id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
14,931
|
V \cdot X = Y \implies V + X \cdot \frac{dV}{dX} = \frac{dY}{dX}
|
633
|
\left(d^l + z^l \Leftrightarrow d + z = 0\right) \implies 0 = z^l + d^l
|
-2,309
|
\frac{1}{17} = -6/17 + \frac{7}{17}
|
17,783
|
(d + b)^2 = b \cdot b + d \cdot d + 2\cdot d\cdot b
|
6,844
|
(1 + q) \cdot q - q - 1 + q + 1 = q^2 - q
|
-6,719
|
90/100 + 3/100 = \frac{1}{100} \cdot 3 + \tfrac{1}{10} \cdot 9
|
11,202
|
u'/u\cdot u\cdot y + u = e^y \implies e^y = u + y\cdot u'
|
-22,213
|
18 + m^2 - 11\cdot m = (9\cdot (-1) + m)\cdot \left(2\cdot (-1) + m\right)
|
-1,977
|
\pi \cdot \dfrac{7}{6} + 7/4 \cdot \pi = \pi \cdot \frac{35}{12}
|
-6,050
|
\dfrac{1}{(x + 4)\cdot (9\cdot \left(-1\right) + x)} = \frac{1}{x^2 - 5\cdot x + 36\cdot (-1)}
|
31,431
|
55 = 4(25 - z - x) - 2x - z = 100 - 4z - 4x - 2x - z = 100 - 6x - 5z
|
4,284
|
\left(-y\right)^{1/2} (-y)^{1/2} = -y
|
15,739
|
(3^{19} - 2^{20} + 1)\cdot 3 = 3^{20} - (2^{20} + \left(-1\right))\cdot 3
|
30,839
|
\sqrt{2} = \frac{2 - \frac{f}{c}}{\frac{f}{c} + (-1)} = \frac{2\cdot c - f}{f - c}
|
25,191
|
\left\{4, 0, 2, 3, \ldots, 1\right\} = \mathbb{N}
|
21,617
|
-8 + a\cdot 4 + 2\cdot f = (-f\cdot 8 + 4\cdot a\cdot f + f^2\cdot 2)/f
|
-19,771
|
-\frac{1}{10}\cdot 16 = -1.6
|
16,472
|
X/p\cdot X^{p + (-1)}\cdot p + (-1) = (-1) + X^p
|
-6,483
|
\tfrac{2t}{(t + 7(-1)) (t + (-1))} = \frac{t*2}{t^2 - 8t + 7}
|
6,702
|
c^{\frac{1}{2}\cdot 3}\cdot 2 = 2\cdot \sqrt{c}\cdot c
|
-9,160
|
-2\cdot 13\cdot a - a\cdot a\cdot 2\cdot 3\cdot 3 = -18\cdot a^2 - 26\cdot a
|
19,046
|
\frac{3}{3 + 2} \cdot \tfrac{1}{3 + 2} \cdot 3 = \frac{9}{25} = 0.36
|
-6,301
|
\frac{5}{x \cdot 2 + 10 \cdot (-1)} = \frac{1}{2 \cdot \left(5 \cdot (-1) + x\right)} \cdot 5
|
21,739
|
j_2 \cdot d_2 \cdot j_1 \cdot d_1 = d_1 \cdot j_2 \cdot j_1 \cdot d_2
|
-4,641
|
\frac{13 + 2 \cdot x}{20 + x^2 + 9 \cdot x} = \tfrac{5}{4 + x} - \dfrac{3}{x + 5}
|
12,371
|
2*(2^{1 + m} + (-1)) = 2^{m + 1} + 2^{1 + m} + 2(-1)
|
-19,459
|
5\cdot 1/3/(1/6) = 5/3\cdot 6/1
|
5,090
|
2 \cdot \sin{\frac{1}{2} \cdot \alpha} \cdot \cos{\alpha/2} = \sin{\alpha}
|
27,772
|
A^{1 + l} = A \cdot A^l
|
-5,138
|
0.82*10^2 = 10^{0 - -2}*0.82
|
2,543
|
-12\cdot 81 + 75\cdot 13 = -81\cdot 12 + 75\cdot (1 + 12)
|
6,296
|
\frac{1}{k n} = \frac{1}{k n}
|
9,970
|
\binom{-l + x_2}{-l + x_1} = \dfrac{(x_2 - l)!}{(-x_1 + x_2)! \cdot \left(x_1 - l\right)!}
|
7,676
|
\int \sqrt{u}\cdot (u + 1)\,\mathrm{d}u = \int (u^{1/2} + u^{\tfrac{3}{2}})\,\mathrm{d}u
|
-20,921
|
\frac{(-42)*s}{(-60)*s} = 7/10*\frac{1}{s*\left(-6\right)}*((-6)*s)
|
35,530
|
\frac{1}{3} = (3 + (-1))/6
|
4,259
|
24^m + (-1) = 2^{m\cdot 3}\cdot 3^m + \left(-1\right)
|
35,344
|
y_2 = 2 - y_1 \implies y_2 = -y_1
|
23,140
|
b + b = b \cdot b = b \cdot 2 \cdot 2 = b \cdot 2
|
6,446
|
2^{2j + 1} - 2^{2j} = 2^{2j} = 4^j
|
-10,659
|
4/4 \cdot (-\frac{1}{q^3 \cdot 3} \cdot \left(6 \cdot (-1) + q \cdot 4\right)) = -\frac{1}{q^3 \cdot 12} \cdot \left(16 \cdot q + 24 \cdot (-1)\right)
|
-1,604
|
-\frac{\pi}{3} + 2\cdot \pi = 5/3\cdot \pi
|
6,755
|
l^2 - l + l + \left(-1\right) = l^2 + \left(-1\right)
|
13,934
|
l = k \Rightarrow l = k + 1
|
35,425
|
1/(2\cdot 2) + \tfrac{1}{2\cdot 2} = \frac14 + \frac14 = \frac12
|
2,342
|
\tan(y) + \tan(x) = \sec(y) \cdot \sin(x + y) \cdot \sec\left(x\right)
|
-5,466
|
\dfrac{1}{4\cdot (t + 10)} = \frac{1}{40 + 4\cdot t}
|
19,985
|
\dfrac{1}{d*(1 + 0)} = 1/d
|
7,391
|
-t + 1 = -t + 1
|
6,686
|
1 = \frac{1}{2} - -\dfrac{1}{2}
|
34,798
|
{1 + n \choose c + 1} = {n \choose c} + {n \choose 1 + c}
|
30,870
|
\beta^2 = x^2 \Rightarrow x = \beta
|
-30,831
|
\pi*972 = \dfrac13*4*\pi*9^3
|
6,514
|
\frac{1}{3*\tfrac{1}{36}}*\frac{1}{36} = \frac13
|
11,770
|
5^{n + 1} + 5 = 5\times 5^n + 5 < 5\times \left(5^{n + 1} + 5\times \left(-1\right)\right) + 5 = 5^{n + 2} + 25\times (-1) + 5 \lt 5^{n + 2}
|
12,490
|
\dfrac{Z}{H} = Z/H
|
10,218
|
\left(3\cdot y^2 = y^4 \Leftrightarrow ((-1) + y^2)^2 = 1 + y \cdot y\right) \Rightarrow 3^{1/2} = y
|
22,555
|
\sqrt{1 + z} = (1 + z)^{\frac12} = 1 + 1/2 \cdot z + ...
|
-27,380
|
620 = 10 \times (-1) + 630
|
-4,542
|
\frac{4}{x + 5\cdot (-1)} - \frac{5}{3 + x} = \frac{37 - x}{15\cdot (-1) + x^2 - 2\cdot x}
|
17,728
|
\dfrac{1}{x^{1/2}} \cdot x = x^{1/2}
|
14,790
|
|1-a|=|a-1|
|
7,058
|
6 \cdot y + 6 = 6 \cdot (y + 1)
|
9,319
|
\psi_1 + 2k\pi = -\psi_1 + 2\psi_2 \implies \psi_2 = \psi_1 + \pi k
|
23,896
|
(-1) + \cos{y} = 0 \Rightarrow y = 0
|
34,318
|
3^{\frac{1}{2}}*18 = y^3 + \dfrac{1}{y^3} \Rightarrow 0 = y^6 - 3^{\frac{1}{2}}*y^3*18 + 1
|
35,890
|
\sqrt{13}/6 - \frac{17}{6} = \left(\sqrt{13} + 1\right)/6 + 3(-1)
|
30,296
|
N \cdot T = N \cdot T
|
23,834
|
16 \cdot (y \cdot y + 16) = 100 \cdot y^2 \Rightarrow y^2 \cdot 84 = 256
|
22,602
|
h^4 - b^4 = (b \cdot b^2 + h \cdot h^2 + h^2\cdot b + h\cdot b^2)\cdot \left(h - b\right)
|
33,613
|
5\cdot 10 + 5 = 55 = \frac12\cdot 110
|
15,057
|
\frac{47\cdot 46}{2} = 1081
|
24,262
|
\frac{d}{dw} \sin^{-1}{w} = \frac{1}{\cos(\sin^{-1}{w})}
|
5,536
|
\frac{1 - \sqrt{t + 1}}{t\sqrt{t + 1}} = -1/t + \dfrac{1}{t\sqrt{1 + t}}
|
-6,631
|
\dfrac{1}{p^2 + 3\cdot p + 40\cdot (-1)}\cdot 5 = \frac{5}{(p + 8)\cdot \left(p + 5\cdot (-1)\right)}
|
35,422
|
\left(\pi\cdot (-1)\right)/3 = -\pi + \frac{2\cdot \pi}{3}
|
3,339
|
\mathbb{E}[\lambda\cdot u] = \lambda^2\cdot u = \lambda\cdot u = \lambda\cdot u
|
19,836
|
\frac{1}{1-x}=1+x+x^2+x^3....=\sum_{n=0}^{\infty}x^n
|
-22,081
|
\frac{1}{10}*6 = \frac{3}{5}
|
24,213
|
795 = -45 \cdot 5 + 1140 + 120 (-1)
|
-2,246
|
\dfrac{3}{16} = -1/16 + \frac{4}{16}
|
24,515
|
\sin^2{x} = (1 - \cos{2x})/2
|
-721
|
e^{2\frac{i\pi}{2}} = (e^{\frac{\pi}{2}i})^2
|
-17,667
|
10 + 9*\left(-1\right) = 1
|
-4,783
|
\frac{1}{x^2 + 6 x + 5} (-x\cdot 5 + 21 \left(-1\right)) = -\frac{1}{x + 5} - \frac{4}{x + 1}
|
-4,556
|
(x + 4\cdot (-1))\cdot (x + 2\cdot (-1)) = 8 + x^2 - 6\cdot x
|
11,056
|
I\cdot K + K\cdot J = (I + J)\cdot K
|
15,414
|
\tfrac{x!}{k!\times (x - k)!} = {x \choose k}
|
2,169
|
t\cdot F\cdot Y = Y\cdot F\cdot t
|
2,728
|
1 + n^3 = (n + 1)\cdot (1 + n \cdot n - n)
|
5,324
|
1 = \dfrac{1}{12} + 1/2 + \tfrac{1}{3} + 1/12
|
17,701
|
6^2 + 1^2 + 2^2 + 3 \cdot 3 + 4^2 + 5^2 = 91
|
34,742
|
218 \cdot 218 + \left(-1\right) = (218 + 1) \cdot (218 + (-1)) = 219 \cdot 217 = 3 \cdot 73 \cdot 7 \cdot 31
|
20,337
|
b*0 = \left(b + b\right)*0
|
-18,423
|
\frac{1}{x \cdot (x + 10)} \cdot \left(10 + x\right) \cdot (4 \cdot (-1) + x) = \dfrac{1}{x^2 + 10 \cdot x} \cdot (x \cdot x + 6 \cdot x + 40 \cdot (-1))
|
10,714
|
A^{24} = A^{16}\cdot A^8
|
-11,968
|
\frac{14}{45} = \frac{s}{6\cdot \pi}\cdot 6\cdot \pi = s
|
-24,370
|
\frac{1}{6 + 8} \times 70 = 70/14 = \frac{70}{14} = 5
|
-15,843
|
-\frac{9}{10} \cdot 5 + \frac{5}{10} = -40/10
|
-28,801
|
2.5 = \frac{2 \cdot \pi}{2 \cdot \pi \cdot \dfrac{1}{2.5}}
|
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