsilon\cdot 3 = 4\cdot l\Longrightarrow l = 3\cdot \epsilon
6,050
\lambda\cdot x = \lambda\cdot x\cdot \frac{Z}{Z} = \lambda\cdot x\cdot Z/Z
30,770
24 = \frac{24}{2}2
-7,543
\frac{1}{-1 - 5*i}*(i*9 + 7) = \dfrac{7 + 9*i}{-5*i - 1}*\frac{i*5 - 1}{-1 + 5*i}
13,936
{n - k + k + (-1) \choose \left(-1\right) + k} = {n + (-1) \choose k + (-1)}
13,117
(1 + 7)\cdot (2 + 1)\cdot (1 + 1) = 48
40,249
\binom{8}{3}*2*(\binom{5}{4} + \binom{5}{3}) = 1680
-3,040
-\sqrt{11} + \sqrt{275} = -\sqrt{11} + \sqrt{25 \cdot 11}
7,342
\tfrac{1}{(-1) + x}*((-1) + x^2) = \frac{1}{x + (-1)}*(x + (-1))*(1 + x)
8,424
\alpha^{l + k} \cdot \alpha = \alpha^{1 + l + k}
25,853
720 + 24 \cdot (-1) + 24 \cdot (-1) + 24 \cdot \left(-1\right) + 24 \cdot (-1) + 6 + 6 + 6 + 2 \cdot (-1) + 2 \cdot (-1) + 1 = 639
-11,080
(x + 4 \cdot \left(-1\right)) \cdot (x + 4 \cdot \left(-1\right)) + b = \left(x + 4 \cdot (-1)\right) \cdot (x + 4 \cdot (-1)) + b = x \cdot x - 8 \cdot x + 16 + b
18,870
\frac{\mathrm{d}}{\mathrm{d}z} e^{((-1) \times z^2)/2} = -z \times e^{\frac12 \times \left((-1) \times z^2\right)}
21,049
\frac{1}{1 + y} = \tfrac{1}{(1 + y)^{\dfrac12} (1 + y)^{1/2}}
-15,832
\dfrac{8}{10}\cdot 6 - 2/10\cdot 9 = 30/10
-18,555
5\cdot y + 9\cdot (-1) = 2\cdot \left(4\cdot y + 3\cdot (-1)\right) = 8\cdot y + 6\cdot (-1)
-27,710
\frac{d}{dp} (-\cos(p)*12) = 12*\sin\left(p\right)
19,134
20 (-1) + (120 + 20 (-1))\cdot 3 = 280
-25,813
\frac{3}{10*6} = \frac{1}{60}3
25,082
S \times \tau \times q^2 = \tau \times S \times q^2
-1,715
4/3\cdot \pi + 5/6\cdot \pi = \tfrac{13}{6}\cdot \pi
20,666
\frac{\mathrm{d}}{\mathrm{d}x} 1/x = -\dfrac{1}{x^2} = -\dfrac{1}{x^2}
-22,215
x^2 + 7\cdot x + 8\cdot (-1) = \left(x + 8\right)\cdot ((-1) + x)
1,844
6 = (7^{1/2} + (-1)) (7^{1/2} + 1)
-19,615
\frac{1}{6} \cdot 40 = 8 \cdot 5/(6)
-7,379
\frac19*4 = \frac19*4
2,205
\dfrac{12}{6} \cdot 4 = 8
21,744
(-1) + 2*\sin\left(y\right) = 0 \implies \sin(y) = 1/2
10,623
(1/2 - i)^2 + i\cdot 2 = (\dfrac{1}{2} + i)^2
11,412
3 + 3\cdot 5 + ... + 3\cdot 5^m = \frac{1}{4}\cdot (-3 + 5^{m + 1}\cdot 3)
7,217
p = L + z\Longrightarrow -L + p = z
14,831
-3 - 3 = 2 \times (-3)
18,522
(z^2)^2 = z^2 \times z^2 = z \times z \times z \times z = z^4 = z^{2 \times 2}
1,353
\left(e^{i*x} - e^{-i*x}\right)/(2*i) = \sin{x} \Rightarrow -e^{-x*i} + e^{i*x} = 2*i*\sin{x}
22,910
(-1) + y^3 - y \cdot y + y = ((-1) + y) \cdot (1 + y^2)
28,846
(\omega \cdot \omega)^4 = (\omega^4)^2 = (\omega + 1) \cdot (\omega + 1) = \omega^2 + 1
-2,028
\frac14 \cdot \pi = -5/12 \cdot \pi + \frac{2}{3} \cdot \pi
3,127
\sqrt{(x + 1)^2 + (-1)} = \sqrt{x^2 + 2 \cdot x}
440
c_1^2 - 2 \cdot c_2 \cdot c_1 + c_2^2 = (c_1 - c_2)^2
31,583
b/c := b/c
26,102
d_k + d_{(-1) + k} + \cdots + d_2 + d_1 = d_1 + d_2 + \cdots + d_{k + (-1)} + d_k
27,053
\frac{1}{2048}\cdot (165 + 55 + 11 + 1) = \frac{29}{256}
-15,830
-39/10 = -5 \cdot \frac{9}{10} + \frac{6}{10}
25,816
9\cdot 2 + 3\left(-3\right) + 4 = 13
-7,793
\dfrac{1}{-4}\cdot (-20 + 20\cdot i) = -20/(-4) + \frac{20\cdot i}{-4}
14,651
\frac{x^{k + 1}}{k \cdot x^k} \cdot (k + 1) = (k + 1) \cdot x/k = (1 + 1/k) \cdot x
-18,763
0.0198 = (-1) \cdot 0.003 + 0.0228
26,770
N*M = M*N
32,825
\frac{1}{4\cdot 4} = \frac{1}{4\cdot 4} = \frac{1}{4\cdot 4}
19,132
x + 3\cdot (-1) \geq 0 rightarrow x \geq 3
-20,121
(10\cdot r + 30\cdot (-1))/(r\cdot 90) = 10/10\cdot (3\cdot \left(-1\right) + r)/(r\cdot 9)
8,772
(a^2 b^2)^{1/2} = (a^2)^{1/2} (b^2)^{1/2} = |a| |b| = -a b
3,906
\frac{\frac{1}{s^2 + a^2} \cdot s}{s^2 + a \cdot a} \cdot 1 = \frac{s}{(a^2 + s^2)^2}
29,548
2^{1092} + (-1) = \left(1 + 2^{273}\right)*(2^{546} + 1)*\left(2^{273} + (-1)\right)
-3,951
\dfrac{44a^5}{55a^5} = \dfrac{44}{55} \cdot \dfrac{a^5}{a^5}
-12,008
1/9 = \dfrac{p}{12 \cdot \pi} \cdot 12 \cdot \pi = p
29,306
3 = 5*\frac{3}{5}
-2,970
(5 + 4 + 2(-1)) \sqrt{11} = 7\sqrt{11}
26,098
4\cdot \pi - 3\cdot \pi = \pi
47,627
1 < 3/2
11,783
-(a^2 - a\times x + x^2) + \left(a + x\right)^2 = 3\times a\times x
14,492
a_2 + a_3 + ... + a_k + a_{k + 1} = a_2 + a_3 + ... + a_k + a_{1 + k}
995
a/f + \frac1af = (a^2 + f * f)/\left(af\right)
29,596
z \cdot z \cdot z \cdot 3 + z \cdot 6 = ((-1) + z)^3 + z^3 + (1 + z)^3
35,070
\left\{0\right\} = ( l, x)^s = ( sl, sx)
-20,904
\frac{90*(-1) + 9*n}{-n*63 + 9} = \frac19*9*\frac{10*(-1) + n}{1 - 7*n}
35,186
x + k*x^2 + k^2*x^3 + \dots = \frac{1}{k}*\left(k*x + (k*x)^2 + \left(k*x\right)^3 + \dots\right) = \frac{1}{1 - k*x}
7,491
y^0 = \frac{\frac{1}{y}*y^2*y^3}{y^4}
21,614
25 w^2 - 10 w + 1 = ((-1) + 5 w) ((-1) + 5 w)