id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
55,881
|
{5 \choose 2} = 10
|
32,010
|
12*23*34*\ldots*((-1) + n)*n = 1234*\ldots*n
|
25,347
|
867 = 3 \times 17^2
|
23,601
|
\frac{1}{2\cdot \left(1 - x\right)} = -\frac{1}{((-1) + x)\cdot 2}
|
31,592
|
x \cdot x + x\cdot 5 + 12\cdot (-1) = 0 \Rightarrow 60\cdot (-1) + 37\cdot x = x^3
|
-7,562
|
\dfrac{60 - 130i + 48i + 104}{41} = \dfrac{164 - 82i}{41} = 4-2i
|
6,245
|
x \geq 4(-1) + x^2 \Rightarrow x \cdot x - x + 4\left(-1\right) \leq 0
|
32,891
|
\sin{8x} = \sin{8(x + T)}\Longrightarrow 8(x + T) = x*8 + 2\pi
|
35,942
|
H^2 + H = 3 \cdot H - x = H^3 + x
|
25,324
|
2 \times 2 = 2 \times 2 = 4
|
-20,954
|
\frac{10\cdot p + 2}{-p\cdot 35 + 7\cdot \left(-1\right)} = \frac{(-1) - 5\cdot p}{(-1) - 5\cdot p}\cdot (-2/7)
|
20,990
|
\left(3*\left(-1\right) + 3*(-1)\right) * \left(3*\left(-1\right) + 3*(-1)\right) = (-3 + 3*(-1))^2
|
19,208
|
y^a\cdot y^b\cdot y^c = y^{c + a + b}
|
34,289
|
\left(g + d + (-1)\right) \cdot 2 = d \cdot 2 + (-1) + 2g + \left(-1\right)
|
-554
|
\left(e^{\pi*i*13/12}\right)^{13} = e^{\frac{\pi*i*13}{12}*13}
|
-7,426
|
\frac{3}{13} \cdot \frac{6}{14} = 9/91
|
-24,925
|
\sin\left(D\right) \cdot \cos(D) \cdot 2 = \sin\left(2 \cdot D\right)
|
9,130
|
7^2 + 61 = 110
|
25,315
|
(x + 2 \times (-1)) \times x \times (x + (-1)) \times \dots \times 3 \times 2 = x!
|
21,757
|
0 + x^2 + x\cdot 0 = x^2
|
14,542
|
a^2 + b^2 = -a \cdot b \cdot 2 + (b + a)^2
|
36,311
|
c^{x + k} = c^x \cdot c^k
|
-4,905
|
3.3\cdot 10^{3 + 5} = 10^8\cdot 3.3
|
5,291
|
92*1/5/100 = 92/500 = \frac{1}{125}*23
|
-29,936
|
\frac{\mathrm{d}}{\mathrm{d}x} (-x^3 + 5 \times x^2 - x \times 8) = 8 \times (-1) - x^2 \times 3 + x \times 10
|
136
|
b\cdot a + a\cdot x = \left(x + b\right)\cdot a
|
-2,319
|
10/17 - 8/17 = \frac{2}{17}
|
3,723
|
\dfrac{1}{1/2 \cdot \left(y + 1\right)} = \frac{2}{y + 1}
|
-10,609
|
\frac44\cdot \frac{3}{3\cdot z + 2} = \frac{12}{8 + z\cdot 12}
|
4,723
|
(\dfrac14)^{1 / 2} = \frac{1}{2}
|
1,504
|
k \cdot k - (k + (-1))^2 = k^2 - k^2 - 2 \cdot k + 1 = 2 \cdot k + \left(-1\right)
|
40,553
|
\frac{1}{\dfrac{1}{y}} = y
|
-11,468
|
8i + 0 + 6\left(-1\right) = 8i - 6
|
5,253
|
B_1 \cap B_2 = \left(B' \cup G\right) \cap (B_1 \cap B_2) = (B_2 \cap (B' \cap B_1)) \cup \left(B_2 \cap (G \cap B_1)\right)
|
-6,723
|
2/10 + \dfrac{5}{100} = \frac{20}{100} + 5/100
|
6,250
|
\mathbb{E}\left[C_1 C_2\right] = \mathbb{E}\left[C_1\right] \mathbb{E}\left[C_2\right]
|
-4,242
|
3/2*z = \frac{z*3}{2}
|
35,815
|
\frac{1}{4 + 2}*4 = \dfrac23
|
36,257
|
\left\{a, b\right\} = \left\{a, b\right\}
|
5,468
|
1 + 3 \cdot t^1 + 5 \cdot t^2 + \dotsm = \frac{2 \cdot t}{(t + \left(-1\right))^2} \cdot 1 - \frac{1}{t + (-1)} = \frac{t + 1}{\left(t + \left(-1\right)\right) \cdot \left(t + \left(-1\right)\right)}
|
2,064
|
0 < x \Rightarrow 0 \gt -x
|
17,293
|
\cos{z} \leq \cos{z \cdot z},\sin{z} < z \Rightarrow 2\cdot z\cdot \cos{z^2} > 2\cdot \sin{z}\cdot \cos{z} = \sin{2\cdot z}
|
-4,529
|
((-1) + y)\cdot (3\cdot (-1) + y) = y \cdot y - y\cdot 4 + 3
|
-24,398
|
8 + \tfrac33 = 8 + 1 = 9
|
11,718
|
\frac{{3 \choose 3}}{{51 \choose 26}}\times {48 \choose 23}\times \frac{1}{27}\times 4 = \frac{1}{22491}\times 416
|
27,706
|
\frac{1}{g*h/g} = 1/(h*g)*g
|
-22,899
|
\tfrac{7\cdot 8}{8\cdot 10} = \frac{56}{80}
|
40,022
|
1/5/4 = \dfrac{1}{20}
|
7,463
|
\frac{1}{-b \cdot z + f} = \frac{1}{b \cdot (\frac{f}{b} - z)}
|
24,789
|
0 = 1 + b \implies b = -1
|
27,535
|
1/\left(x*c\right) = 1/(x*c)
|
4,263
|
3^3 - 3*3^2 + 3 (-1) + 3 = 3^3 - 3 3 3 + 0 = 0
|
21,047
|
\frac183 = -\dfrac{5}{8} + 1
|
23,956
|
\sin{a} = \sin\left(-a + \pi\right)
|
-24,661
|
\dfrac{2}{4\cdot 2}\cdot 3 = \dfrac{6}{8}
|
5,459
|
c^2 + x \cdot x - 2 \cdot c \cdot x = (x - c)^2
|
15,857
|
\tfrac{1}{2} + 1/3 + \frac{1}{6} = 1
|
29,244
|
4 \times (m + 1) = 4 \times m + 4 \lt 2^m + 4
|
20,397
|
\dfrac{1}{m^2}\cdot (m^2 + (-1)) = 1 - \frac{1}{m^2}
|
1,598
|
\binom{m}{m - i} = \frac{m!}{(m - i)! \cdot (m - m - i)!} = \dfrac{m!}{\left(m - i\right)! \cdot i!} = \binom{m}{i}
|
2,606
|
\frac{1}{36} + \left(1 - 1/36\right) \cdot 216/1111 = \frac{8671}{39996} \approx 0.2168
|
-5,776
|
\dfrac{P}{15\cdot (-1) + P^2 - P\cdot 2}\cdot 5 = \dfrac{P\cdot 5}{(3 + P)\cdot (5\cdot \left(-1\right) + P)}
|
28,495
|
-101\cdot 19 + 64\cdot 30 = 1
|
20,148
|
i \cdot l = (i \cdot i + (-1)) \cdot ... \cdot \left(l + l\right)
|
31,136
|
-(\sqrt{5})^2 + \left(z + 5\cdot (-1)\right)^2 = 5\cdot (-1) + z \cdot z - 10\cdot z + 25
|
24,351
|
\left(1 + \cos(p\cdot 2)\right)/2 = \cos^2(p)
|
9,601
|
(y/g g)^i = y^i/g g
|
-6,009
|
\frac{4}{\left(4 + x\right)\cdot 2} = \frac{4}{2\cdot x + 8}
|
10,951
|
{t + 1 \choose 2} + {s + (-1) \choose 2} - {t \choose 2} - {s \choose 2} = 1 + t - s
|
14,531
|
i\cdot 4 = (i + 1)^2 - (i + \left(-1\right))^2
|
27,332
|
\sqrt{5} = \sqrt{2 \cdot 2 + (-1)^2}
|
-9,175
|
y\cdot 2\cdot 3 - 2\cdot 2\cdot 3\cdot 5 = 60\cdot (-1) + y\cdot 6
|
106
|
e^z = \sum_{l=0}^\infty \dfrac{z^l}{l!} = 1 + z + \sum_{l=2}^\infty \frac{z^l}{l!}
|
6,469
|
-3\cdot a\cdot d_1\cdot d_2 + a^3 + d_1^3 + d_2 \cdot d_2 \cdot d_2 = (-a\cdot d_2 + a \cdot a + d_1^2 + d_2 \cdot d_2 - a\cdot d_1 - d_1\cdot d_2)\cdot (d_2 + a + d_1)
|
-5,780
|
\frac{1}{5 \cdot n + 15} = \tfrac{1}{5 \cdot (3 + n)}
|
35,156
|
2^{99} + 2^{49} = \frac{1}{2} \cdot (-2^{50} + 4^{50}) + 2^{50}
|
18,792
|
\mathbb{E}\left[Z_1\right]\cdot \mathbb{E}\left[Z_2\right] = \mathbb{E}\left[Z_1\cdot Z_2\right]
|
-4,909
|
\frac{7.4}{10} = \frac{1}{10} \cdot 7.4
|
726
|
((n + 1)/n)^{1 + n} = (1 + \frac{1}{n})^{1 + n}
|
36,106
|
2015 = 335\times 6 + 5
|
-1,739
|
5/4 \pi + 7/6 \pi = 29/12 \pi
|
15,204
|
(n + r - r)^{r + n} = n^{r + n}
|
10,979
|
x \cdot 7 + 3 \cdot y + 1 = 2 \cdot (x + y \cdot 6 + \left(-1\right)) \implies 0 = x \cdot 5 - 9 \cdot y + 3
|
7,798
|
8 = 0^2 + 0 \cdot 0 + 2^3
|
13,331
|
\dfrac{1}{1 - -x^2} = \frac{1}{1 + x^2} = 1 - x * x + x^4 - x^6 + \dotsm
|
19,989
|
B/f\cdot f/f = B/f
|
28,993
|
\cos(w - w) = \sin^2\left(w\right) + \cos^2(w)
|
5,976
|
(9 + 1)\cdot \ln(9 + 1) + 9\cdot \left(-1\right) = 10\cdot \ln\left(10\right) + 9\cdot (-1) = 10 + 9\cdot (-1) = 1
|
-20,345
|
2/2\cdot \dfrac{1}{x\cdot 9 + 8}\cdot (4 + 2\cdot x) = \frac{8 + 4\cdot x}{18\cdot x + 16}
|
8,960
|
|(-1)*\left(-1\right) + y| = |1 + y|
|
20,640
|
x^x \cdot x = x^x \cdot x
|
33,700
|
\binom{S + 8\cdot (-1) + 4 + (-1)}{4 + (-1)} = \binom{S + 5\cdot (-1)}{3}
|
29,350
|
(z - a)^2 = (-a + z) (z - a)
|
10,885
|
\frac12 + \frac12 + 1/2 = 3/2 = 1.5
|
9,170
|
(H \cdot D - D \cdot H)^Q = \left(H \cdot D\right)^Q - \left(D \cdot H\right)^Q = D^Q \cdot H^Q - H^Q \cdot D^Q
|
7,990
|
\binom{\frac{1}{2}(m_2 - m_1) + m_1 + \left(-1\right)}{m_1 + (-1)} = \binom{\dfrac12(m_2 + m_1 + 2\left(-1\right))}{m_1 + (-1)}
|
16,278
|
(1 + x)^{k + 1} = (1 + x) (1 + x)^k \geq (1 + x) \left(1 + kx\right)
|
8,487
|
z^3 + 1729 = z^3 + 12^3 + 1^3 = z^3 + 10^3 + 9 * 9 * 9
|
35,741
|
h - x\cdot |x|^{t + 2\cdot \left(-1\right)} = 0 \implies h = |x|^{2\cdot (-1) + t}\cdot x
|
20,541
|
1 + 1/2 + \frac{1}{3} = \dfrac{11}{6}
|
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