id
int64
-30,985
55.9k
text
stringlengths
5
437k
-9,266
-y*2*3*7 = -42*y
-4,764
\frac{7\cdot (-1) + 6\cdot x}{x^2 - 3\cdot x + 2} = \dfrac{1}{x + 2\cdot (-1)}\cdot 5 + \frac{1}{x + (-1)}
19,778
\dfrac{1}{\phi^2} = \frac{\phi^2 - \phi}{\phi \cdot \phi} = 1 - (\phi^2 - \phi)/\phi = 2 - \phi
47,973
1/100 = 92/93\cdot 94/95\cdot 97/98\cdot 99/100\cdot 98/99\cdot \frac{96}{97}\cdot 95/96\cdot 93/94\cdot \frac{1}{92}\cdot 91/91
29,820
3 = z z z \Rightarrow 3 (-1) + z^3 = 0
-3,797
9/4 \cdot y^2 = y^2 \cdot 9/4
3,467
5/7\cdot 7 = 5
26,383
35 = 50 + 3\cdot \left(-1\right) + 12\cdot (-1)
-2,660
\sqrt{11}*\sqrt{16} + \sqrt{11} = \sqrt{11} + 4*\sqrt{11}
5,977
z^2 - q^2 = 1 rightarrow \sqrt{q^2 + 1} = z
11,487
\sqrt{2} \cdot 11 + 9\sqrt{3} = (\sqrt{3} + \sqrt{2})^3
27,820
c*x + x = (-1) - c*3 \Rightarrow c = -\frac{x + 1}{x + 3}
5,287
(x^4 + x^2*8 + 3x^2)/12 = 11/12 x * x + \dfrac{x^4}{12}
14,680
C\cdot A + A\cdot D + B\cdot C + D\cdot B = (A + B)\cdot (D + C)
13,658
111111111 \cdot \left(-1\right) + 123456789 = 999999999 + 987654321 \cdot (-1)
456
2D'^2 + D \cdot D + D' D\cdot 3 = (D + D'\cdot 2) \left(D' + D\right)
35,175
{i \choose x} = {i + (-1) \choose x + (-1)} + {i + (-1) \choose x} = {i + (-1) \choose x + (-1)} + {i + 2 \left(-1\right) \choose x + \left(-1\right)} + {i + 2 \left(-1\right) \choose x}
-6,564
\frac{j}{j^2 - j \cdot 10 + 21} = \dfrac{1}{(j + 3 \cdot (-1)) \cdot (7 \cdot (-1) + j)} \cdot j
17,527
\sin(2\times \pi/3 + \pi/3) = \sin\left(\pi\right) = 0
29,276
(\sqrt{2} + 3)^3 = 45 + 29 \cdot \sqrt{2}
20,332
|g_m|^{\frac1m} \leq 1/t = 1/t\Longrightarrow t^{-m} \geq |g_m|
39,305
1 - (\frac12)^i = 1 - \dfrac{1}{2^i} = \tfrac{1}{2^i}(2^i + (-1)) = \frac{1}{2^{m - x}}(2^{m - x} + (-1)) \Rightarrow \tfrac{-(1/2)^i + 1}{2^{\left(-1\right) + x}} = \frac{1}{2^{m + (-1)}}\left(2^{m - x} + (-1)\right)
16,961
h^N h^z = h^{N + z}
-2,308
-2/17 + \frac{3}{17} = \frac{1}{17}
-2,171
\pi*35/12 = \dfrac12*3*\pi + \frac{1}{12}*17*\pi
32,878
(1 + z) \cdot (z + (-1)) = (-1) + z^2
49,755
\sin(2^n) = \sin(2\pi \dfrac{2^n}{2\pi}) = \sin(2\pi \frac{1}{\pi}2^{n + (-1)})
27,966
\dfrac{\sqrt{3}\cdot 16}{9} 1 = \dfrac{16}{3 \sqrt{3}}
1,421
1/((-1)\cdot b) = \frac{1}{(-1)\cdot b} + \frac0b = \frac{1}{(-1)\cdot b} + \frac1b\cdot (1 - 1) = \dfrac{1}{(-1)\cdot b} + 1/b - \frac{1}{b}
17,919
1/2 - 1/8 = 3/8
-2,664
\sqrt{3}\cdot \left(3 + 4 + 5\right) = \sqrt{3}\cdot 12
-4,324
\dfrac{c^4}{10 \cdot c^2} = \tfrac{1}{10} \cdot \frac{1}{c^2} \cdot c^4
-19,576
\dfrac45\cdot \frac15\cdot 2 = 1/5\cdot 2/\left(5\cdot 1/4\right)
-3,099
3 \cdot \sqrt{13} = \sqrt{13} \cdot \left(4 + (-1)\right)
12,252
2^{f_2} \cdot 2^{f_1} = 2^{f_1 + f_2}
6,747
\tfrac{1}{(n - x)!}\cdot n! = n\cdot (n + (-1))\cdot \dots\cdot (n - x + 1)
29,804
(-\frac{1}{1 + y} + \frac{1}{\left(-1\right) + y}) \frac{y^2}{2} = \dfrac{y^2}{(-1) + y^2}
-5,000
10^9*17.4 = 10^{6 + 3}*17.4
3,810
V^3 = -V + (-1) = 4 \times V + 4
18,357
(12 \cdot 2^{1/2} + 19) \cdot (19 - 12 \cdot 2^{1/2}) = 73
4,314
\tfrac{1}{(2 \times x + (-1)) \times (2 \times x + (-1))} = \frac{1}{(2 \times (x - 1/2))^2} = \frac{1/4}{(x - 1/2)^2}
2,698
\left(\frac2x + 1 - x\right)^5 = \frac{1}{x^5}(-x^2 + 2 + x)^5
25,357
(x + Q^{1/2}*y - C^{1/2}*z)*(z*C^{1/2} + x + Q^{1/2}*y) = x^2 + Q*y^2 + 2*Q^{1/2}*y*x - z * z*C
-15,799
-6/10*5 + 4/10*6 = -6/10
31,194
\sin{2z} = 2\sin{z} \cos{z} + 0(-1) = 2\sin{z} \cos{z}
-17,808
41 = 56 + 15 (-1)
-4,047
\frac{28}{7} \cdot \frac{y^5}{y^2} = \frac{y^5 \cdot 28}{7 \cdot y^2}
9,086
\int_1^2 \tfrac{1}{2 \cdot w}\,dw = (\int_1^2 {1/w}\,dw)/2
31,414
72 = \binom{4}{2}\cdot 2\cdot 3!
4,162
x \cdot b = \frac{1}{2} \cdot (x^2 + b^2 - (-b + x)^2)
48,651
16*(-1) + 17 = 1
16,181
\operatorname{E}(Z) - \operatorname{E}(V) = \operatorname{E}(Z - V)
11,831
d \cdot E = d \cdot E
24,425
2 \cdot ((-1) + x) \cdot \left(1 + x\right) = 2 \cdot \left(-1\right) + 2 \cdot x^2
8,740
h_2 d_2 + d_1 h_1 = h_1 d_1 + d_2 h_2
34,595
B \cdot C^m = B \cdot C^m
11,287
\sin(\frac{5\pi}{2})=\sin(\frac{\pi}{2})=1
27,459
Ax=\lambda x \implies A^{-1}Ax=A^{-1}\lambda x
18,420
2 \cdot (-1) + y \cdot y + y = (y + 2) \cdot ((-1) + y)
23,592
\frac{5}{77} = 5/21\cdot \dfrac{1}{22}\cdot 6
21,984
-\frac12 \cdot \pi = (\left(-1\right) \cdot \pi)/2
-22,404
-4 = 6 (-1) + 2
31,502
\frac{1}{y} \cdot (y \cdot y + y) = y + 1
27,098
\cos{\frac{\pi}{2}} = \cos{3*\pi/2} = 0
32,190
\left(1 + y + \dots + y^4\right)^{1 + n} = (1 + y + \dots + y^4)^n\cdot (1 + y + \dots + y^4)
7,979
x + 2 (-1) > 0 \implies 2 < x
33,752
25 = f^2\Longrightarrow \sqrt{f \cdot f} = \sqrt{25}
-1,776
-5/3\cdot \pi = \pi/4 - \dfrac{1}{12}\cdot 23\cdot \pi
-2,010
-\frac{2}{3}*\pi = \dfrac{1}{12}*\pi - \frac{3}{4}*\pi
46,783
1111 = 11 \cdot 101
16,312
\dfrac{n^2}{2^{-\sqrt{n}}} = n^2*2^{\sqrt{n}}
20,011
\frac{2}{((-1) + z) (1 + z)} = \frac{1}{((-1) + z) (1 + z)} (-(\left(-1\right) + z) + z + 1)
1,186
(2*\tfrac13)^2 + (2*\frac{2}{3})^2 = \dfrac{20}{9} \gt 2
19,751
\frac{\pi}{2^{\frac{1}{2}}} = 2^{1 / 2} \cdot \pi/2
4,867
s^4 - 20*s^2 + 19 = (s * s + 19*\left(-1\right))*((-1) + s * s)
29,410
3 + \frac12 = \frac{7}{2}
-19
-5 - 3 = -8
30,324
(h + b)\cdot (1 + h\cdot \chi) = h^2\cdot \chi + h\cdot (1 + b\cdot \chi) + b
-3,138
\sqrt{25 \cdot 2} + \sqrt{16 \cdot 2} + \sqrt{9 \cdot 2} = \sqrt{32} + \sqrt{18} + \sqrt{50}
16,428
(z^2 - z \cdot 4 + 3) \cdot (4 + z) + 13 \cdot (z + (-1)) = (-1) + z^3
28,917
0 = -\frac35 + 3/5
17,433
x^i a_i = x^i + (a_i + (-1)) x^i
28,224
y \cdot 2 + 5 \cdot y = 7 \cdot y
17,747
\dfrac{1}{xx^V} = \frac{1}{xx^V}
24,103
{n \choose r} = \dfrac{1}{r!\cdot (n - r)!}\cdot n!
9,497
c*a + a*f = (c + f)*a
10,525
\pi\cdot 2 - \frac{\pi}{6} = \frac{\pi}{6}\cdot 11
1,268
\left(\mu^2 + n^2\right)^2 - (\mu^2 - n^2) \cdot (\mu^2 - n^2) = (2\mu n) \cdot (2\mu n) = 2 \cdot 2\mu^2 n \cdot n
15,742
\dfrac{1}{m^{d_2 - d_1}} = \frac{m^{d_1}}{m^{d_2}}
38,655
\sqrt{h} \cdot \sqrt{b} = \sqrt{h \cdot b} = \sqrt{h \cdot b}
38,423
(z + 1)*(z + 3) = (z + 1)*z + (z + 3)*3 = z^2 + z + 3*z + 9 = z^2 + 4*z + 9
52,561
680\times 211=143480=199\times 721+1
4,951
(n \cdot 2 + 1)^2 + ((-1) + 2 \cdot n)^2 = 2 + 8 \cdot n^2
-446
e^{\pi\cdot i\cdot 4/3\cdot 16} = \left(e^{4\cdot \pi\cdot i/3}\right)^{16}
46,439
2\cdot 126 = 252
23,282
C/(E_2) + A/(E_1) = (CE_1 + E_2 A)/(E_2 E_1)
-3,414
(3 + 2 + 5) \times 11^{1 / 2} = 11^{\frac{1}{2}} \times 10
-10,389
\frac{100}{60\cdot t + 240\cdot (-1)} = \frac{5}{t\cdot 3 + 12\cdot (-1)}\cdot 20/20
-30,322
1 = 3\cdot (-1) + 4
-17,594
84 + 66 \cdot (-1) = 18