id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-28,756
|
3 - \frac{5}{3 + x} = \dfrac{4 + 3 x}{x + 3}
|
32,419
|
\frac{1}{57}\cdot 350 = \frac{8}{57} + 6
|
-21,799
|
\frac79 = \frac{7}{9}
|
4,088
|
g\cdot e\cdot c = g\cdot (e + c + 2\cdot e\cdot c) = g + e + c + 2\cdot e\cdot c + 2\cdot g\cdot e + 2\cdot g\cdot c + 4\cdot g\cdot e\cdot c
|
-233
|
\frac{7!}{5!*(5*(-1) + 7)!} = \binom{7}{5}
|
18,812
|
W_0/6 = W_0 \cdot \dfrac{6}{36}
|
1,887
|
x = 5*3x + -2x*7
|
-2,186
|
25/12\cdot \pi = \pi\cdot 5/4 + \pi\cdot \frac16\cdot 5
|
22,655
|
\operatorname{E}[X_l^2] \cdot \operatorname{E}[X_j^2] = \operatorname{E}[X_j^2 \cdot X_l^2]
|
14,384
|
\dfrac{1}{(x \cdot x)^{\frac{1}{3}}} = \frac{1}{x^{2/3}} = x^{-\frac13 \cdot 2}
|
1,275
|
\sin(2 \cdot \pi + z) = \sin(z)
|
-20,538
|
\frac{1}{15 \cdot q + 10 \cdot \left(-1\right)} \cdot (9 \cdot q + 6 \cdot (-1)) = \frac{2 \cdot (-1) + q \cdot 3}{2 \cdot (-1) + 3 \cdot q} \cdot 3/5
|
-2,027
|
7/3\cdot \pi = \pi\cdot 19/12 + \pi\cdot 3/4
|
13,980
|
X^4 + 1 = (X \cdot X + (-1))^2 - \left(g \cdot X\right)^2 = \left(X^2 - g \cdot X + (-1)\right) \cdot (X \cdot X + g \cdot X + (-1))
|
11,227
|
(x + 3\cdot (-1))\cdot (x + 3) = 9\cdot (-1) + x \cdot x
|
13,278
|
0 = 2 + 4 \times (-1) + y''\Longrightarrow y'' = 2
|
17,750
|
-6 \cdot x + x^2 = (x + 3 \cdot (-1)) \cdot (x + 3 \cdot (-1)) + 9 \cdot (-1)
|
52,022
|
10000 = 100 * 100
|
32,154
|
x\cdot C = C\cdot x
|
20,048
|
x^2\cdot 4\cdot (-2) = -x^2\cdot 8
|
-20,861
|
\dfrac{-9t}{t + 6} \times \dfrac{5}{5} = \dfrac{-45t}{5t + 30}
|
701
|
\sin(-\omega\times t) = -\sin(t\times \omega)
|
-10,328
|
-47/40 = -\frac{1}{40}\cdot 47
|
-532
|
\frac{4}{3} \pi = \pi\cdot 22/3 - 6\pi
|
-6,485
|
\frac{1}{42 + 6t^2 - t*48}(-t*12 + 4t + 28 (-1) - 12 t + 12) = \frac{-t*20 + 16 (-1)}{42 + t^2*6 - 48 t}
|
21,517
|
5^3*4200*5^4*1^3 = 328125000
|
-6,924
|
576 = 12\cdot 6\cdot 8
|
14,545
|
(-1) + 8^x = (-1) + 2^{x \cdot 3}
|
24,573
|
z * z + z^2 = 2*z^2
|
-10,677
|
\frac{1}{s \cdot 75}6 = \frac{1}{s \cdot 25}2 \cdot \frac33
|
11,102
|
15 = 28 + 13\cdot (-1)
|
13,726
|
d \cdot c/b = \frac{d}{b \cdot 1/c}
|
19,028
|
60 = 3 \cdot 5 \cdot 8/2
|
49,836
|
23 \cdot 89 = 2047
|
30,804
|
x \cdot 5 = 1 \Rightarrow 1/5 = x
|
6,846
|
1/2 \cdot \frac12 + 1/2 \cdot \frac12 = \frac{1}{2}
|
9,452
|
(h_2 + h_1)^2 = h_2^2 + 2\times h_2\times h_1 + h_1^2 = i + 2\times h_2\times h_1 - i = 2\times h_2\times h_1
|
22,190
|
-\frac{1}{m + 2} + \frac{1}{m + 2 \cdot (-1)} = \frac{1}{m \cdot m + 4 \cdot (-1)} \cdot 4
|
11,434
|
\frac{\partial}{\partial x} \left(D_2 + D_1\right) = \frac{\partial}{\partial x} D_2 + \frac{\partial}{\partial x} D_1
|
40,073
|
\dfrac{1}{3}\cdot 2 = \dfrac13\cdot 2
|
10,592
|
(-((-1) + 1000)*71 + ((-1) + 100)*717)/(999*99) = 717/999 - 71/99
|
-26,422
|
\dfrac{1}{y^m} \cdot y^k = y^{k - m}
|
-1,375
|
-8/1\cdot 7/5 = 7\cdot \frac15/((-1)\cdot \frac{1}{8})
|
-30,242
|
z^2 - 8 \cdot z + 16 = (z + 4 \cdot (-1)) \cdot (z + 4 \cdot (-1))
|
14,457
|
\left(\left(-1\right)*π\right)/2 = -\frac{π}{2}
|
-5,342
|
\tfrac{11.0}{10000} = \frac{11.0}{10000}
|
10,950
|
(\left(-1\right) + r)\cdot r/2 = \binom{r}{2}
|
53,417
|
k^2/2 - 2 k/4 (k/2 + 1) = k/2 (k/2 + (-1)) = k k/4 - \frac12 k
|
28,803
|
-s\cdot 41 + e\cdot 24 = -s + 4\cdot (6\cdot e - s\cdot 10)
|
-1,253
|
54/56 = 54*\tfrac12/(56*1/2) = \frac{27}{28}
|
15,442
|
(B + A) \cdot C = C \cdot B + C \cdot A
|
23,336
|
12\times (-1) + 40 = 28
|
8,367
|
\left(1 + i\right)^{11} = \left(\left(1 + i\right)^2\right)^5 \cdot \left(i + 1\right)
|
-3,414
|
11^{1/2}\cdot (5 + 3 + 2) = 10\cdot 11^{1/2}
|
-630
|
\left(e^{11 \cdot \pi \cdot i/12}\right)^{12} = e^{12 \cdot 11 \cdot i \cdot \pi/12}
|
17,911
|
3\cdot \sin{y}\cdot \cos^2{y} - \sin^3{y} = \sin{3\cdot y}
|
7,721
|
q^{-1}[cl(B)] = cl(q^{-1}[B])
|
43,009
|
\tau*\rho = \rho*\tau
|
17,861
|
\frac{1}{2 + 0*(-1)} = 1/2
|
-2,443
|
\sqrt{13} + \sqrt{13} \cdot 5 = \sqrt{25} \cdot \sqrt{13} + \sqrt{13}
|
1,869
|
(z + x) \cdot (z - x) = z^2 - x \cdot x
|
-7,081
|
\dfrac{3}{7}\times 0 = 0
|
18,897
|
gq = q = qg
|
13,166
|
\frac{\mathrm{d}z}{\mathrm{d}y} = (3*z - y^2)/y = 3*\frac{z}{y} - y
|
7,180
|
\sin(G) + \sin\left(Z\right) = 0\Longrightarrow \sin(G) = -\sin(Z)
|
2,799
|
\dfrac{20}{132} = \frac{5}{12}\cdot \dfrac{4}{11}
|
10,138
|
10 = 4\cdot 5/(2)
|
29,234
|
x + 2 + \tfrac{1}{x + 2 \times (-1)} \times 4 = \dfrac{1}{x + 2 \times (-1)} \times x^2
|
28,963
|
\mathbb{E}[X^4] = 0 \Rightarrow \mathbb{E}[X \cdot X] = 0
|
2,969
|
(j + 1)! = 1 \times 2 \times \cdots \times j \times (j + 1) = j! \times \left(j + 1\right)
|
6,319
|
h^2 + (-1) = (h + \left(-1\right)) \cdot (1 + h)
|
-9,356
|
p \cdot 10 + 50 \cdot (-1) = p \cdot 2 \cdot 5 - 2 \cdot 5 \cdot 5
|
-189
|
\dfrac{10!}{5! \left(10 + 5\left(-1\right)\right)!} = \binom{10}{5}
|
-29,339
|
\left(2*z + 5\right)*(2*z + 5*(-1)) = (2*z)^2 - 5 * 5 = 4*z^2 + 25*(-1)
|
13,333
|
0 = \left(-52\right)^2 + 52 (-52)
|
-20,499
|
3/3 \cdot \frac{6}{9 \cdot (-1) + y} = \frac{18}{3 \cdot y + 27 \cdot \left(-1\right)}
|
8,898
|
|(-3/2 + z)^2 - \dfrac{1}{4}| = |z \cdot z - 3 \cdot z + 2|
|
-6,739
|
\frac{1}{10} \cdot 3 + 7/100 = \frac{7}{100} + 30/100
|
-10,272
|
-\frac{50}{40\cdot s} = 10/10\cdot (-\dfrac{5}{s\cdot 4})
|
-24,387
|
\frac{78}{8 + 5} = 78/13 = \frac{1}{13}78 = 6
|
-3,561
|
6/12\cdot \frac{q}{q^2} = \frac{6\cdot q}{12\cdot q^2}
|
11,335
|
\cos\left(2\alpha\right) = \cos^2(\alpha) - \sin^2(\alpha)
|
-8,014
|
\frac{6i + 8}{-2 + i} = \frac{8 + 6i}{-2 + i} \frac{-i - 2}{-2 - i}
|
26,583
|
-(k + 1) + n = n - k + (-1)
|
-30,557
|
\frac{12.5}{25} = \frac{1}{50}*25 = 50/100 = \frac{1}{2}
|
-7,988
|
\frac{1}{2 + i}\cdot \left(6 + 13\cdot i\right)\cdot \frac{1}{-i + 2}\cdot (-i + 2) = \frac{6 + 13\cdot i}{i + 2}
|
-1,242
|
\frac23 \cdot (-\frac54) = \dfrac{1/4 \cdot (-5)}{\dfrac12 \cdot 3}
|
24,868
|
(x \cdot 2)^{1 / 2} = \int \tfrac{1}{\left(2 \cdot x\right)^{\frac{1}{2}}}\,dx
|
26,907
|
\frac11*6 + 6/6 + 6/5 + \dfrac64 + \frac13*6 + \frac12*6 = 14.7
|
-14,037
|
8 + \dfrac{48}{6} = 8 + 8 = 8 + 8 = 16
|
22,234
|
1/(s\cdot t) = \frac{1}{s\cdot t}
|
5,932
|
\operatorname{asin}\left(z\right) = y_1 rightarrow z = \sin{y_1}
|
-17,505
|
3 = 75*\left(-1\right) + 78
|
-9,341
|
x \cdot 11 - 7 \cdot 11 = x \cdot 11 + 77 \cdot (-1)
|
-6,751
|
\frac{5}{100} + \frac{1}{10}5 = 5/100 + 50/100
|
20,825
|
(1 + d \cdot 3)/3 = 1/3 + d
|
6,221
|
\cos{y} = \frac{\sin{2 y}}{2 \sin{y}}
|
9,859
|
-Q + W < Q \Rightarrow W \lt 2\cdot Q
|
34,200
|
-1 = (-1)^{\frac{1}{2} 2} = ((-1) (-1))^{1/2} = 1^{1/2} = 1
|
24,583
|
(-1/2 + 1)\cdot \left(1 + 1/2\right) = 1 - \dfrac{1}{4}
|
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