id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
20,178
|
\frac{\frac{1}{6}}{2}\cdot π = \frac{π}{12}
|
3,197
|
\frac{24 \cdot 30}{3 \cdot 5 \cdot 2} \cdot 28 = 672
|
1,836
|
G_j\cdot G_k = G_j\cdot G_k
|
7,690
|
n \cdot 14 + 3 = 1 + \left(1 + n \cdot 7\right) \cdot 2 \Rightarrow 1 = \left( 21 \cdot n + 4, 3 + 14 \cdot n\right)
|
12,142
|
k^b k^c = k^{b + c}
|
-8,065
|
\tfrac{5 + i \cdot 45}{5 - 5 \cdot i} \cdot \frac{5 + 5 \cdot i}{5 + 5 \cdot i} = \frac{5 + i \cdot 45}{5 - 5 \cdot i}
|
5,796
|
\left|{B}\right| = \left|{H}\right|\cdot \left|{B}\right| = \left|{H\cdot B}\right|
|
27,146
|
\operatorname{im}{(z)} = \sin{π*m/x} \implies e^{i*m*π/x} = z
|
41,177
|
\lambda\cdot \frac{(-1)^{n + (-1)}}{2^{n + (-1)}} = y_n - \alpha_n - \alpha_{n + \left(-1\right)}\cdot 2 rightarrow -2\cdot \alpha_{n + \left(-1\right)} + y_n + \lambda\cdot \dfrac{(-1)^n}{2^{(-1) + n}} = \alpha_n
|
24,678
|
1 = -(\cosh{x} + \sinh{x}) (\sinh{x} - \cosh{x}) \Rightarrow 1 = 5 \left(\cosh{x} + \sinh{x}\right)
|
169
|
U \cdot \Sigma \cdot C = \Sigma \cdot U \cdot C
|
24,891
|
(2 + (2 + (2 + \cdots)^{1/2})^{1/2})^{1/2} = y = \left(2 + y\right)^{1/2}
|
-29,344
|
(h + a)*(-h + a) = -h^2 + a * a
|
18,438
|
(x + 1) \cdot (5 \cdot (-1) + x) = 5 \cdot (-1) + x \cdot x - 4 \cdot x
|
14,230
|
(m + 1)^2 - m * m = 1 + 2*m
|
4,459
|
(2 + n) \times (2 + n) = 4 + n^2 + 4\times n
|
-20,343
|
\frac{3\times p}{30\times (-1) + 12\times p} = 3/3\times \frac{p}{10\times \left(-1\right) + 4\times p}
|
-18,374
|
\frac{(3 + c)\cdot c}{(2\cdot (-1) + c)\cdot (c + 3)} = \frac{c\cdot 3 + c^2}{c^2 + c + 6\cdot (-1)}
|
33,248
|
(-1)^{6/2} = (-1) * (-1) * (-1)
|
-20,767
|
\frac{12}{3x + 15} = \frac{4}{5 + x} \cdot 3/3
|
3,019
|
\frac{m}{(m + 1)^2}\cdot (m + 2) = \dfrac{2\cdot m + m^2}{(m + 1)^2}
|
29,781
|
1 + y^2 + 2*y = (y + 1)*(y + 1)
|
-19,192
|
7/24 = A_r/(64\cdot \pi)\cdot 64\cdot \pi = A_r
|
929
|
x b + x^2 \Rightarrow (x + b/2)^2 - (b/2)^2
|
28,674
|
\left(b b a = a^3 \Rightarrow (b a b)^n = b a^n b = a^{3 n}\right) \Rightarrow a^{3 n} b = b a^n
|
1,044
|
\sin\left(x + 180\right) = \sin{x} \cdot \cos{180} + \sin{180} \cdot \cos{x} = -\sin{x}
|
-5,859
|
\frac{4}{\left(t + 7 \cdot (-1)\right) \cdot (t + 2)} = \frac{4}{t^2 - 5 \cdot t + 14 \cdot (-1)}
|
32,174
|
41 + 40 + 39 + \ldots + 1 = \frac{41}{2}\cdot 42 = 861
|
7,715
|
q^{F + (-1)}*F = \frac{\partial}{\partial q} q^F
|
33,949
|
-x^2 + 1 = (1 + x)\cdot \left(-x + 1\right)
|
-570
|
\frac{25}{4}\cdot \pi - 6\cdot \pi = \frac{\pi}{4}
|
32,485
|
5\cdot s\cdot 7\cdot s\cdot 3\cdot s + -3\cdot s\cdot 3\cdot s\cdot \left(-3\cdot s\right) = 105\cdot s^3 + 27\cdot s^3 = 66\cdot s
|
35,265
|
\sin{2 \cdot T} = 2 \cdot \sin{T} \cdot \cos{T}
|
12,278
|
\tan{z} = \frac{z - \frac{1}{3!}\cdot z^3 + z^5/5!\cdot \ldots}{1 - z^2/2! + \frac{z^4}{4!}\cdot \ldots}
|
37,397
|
-23 \cdot ((-13) \cdot 19) + 100 \cdot (\left(-3\right) \cdot 19) = -19
|
-3,995
|
\frac{7}{6} m = \frac{7m}{6}
|
-16,328
|
i = 3\zeta = \zeta + 4
|
33,267
|
15 \cdot 4/120 = \dfrac{1}{2}
|
21,756
|
\tfrac{1}{1 + \epsilon^2} = \frac{d}{d\epsilon} \operatorname{atan}(\epsilon)
|
11,475
|
\frac{10!}{(10 + 3 \cdot (-1))!} = 720
|
30,225
|
3/6\cdot 4/7 = 2/7
|
24,528
|
3 = \frac12(7 + (-1))
|
-20,399
|
z*15/(3*z) = 5/1*\frac{z*3}{3*z}
|
23,601
|
\frac{1}{(1 - x) \cdot 2} = -\dfrac{1}{2 \cdot (x + \left(-1\right))}
|
-19,026
|
3/4 = \dfrac{A_x}{16\times \pi}\times 16\times \pi = A_x
|
7,593
|
y_1 = y_1 + 9*\left(-1\right)
|
45,386
|
\frac51 = 5
|
30,056
|
x = e^{\frac{\pi\cdot x}{2}\cdot 1} = \cos{\pi/2} + x\cdot \sin{\tfrac{\pi}{2}} = 0 + x = x
|
38,423
|
(z + 1)\cdot \left(z + 3\right) = (z + 1)\cdot z + (z + 3)\cdot 3 = z^2 + z + 3\cdot z + 9 = z^2 + 4\cdot z + 9
|
6,522
|
((-1) + y)\cdot \left(y^2 + y + 1\right) = y^3 + (-1)
|
31,552
|
z^2 \cdot z + 1 = z^3 + (-1) = (z + \left(-1\right)) \cdot \left(z^2 + z + 1\right) = (z + 1) \cdot (z^2 + z + 1)
|
23,873
|
4^n + (-1) = (2^n + (-1)) (2^n + 1)
|
16,603
|
128/225 = \frac{8}{45} + 8/25 + \dfrac{1}{225}\cdot 16
|
1,512
|
15 = \frac12\cdot 8\cdot 4 - \dfrac{1}{2}\cdot 2
|
22,210
|
11/36 = 1 - (\frac{5}{6}) \cdot (\frac{5}{6})
|
420
|
\cos(\dfrac{1}{5}\cdot π) = -\cos\left(\dfrac{π}{5}\cdot 4\right)
|
-1,507
|
\frac{\frac13 \cdot 4}{1/5 \cdot 9} = \frac43 \cdot \frac19 \cdot 5
|
4,770
|
x^2 = xd_1 + d_2 \implies x^2 - d_1 x - d_2 = 0
|
9,547
|
-(l + l_1) + l_2 = l_2 - l - l_1
|
18,388
|
\frac{1}{(2 + (-1))^2} \cdot 8 - \frac{8}{(2 + 1) \cdot (2 + 1)} = 8 - 8/9 = \frac{64}{9}
|
37,869
|
3 = 4 \cdot \left(-1\right) + 6 + 1
|
33,960
|
\dfrac{2\cdot \pi}{12}\cdot 1 = \dfrac{1}{6}\cdot \pi
|
3,746
|
\tfrac{1}{2\cdot y^{\frac{1}{2}}} = \frac{\text{d}}{\text{d}y} \sqrt{y}
|
36,859
|
36 + (6 + n)\cdot (6\cdot (-1) + n) = n^2
|
4,741
|
24 = 2*(3 + 1 + 4*2)
|
2,794
|
(a\cdot d)^{1 - k} = a\cdot d\cdot (a\cdot d)^{-k} = a\cdot d\cdot d^{-k}\cdot a^{-k} = a\cdot d^{1 - k}\cdot a^{-k}
|
9,800
|
k\cdot 47^2 + 47\cdot (-1) = 47\cdot ((-1) + 47\cdot k)
|
-11,582
|
-4 - 2\cdot i = -1 + 3\cdot (-1) - 2\cdot i
|
33,332
|
\int\limits_{e_2}^b e_1\,dy = \lim_{y \to b} \int\limits_{e_2}^y e_1\,dy
|
881
|
1 + \left(y + 1\right)^2 \cdot 3 + \left(1 + y\right)^3 = y^3 + y^2 \cdot 6 + 9 \cdot y + 5
|
9,587
|
\frac{1}{5!} \cdot 8! = \frac{5!}{5!} \cdot 8 \cdot 7 \cdot 6 = 8 \cdot 7 \cdot 6
|
19,122
|
\sqrt{\left( x^2, z^3\right)} = \sqrt{x^2 z \cdot z \cdot z} = \sqrt{x^2} \sqrt{z^3} = xz = [x, z]
|
18,014
|
5k^2 + k*2 + 1 = (k + 1)^2 + (k*2) * (k*2)
|
23,370
|
91^{1/2} \cdot 2 = (10^2 - 3 \cdot 3)^{1/2} \cdot 2
|
-1,210
|
((-3)*1/5)/\left(1/9\right) = -\dfrac35*9/1
|
4,385
|
(2\cdot z + y)^2 = 4\cdot z\cdot y + y^2 + 4\cdot z^2
|
-20,474
|
\frac{s + 6}{48 + 8s} = \dfrac{1}{6 + s} \left(s + 6\right)/8
|
-21,032
|
(72*(-1) - z*45)/72 = \dfrac19*9*(-5*z + 8*(-1))/8
|
16,949
|
\left((-1) + 3^k\right)/2 = 1 + 3 + 3^2 + \ldots + 3^{k + \left(-1\right)}
|
-2,986
|
\sqrt{25*10} - \sqrt{10} = \sqrt{250} - \sqrt{10}
|
17,147
|
x^2 - 5 \cdot x + 6 = (2 \cdot (-1) + x) \cdot (3 \cdot (-1) + x)
|
10,381
|
-1 = \left\{( 1, 2), \left( 0, 1\right), ( 2, 3), \dots\right\}
|
-10,358
|
4 = -2 + 4 \times n + 6 \times (-1) = 4 \times n + 8 \times (-1)
|
15,426
|
1/(2) = 1/2
|
-1,822
|
4/3 \cdot \pi = \pi/4 + 13/12 \cdot \pi
|
2,659
|
\left(1 + 164 + 5\cdot (-1)\right)/5 + 1 = 33
|
1,747
|
3*(-1) + n^2 + 2*n = \left(n + 3\right)*\left((-1) + n\right)
|
12,623
|
-2 = \left(-1\right) (-1) (-1)*2
|
26,019
|
y\cdot (1 + l)/l = \tfrac{y^{1 + l}}{l\cdot y^l}\cdot (1 + l)
|
19,869
|
\sqrt{1 - m_t \cdot m_t} = m_t
|
21,332
|
6! = \dfrac{1}{7!}\cdot 10!
|
19,888
|
\dfrac{4}{32} = \frac18
|
8,687
|
\frac{1}{12}\cdot 14 = 7/6
|
11,604
|
13 + \frac{2}{7} = 93/7
|
1,644
|
\frac{4}{5 + 4}\cdot \frac{1}{1 + 7 + 6}\cdot (6 + 1) = 28/126
|
16,444
|
1/3 + \frac{1}{5} + 1/6 = \frac{7}{10} \lt 3/4
|
-30,279
|
z + 5 + \frac{2}{2 + z} = \frac{z^2 + z\cdot 7 + 12}{2 + z}
|
3,704
|
\frac{1}{1.5} = \frac{1}{3} \cdot 2
|
-6,335
|
\frac{3 \times p}{p^2 + p + 6 \times (-1)} = \frac{3 \times p}{\left(3 + p\right) \times (2 \times (-1) + p)}
|
-1,321
|
\frac{1/2 \cdot 5}{9 \cdot \frac15} = \tfrac59 \cdot 5/2
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.