id
int64
-30,985
55.9k
text
stringlengths
5
437k
8,533
\left(n + 1\right)\cdot (n + 2) = n^2 + 3\cdot n + 2 > 2\cdot n
27,536
-\left(-1\right) \cdot w = w
24,767
Z\cdot Z^2 = Z^3
16,251
x^9 + \psi^9 = (x^6 - \psi^3 x^3 + \psi^6) (\psi^3 + x^3)
-937
3/2 = \frac{1}{2}\cdot 3
-18,352
\frac{1}{p*(p + 10)}*\left(p + 10\right)*(7 + p) = \frac{p^2 + 17*p + 70}{p*10 + p^2}
-22,964
\frac{3*12}{12*10} = 36/120
35,117
|1 - y| = |(-1) + y|
-4,598
\frac{24*(-1) - 2*y}{16*(-1) + y * y} = -\frac{4}{y + 4*(-1)} + \frac{2}{y + 4}
-2,549
\sqrt{5}\cdot 3 = \sqrt{5}\cdot (2 + 4\cdot (-1) + 5)
30,743
g_j^Z \mu g_j = (\mu l)^Z \mu g_j = l\mu^Z \mu g_j
30,257
4^{2n} + (-1) = 16^n + (-1) = (16 + (-1)) (16^{n + \left(-1\right)} + 16^{n + 2(-1)} + \dots + 1)
41,715
\dfrac{x^2}{(x^2 + 3)^{\frac52}} = \frac{1}{\left(x^2 + 3\right)^{5/2}} \cdot (x \cdot x + 3) - \tfrac{1}{(x \cdot x + 3)^{5/2}} \cdot 3 = \frac{1}{(x \cdot x + 3)^{3/2}} - \frac{3}{(x^2 + 3)^{5/2}}
4,314
\frac{1}{(2 \cdot x + (-1))^2} = \tfrac{1}{(2 \cdot (x - \frac{1}{2}))^2} = \frac{1/4}{(x - 1/2)^2}
21,686
((x_r + \Psi_r) (x_r + \Psi_r) - (\Psi_r - x_r)^2)/4 = \Psi_r x_r
17,706
\sin{1/y} = \frac{1}{y + 0\cdot (-1)}\cdot (y\cdot \sin{\frac{1}{y}} + 0\cdot (-1))
32,813
E \cup (E \cup \ldots) = E
40,243
q \Delta = q \Delta
10,715
\frac{1}{-Y + 1}\cdot (1 - Y^{l + 1}) = 1 + Y + Y^2 + \ldots + Y^l
6,047
-c_1 b_1 + c_2 b_2 - c_2 b_1 + b_1 c_2 = -b_1 c_1 + b_2 c_2
9,628
3 + m\cdot 2 = m + 2 + m + 1
-2,819
\sqrt{2} = \sqrt{2}\cdot (4\cdot (-1) + 5)
31,874
(15 + \frac{120}{13})\cdot 12/11 = 3780/143
21,803
b \cdot b = (-b) \cdot (-b)
-7,233
\frac{4}{10} \cdot 2/11 = 4/55
31,462
\frac12\cdot 3 = -\frac12 + 2
6,115
-1 = \sqrt{-1}^2 = \sqrt{(-1)^2} = \sqrt{1} = 1
-15,825
0 = -5*\frac{5}{10} + 5*5/10
27,898
\frac{2^x - x^2}{x + 2(-1)} = \frac{1}{x + 2(-1)}(2^x + 4(-1) + 4 - x^2) = 4\frac{1}{x + 2(-1)}\left(2^{x + 2\left(-1\right)} + (-1)\right) - x + 2
2,285
\left\{N/g \cdot g, N\right\} \implies g \cdot \frac1g \cdot N = N
12,881
\sin(\pi\times l + y) = \sin{\pi\times l}\times \cos{y} + \cos{\pi\times l}\times \sin{y} = (-1)^l\times \sin{y}
931
x = z \cdot e^z \Rightarrow z = e^{-z} \cdot x
7,811
(x+y)(x-y)(x^4+x^2y^2+y^4)=(x^2+y^2)(x^4+x^2y^2+y^4)=x^6-y^6
3,551
z_2*z_1 = \frac14*\left((z_1 + z_2)^2 - (-z_2 + z_1)^2\right)
-9,112
\dfrac{1}{100} 22.2 = 22.2\%
26,589
78 = 13 \cdot (13 + 1 + 2 \cdot (-1))/2
-4,140
\frac{8}{x \cdot x \cdot x \cdot 11} = \dfrac{8}{x^3}\tfrac{1}{11}
-20,175
\dfrac{-6p + 2}{2 - 6p} \left(-7/4\right) = \frac{1}{-p*24 + 8}\left(p*42 + 14 (-1)\right)
-15,860
-5/10*8 + \frac{1}{10}*5*7 = -5/10
11,419
5 + 10^{0 + 1} + 10^0*3 = 18
-7,022
\frac{2}{15} = \dfrac15 \cdot 2 \cdot 2/6
26,369
2\cdot \left(1 + \pi^2/4\right)^2 = \left(4 + \pi^2\right)^2/8
50,967
3\cdot 4\cdot 2 = 24
-12,073
2/15 = \dfrac{s}{20 \cdot \pi} \cdot 20 \cdot \pi = s
12,509
e^{-z} = 1 - z + z^2/2 - \dots
-2,651
\sqrt{7} \times \left(5 + 1\right) = 6 \times \sqrt{7}
21,689
e^{d + b} = e^b\cdot e^d
25,199
2^{20} + \left(-1\right) = (2^{10} + (-1)) (2^{10} + 1) = (2^5 + (-1)) (2^5 + 1) (2^{10} + 1)
-10,247
\frac{76}{100} = 19/25
-20,522
\frac{10\cdot r + 90\cdot (-1)}{r\cdot 7 + 63\cdot (-1)} = \frac{1}{9\cdot (-1) + r}\cdot (r + 9\cdot (-1))\cdot 10/7
27,600
(\tfrac{1}{5}*4)^2 + (3/5)^2 = 1
824
\left(q + q\cdot s\right)\cdot \dfrac{1}{1 - \dfrac{1}{2}\cdot (1 + s - q - q\cdot s)}/2 = \frac{q + s\cdot q}{s\cdot q + 1 - s + q}
-2,318
\tfrac{1}{17} = 2/17 - \frac{1}{17}
20,111
2\times y\times n - n \times n = y^2 - (-n + y)^2
44,912
2\times 10 = 20 = 8
19,909
\cos^2{2\cdot x} = (1 - \sin^2{x})^2 = 1 - 4\cdot \sin^2{x} + 4\cdot \sin^4{x}
-2,228
-\frac{1}{12} + \dfrac{8}{12} = \frac{1}{12} \cdot 7
-22,248
y^2 - y\cdot 12 + 20 = (2 (-1) + y) (10 \left(-1\right) + y)
-17,166
-8 = -8r - 32 = -8r - 32 = -8r + 32 (-1)
34,624
-1 = x + \left(-1\right) rightarrow x = 0
6,569
-z_1^2 + z_2^2 = (z_1 + z_2)\cdot \left(z_2 - z_1\right)
-20,244
-\frac{1}{1}10 \dfrac{1}{z + 4(-1)}(4(-1) + z) = \frac{1}{z + 4(-1)}(-z \cdot 10 + 40)
-9,549
-\frac{17}{50} = -\tfrac{34}{100}
9,067
m \cdot m - \left(m + (-1)\right)^2 = (-1) + m \cdot 2
9,653
x^a \cdot x^g = x^{a + g} \neq x^{a \cdot g}
28,131
2/3 = 1/6 + \frac{1}{6} + 1/6 + 1/6
21,451
77 = 23\times (-1) + 100
5,422
-x + x^2 = ((-1) + x) x
-3,208
208^{1 / 2} + 325^{1 / 2} = \left(25 \cdot 13\right)^{1 / 2} + (16 \cdot 13)^{\frac{1}{2}}
14,479
X\cdot X^x\cdot G = X\cdot X^x\cdot G = X^{x + 1}\cdot G
9,951
x^3 - a^3 = (x - a)\cdot (a^2 + x^2 + a\cdot x)
-10,420
-\frac{12}{12*(-1) + 20*c} = -\dfrac{1}{10*c + 6*(-1)}*6*2/2
2,882
(11 - 7*\sqrt{2})*(2 + \sqrt{2}) = (-\sqrt{2} + 2)*(5 + \sqrt{2})
-20,212
\frac{1}{p*35 + 56*(-1)}*\left(-10*p + 16\right) = \frac{p*5 + 8*\left(-1\right)}{8*(-1) + 5*p}*(-\dfrac17*2)
27,304
(I^2 + 2 \cdot I + 2) \cdot (I^2 - 2 \cdot I + 2) = I^4 + 4
31,953
x * x - z! = 2001 \implies x^2 = 2001 + z!
42,660
45 \cdot 50 = 2250
-5,462
\frac{1}{3 \cdot (r + 10)} \cdot 2 = \frac{1}{30 + 3 \cdot r} \cdot 2
14,792
(-1) + (k + 1)! \cdot \left(1 + k + 1\right) = (1 + k)! + (-1) + \left(k + 1\right)! \cdot (1 + k)
1,908
5(-1) + z*6 - z^2 = -(z + 3\left(-1\right))^2 + 2^2
24,915
\left(a + f\right) f = (f + a) f
-4,423
\frac{3 \cdot z + 9}{5 \cdot (-1) + z^2 + z \cdot 4} = \frac{1}{z + 5} + \frac{2}{(-1) + z}
12,150
(z^2 + 2) (z^2 + 2 \left(-1\right)) = z^4 + 4 (-1)
23,711
1^2 + 7^2 + 3 \cdot 3 + 3^2 + 1^2 = 69
36,330
\cos{x} = \cos{-x} = \sin\left(-x + \pi/2\right)
430
(f + c) \cdot (c^2 + f^2 - f \cdot c) = f^2 \cdot f + c^3
9,516
m_1 = \sqrt{y + 4 \cdot (-1)} \Rightarrow 4 + m_1^2 = y
-3,757
\frac{y^3*96}{y^3*120} 1 = 96/120 \tfrac{y^3}{y^3}
27,658
P - D \cup G = P \cap \left(D \cup G\right)
-23,610
5\cdot \frac16/5 = \tfrac{1}{6}
-20,506
-1/5\cdot \dfrac{(-1)\cdot 10\cdot k}{k\cdot (-10)} = \frac{k\cdot 10}{k\cdot (-50)}
-1,075
-\dfrac{1}{18}63 = \frac{1}{18*\frac19}(\left(-63\right)*1/9) = -7/2
12,565
\dfrac{s^3}{s^{1/2}} = s^{\frac{5}{2}}
11,225
\binom{n + t + 5 \cdot (-1)}{t + 2 \cdot (-1)} = \binom{\left(-1\right) + n + 2 \cdot (-1) + t + 2 \cdot \left(-1\right)}{t + 2 \cdot (-1)}
11,295
24 * 24 + 7^2 = 25^2
-17,110
8 = 8\times 3\times i + 8\times 2 = 24\times i + 16 = 24\times i + 16
14,263
6 = 2 \cdot l_2 \cdot l_1 \implies l_2 \cdot l_1 = 3
31,223
t + t = 0 rightarrow 0 = t
15,655
\frac{-X_l + X}{X_l X} = \dfrac{1}{X_l} - 1/X
10,652
z_1 - x_1 = \varphi \Rightarrow x_1 = -\varphi + z_1