id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
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
|
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