id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
41,640
|
-\sqrt{-1} = \sqrt{-1} \cdot \sqrt{-1} \cdot \sqrt{-1}
|
2,941
|
286 = 10^0*6 + 10^2*2 + 8*10^1
|
3,232
|
\dfrac{1}{a\cdot b} = 1/\left(b\cdot a\right) = 1/\left(a\cdot b\right)
|
32,903
|
N \cdot Z \cdot N = Z \cdot N \cdot N = Z \cdot N
|
-15,069
|
\frac{m^5}{\dfrac{1}{m^3} \cdot q^4} = \frac{m^5}{q^4} \cdot \frac{1}{\frac{1}{m^3}} = \frac{1}{q^4} \cdot m^{5 - -3} = \frac{m^8}{q^4}
|
9,385
|
\mathbb{E}[Y]*\mathbb{E}[R] = \mathbb{E}[R*Y]
|
31,500
|
\left(0 = 2 - (12*(-1) + 4^2)^{1 / 2} \Rightarrow -(12*(-1) + 16)^{\frac{1}{2}} + 2 = 0\right) \Rightarrow 0 = 0
|
-27,714
|
\frac{d}{dz} \left(-10 \cdot \cos{z}\right) = 10 \cdot \sin{z}
|
-20,232
|
\frac{1}{x + (-1)}*(-x*10 + 10) = \dfrac{1}{x + \left(-1\right)}*(\left(-1\right) + x)*\left(-10/1\right)
|
14,055
|
\tfrac1s*t = 1 = s/t
|
4,856
|
(-x + 1) \cdot \left(1 + x\right) = -x \cdot x + 1
|
46,173
|
\frac{96}{30} = 3.2
|
1,135
|
x \cdot g \cdot K = g \cdot K \cdot x
|
21,487
|
(-2) \cdot 3 = (-6)^{1/2} \cdot \left(-6\right)^{1/2}
|
25,432
|
z^3 + z * z = 2*z - 2*z^2 + z^2 = 2*z - 2*z^2 + z * z = 2*z - z^2
|
44,550
|
96 = 4 \times 24
|
21,185
|
-\frac{1}{5 z - 8 \mu} \left(3 x + 4 y\right) = -\frac{(3 x - 4 y) (-1)}{(5 z - 8 \mu) (-1)} = \frac{3 x + 4 y}{8 \mu - 5 z}
|
52,438
|
4=0!+1!+2!
|
26,302
|
\frac{dy}{dz} = z^2\cdot y + z \cdot z - y + 1 = (y + 1)\cdot (z^2 + \left(-1\right))
|
6,332
|
n = n + (-1) + 1 = n + 2*(-1) + 2 = ... = \frac12*(n + 1) + \frac{1}{2}*(n + \left(-1\right))
|
30,937
|
-c_{-1} = c_{-1} \implies 0 = c_{-1}
|
-23,103
|
\frac32 \cdot 2 = 3
|
3,894
|
\frac18\cdot 3 = \frac{\left(-1\right) + 4}{4\cdot (4 + 2\cdot (-1))}
|
40,125
|
n^2 = n*n = n + \left(n + (-1)\right)*n
|
29,290
|
\dfrac{1}{4} = 3 \times 1/6/2
|
-2,748
|
(3 + 4) \sqrt{3} = \sqrt{3}*7
|
34,516
|
x^2*2 - 6x = 2\left(x^2 - 3x\right)
|
-57
|
-11 = -6 + 5\cdot \left(-1\right)
|
36,191
|
5^1 = 2^2 + 1 \cdot 1
|
22,857
|
(i + 1) \cdot (i + 1) - 31 \cdot i + 257 = i^2 + 2 \cdot i + 1 - 31 \cdot i + 257 = i \cdot i - 29 \cdot i + 258
|
7,603
|
23^3 + 1 * 1 * 1 + 9^3 + 15^3 = 21^2 * 21 + 3^2 * 3 + 5^3 + 19^3
|
14,984
|
5 + x^2 - x*6 = (x + 5*\left(-1\right))*((-1) + x)
|
-17,368
|
0.633 = \dfrac{1}{100}*63.3
|
14,257
|
\cot\left(\frac{3}{2} \cdot \pi - x\right) = \cot(\pi - x - \dfrac{\pi}{2}) = -\cot(x - \dfrac{\pi}{2}) = \cot(\pi/2 - x) = \tan(x)
|
7,045
|
(-\omega + z)\cdot (z + \omega) = -\omega^2 + z^2
|
-30,288
|
\dfrac12\cdot (0 + 80) = \frac12\cdot 80 = 40
|
3,017
|
\cos^4{y} = (\cos^2{y})^2 = (1 + 2 \times \cos{2 \times y} + \cos^2{2 \times y})/4
|
5,670
|
0 = (-1) + 2c^2 - 2c rightarrow (1 \pm \sqrt{3})/2 = c
|
18,503
|
\dfrac{1}{13} = 76923/999999 = \frac{1}{10^6 + \left(-1\right)}\cdot 76923
|
20,387
|
2 \times k = 2^{k - t} - 2^t = 2^t \times (2^{k - 2 \times t} + \left(-1\right))
|
-10,744
|
\frac{1}{r^3\cdot 8}\cdot (5 + r)\cdot 5/5 = \frac{1}{40\cdot r^3}\cdot (5\cdot r + 25)
|
16,371
|
11^2 + 5^2 + 1^2 = 3*7 * 7
|
36,509
|
55 = 5^2 + 1^2 + 2 \cdot 2 + 3^2 + 4^2
|
15,529
|
m\cdot 4\cdot \left(m\cdot 4 + 1\right)/2 = 8\cdot m^2 + m\cdot 2
|
26,721
|
\frac{1}{27}\cdot 13 = \frac{1}{3} + \frac{2}{3}\cdot 2/9
|
6,603
|
r = r\frac1uu = r/u
|
-7,409
|
\tfrac{2}{12}\cdot 6/13 = \frac{1}{13}
|
20,579
|
1 - \frac{1}{2^5}(\binom{5}{0} + \binom{5}{2}) = 1 - (1 + 5)/32 = 0.8125
|
27,349
|
\left(d + (-1)\right)^1 = \left(-1\right)^1 + d^1
|
14,045
|
\dfrac{1}{|H_{i + 1}|} \times |H_i| = |\frac{H_i}{H_{1 + i}}|
|
-2,350
|
\frac{1}{20} = -\frac{1}{20}4 + \frac{5}{20}
|
-20,366
|
\frac15*1 = \dfrac{6 + t*9}{45*t + 30}
|
33,217
|
h = -h + h\cdot 2
|
1,785
|
F = (1 + E_1)/6 + \frac56 (1 + F)\Longrightarrow 6 + E_1 = F
|
35,130
|
\tfrac{1}{(2 + 2)^2} = 2^{-2 + 2 \cdot (-1)}
|
10,733
|
1/q = \dfrac{1}{1 - 1 - q}
|
25,530
|
(m + 1)^3 = 3\cdot (1^1 + 2^2 + \cdots + m^2) + 3\cdot (1 + 2 + \cdots + m) + m + 1
|
30,115
|
\frac{280}{13} = \tfrac{1}{13}\cdot 2\cdot \frac13\cdot 7\cdot 60
|
25,749
|
(k + m)\cdot q = q\cdot m + q\cdot k
|
-20,570
|
\frac13 \cdot 3 \cdot \frac{8 \cdot k}{2 + k \cdot 9} \cdot 1 = \frac{k \cdot 24}{27 \cdot k + 6} \cdot 1
|
9,537
|
\sin(a)\cdot \cos(b) - \cos\left(a\right)\cdot \sin(b) = \sin\left(-b + a\right)
|
-20,526
|
\dfrac{-10}{1} \times \dfrac{r - 7}{r - 7} = \dfrac{-10r + 70}{r - 7}
|
-4,938
|
9.2/10 = 9.2\cdot 10^{-1}/10 = 9.2/100
|
-26,580
|
(-2*x + 9)*(2*x + 9) = -x * x*4 + 81
|
45,266
|
5 = 4\times 1.25
|
118
|
\frac{\left(-1\right) a}{3} = -\frac13 a/3 = -\frac13a
|
10,510
|
2^2 - 4 \times 1 = 0
|
-20,477
|
(f*4 + 9)/\left(-3\right)*5/5 = (20 f + 45)/(-15)
|
5,225
|
{42 \choose 2} = {40 + 3 + (-1) \choose (-1) + 3}
|
-5,301
|
\frac{1}{10000}\times 2.8 = 2.8/10000
|
13,817
|
33\cdot 1063 = (2^5 + 1)\cdot (2^{10} + 2^5 + 2^3 + \left(-1\right)) = 2^{15} + 2^{11} + 2^8 + 2 \cdot 2^2 + \left(-1\right)
|
-6,517
|
\frac{4}{x^2 + x\cdot 5 + 36\cdot (-1)} = \frac{1}{(9 + x)\cdot (x + 4\cdot (-1))}\cdot 4
|
35,484
|
22050 = 7 \cdot 7 \cdot 2 \cdot 3^2 \cdot 5^2
|
38,730
|
4 = 5 + -2/5*2.5
|
19,231
|
2 - w = 1 - w + (-1)
|
19,245
|
\frac{1}{2! \times 2! \times 3!} \times 10! = 151200
|
45,987
|
((-1) \cdot (-1))^{1/3} = 1
|
35,101
|
(a^2 + 1) \cdot (1 + a) \cdot (1 - a) = 1 - a^4
|
-2,286
|
-\frac{1}{15} + \frac{1}{15} \cdot 2 = \dfrac{1}{15}
|
-6,087
|
\tfrac{4}{28\cdot (-1) + t\cdot 4} = \dfrac{4}{(t + 7\cdot \left(-1\right))\cdot 4}
|
1,620
|
m n = 1 \Rightarrow m = n = 1
|
-26,490
|
\left(-x \cdot 7 + 10\right)^2 = 49 \cdot x \cdot x + 100 - 140 \cdot x
|
-14,220
|
\frac{1}{8 + 2*(-1)}*18 = 18/6 = 18/6 = 3
|
10,164
|
e\cdot b\cdot e = b = e\cdot b\cdot e
|
-11,719
|
(\frac23)^4 = \frac{1}{81} 16
|
32,116
|
(2 + x) \cdot (-x + 1) = 2 - x^2 - x
|
21,241
|
27720 = 12!/(1!*1!*4!*6!)
|
-4,860
|
10^5\cdot 63 = 63\cdot 10^{2 + 3}
|
-7,076
|
\frac{1}{10} 2 / 11 = 1/55
|
4,486
|
\cos(a)\cdot \cos(g) + \sin(a)\cdot \sin\left(g\right) = \cos(a - g)
|
13,978
|
\binom{\left(-1\right) + x + i}{x} = \binom{(-1) + x + i}{i + \left(-1\right)}
|
48,068
|
\frac{(n+1)^{n+1}/((n+1)!)^2}{n^n/(n!)^2}= \left(\frac{n!}{(n+1)!}\right)^{\!2}\left(\frac{n+1}{n}\right)^{\!n}(n+1) =\frac{1}{n+1}\left(1+\frac{1}{n}\right)^{\!n}\to0
|
3,571
|
1 + z^4 = 1 + 2z^2 + z^4 - 2z * z = (1 + z * z) * (1 + z * z) - (\sqrt{2} z) * (\sqrt{2} z)
|
-13,365
|
9 + 4\cdot 8 - 2\cdot 10 = 9 + 32 - 2\cdot 10 = 41 - 2\cdot 10 = 41 + 20\cdot (-1) = 21
|
2,760
|
\sqrt{6} = \sqrt{3\cdot 2} = \sqrt{3} \sqrt{2}
|
-19,301
|
\frac{1}{\frac{9}{5}\cdot 5} = \frac{\frac{5}{9}}{5}\cdot 1
|
32,498
|
881 = 9\cdot (-1) + 900 + 10\cdot (-1)
|
-9,123
|
r \cdot 2 \cdot 2 \cdot 3 \cdot 3 - 2 \cdot 2 \cdot 3 = 36 \cdot r + 12 \cdot (-1)
|
-2,239
|
-\frac{6}{16} + \frac{9}{16} = \dfrac{3}{16}
|
25,772
|
\sin^2(y) - \cos\left(y\right) \cdot (1 - \cos(y)) = \sin^2(y) + \cos^2(y) - \cos(y) = 1 - \cos(y)
|
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