id
int64 -30,985
55.9k
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stringlengths 5
437k
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9,924 |
(-z + 1)*(1 + z + z^2) = 1 - z^3
|
-7,873 |
\frac{1}{-3 - i}(2 - i\cdot 16) = \dfrac{2 - i\cdot 16}{-3 - i} \dfrac{-3 + i}{-3 + i}
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28,637 |
\cos\left(x\cdot 2\cdot \pi\right) = \cos\left(\frac{1}{3}\cdot \pi\cdot 6\cdot x\right)
|
1,277 |
\frac{r^{n + 1} + (-1)}{(-1) + r} = 1 + r + \dotsm + r^n
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-30,612 |
2 \cdot y^2 + 14 \cdot (-1) = 2 \cdot (y^2 + 7 \cdot (-1))
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28,759 |
\sin{3 \cdot L} = 3 \cdot \sin{L} - \sin^3{L} \cdot 4
|
9,833 |
12^3 + 1^3 = 9^3 + 10 * 10^2
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18,735 |
5(-1) - T^2*2 - 2T = -2T + 3(-1) - 2\left(T^2 + 1\right)
|
139 |
\tfrac{4}{27} = 2\cdot \frac13\cdot 1/3\cdot 2/3
|
6,109 |
\lambda^3*2/\lambda = \lambda * \lambda*2
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9,824 |
(g\cdot h/g)^n = g\cdot h^n/g
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10,865 |
3/7 = 3/7 + 0 + 0 + 0
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24,590 |
\frac{1}{z + (-1)} = -\frac{1}{1 - z} = \frac{1}{z} + \frac{1}{z^2} + \frac{1}{z^3} + \ldots
|
59 |
\dfrac{1}{(l - i + 1) \cdot (l - i + 1)} \cdot (i + (-1)) = \frac{1}{\left(l - i + 1\right) \cdot \left(l - i + 1\right)} \cdot (-(l - i + 1) + l)
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-30,563 |
3750/750 = \frac{1}{150}*750 = \tfrac{150}{30} = 5
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8,230 |
K = (d\cdot K)^x = d^x\cdot K
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37,580 |
\dfrac{{13 \choose 1}}{{52 \choose 3}} \cdot {39 \choose 2} = 38/50 \cdot 39/51 \cdot 13/52 + \dfrac{38}{50} \cdot 13/51 \cdot \frac{1}{52} \cdot 39 + \frac{39}{52} \cdot \frac{1}{51} \cdot 38 \cdot 13/50
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16,544 |
n \cdot (-Q + l) = ln - nQ
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-20,314 |
9/4\cdot \frac{1}{5\cdot r + 7}\cdot (7 + 5\cdot r) = \frac{63 + 45\cdot r}{28 + 20\cdot r}
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27,965 |
{n \choose k} = \frac{1}{k!\cdot \left(n - k\right)!}\cdot n!
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24,583 |
(1 + 1/2) (-1/2 + 1) = 1 - 1/4
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12,421 |
q^2*\pi*2*Q*\pi = 2*q^2*Q*\pi^2
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-2,185 |
\frac{6}{12} - 1/12 = \dfrac{5}{12}
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18,627 |
x^2 = x^{1/2}\cdot x\cdot x^{1/2}
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17,714 |
a^1 \cdot a^k = a \cdot a \cdot \dots \cdot a = a \cdot a \cdot \dots \cdot a = a^{1 + k}
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-1,607 |
\pi \cdot \tfrac{1}{12} \cdot 7 = \frac{31}{12} \cdot \pi - 2 \cdot \pi
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10,019 |
s^{(-1) + m}\cdot s = s^m
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16,128 |
1 - y \cdot y \cdot y = (-y + 1)\cdot (y^2 + y + 1)
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7,521 |
\frac{f}{b^2 + f f} = f^2\cdot \frac{1}{b b + f^2}/f
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6,838 |
1/6 = \frac{2 / 3}{4}\times 1
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11,851 |
\frac{1}{\left(1 - z\right) \cdot \left(1 - z\right)} = \frac{1}{1 - z} + \frac{z}{(-z + 1)^2}
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34,006 |
q^2\cdot 2 + r^2 - 2\cdot q\cdot r = q^2 + (-q + r) \cdot (-q + r)
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44,737 |
2048 = 13 \times 111 + 605
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-20,200 |
\dfrac{9}{8} \cdot \frac{9 + x}{9 + x} = \frac{81 + x \cdot 9}{8 \cdot x + 72}
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16,232 |
g = g + h + \left(-1\right) \gt g + h + 2 \cdot (-1)
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5,356 |
x\Longrightarrow (x^2 - 3\cdot x + 1) \cdot (x^2 - 3\cdot x + 1) - 3\cdot (x^2 - 3\cdot x + 1) + 1 = x^2 - 3\cdot x + 1 = x
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7,903 |
\frac{1}{\frac1c\cdot f} = c/f
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-22,938 |
24/36 = 12\cdot 2/\left(12\cdot 3\right)
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-1,991 |
\pi/2 - \frac{7}{12}\cdot \pi = -\frac{\pi}{12}
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23,489 |
\frac{49 + 6\cdot \left(-1\right)}{4\cdot (-1) + 49} = \frac{1}{45}\cdot 43
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-2,856 |
5 \sqrt{6} = \sqrt{6}*(4 + 1)
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-4,479 |
\tfrac{1}{12 + z^2 + 7\cdot z}\cdot (24 + z\cdot 7) = \frac{3}{3 + z} + \frac{4}{4 + z}
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-10,515 |
-\tfrac{6}{15 \times m} \times \frac{4}{4} = -\dfrac{24}{m \times 60}
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5,992 |
a * a^2 + f^3 + c^3 = (a + f + c)*(a * a + f * f + c^2 - a*f - f*c - c*a) + 3*a*f*c = 3*a*f*c
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28,819 |
1/27 = \frac{8}{216}
|
4,005 |
\sin(\frac{3}{9}\cdot \pi) = \sin(\pi/3)
|
-522 |
\frac{361}{12}\cdot \pi - 30\cdot \pi = \pi/12
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-20,326 |
\dfrac{90}{-40} = -\dfrac94\cdot (-10/(-10))
|
25,001 |
-\frac3n + 1 = \frac1n \cdot \left(n + 3 \cdot (-1)\right)
|
25,921 |
m \cdot n + 3 \cdot (m + n) = 0\Longrightarrow \left(3 + n\right) \cdot (m + 3) = 9, m, n \leq 0
|
35,605 |
(g + g)\cdot g + g\cdot (g + g) = \left(g + g\right)\cdot (g + g)
|
14,579 |
(x + 1) \cdot (x + 3 \cdot (-1)) = (x + (-1) + 2) \cdot (x + (-1) + 2 \cdot \left(-1\right)) = (x + \left(-1\right))^2 + 4 \cdot (-1)
|
-4,764 |
\frac{6*y + 7*(-1)}{y^2 - y*3 + 2} = \frac{1}{(-1) + y} + \frac{5}{y + 2*(-1)}
|
-3,936 |
\dfrac{t^5}{t^2} = \dfrac{t \cdot t \cdot t \cdot t \cdot t}{t \cdot t} = t^3
|
23,360 |
3\cdot {x + 1 \choose 4} = {{x \choose 2} \choose 2}
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-18,320 |
\frac{q^2 - 2q}{8 + q^2 - 6q} = \dfrac{(q + 2(-1)) q}{(2(-1) + q) (4(-1) + q)}
|
10,314 |
{13 \choose 4} = {9 + 5 + (-1) \choose 5 + \left(-1\right)}
|
23,959 |
\tan\left(2\cdot x + x\right) = \tan(3\cdot x)
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-23,158 |
-8/9 \cdot (-\frac23) = 16/27
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30,041 |
\frac{1}{2^6} \cdot (1^2 + 3^2 + 3 \cdot 3 + 1^2) = 20/64 = 5/16
|
24,514 |
(-z)^{1/2}\cdot (-z)^{1/2} = \left((-z)^{1/2}\right)^2 = -z
|
-15,773 |
\dfrac{6}{10} = 1 - 4/10
|
-15,571 |
\frac{1}{y^{25}\cdot (\dfrac{y}{k^5})^3} = \frac{1}{y^{25}\cdot \frac{1}{k^{15}}\cdot y^3}
|
16,365 |
m = k + 2*(m - t - k) = 2*m - 2*t - k\Longrightarrow k = -2*t + m
|
-15,934 |
10 \cdot \frac{5}{10} - 5 \cdot 5/10 = 25/10
|
28,461 |
26 = 5^2 + 1 \cdot 1 = 4^2 + 3^2 + 1^2 = 3 \cdot 3 + 3^2 + 2^2 + 2^2
|
21,546 |
\frac{1}{l_1 l_2 + 2(-1)}(l_1 l_2 + 2(-1) - ((-1) + l_1) \cdot 2) = \frac{(l_2 + 2(-1)) l_1}{l_1 l_2 + 2\left(-1\right)}
|
20,941 |
r^2 - 2\cdot r + 2 = (r + (-1))^2 + 1
|
12,174 |
\frac12 + 1/4 = \dfrac{3}{4}
|
30,225 |
\frac{3}{6}\times \dfrac47 = \frac{1}{7}\times 2
|
28,271 |
\cos^2(y) = (\cos(2y) + 1)/2
|
49,808 |
20\cdot 59 + 10\cdot 32 = 1500
|
34,196 |
\dfrac{1.8}{2} = 0.9
|
911 |
(n + \left(-1\right))^2 - 2 \cdot (n + (-1)) + (-1) = n \cdot n - 2 \cdot n + 1 - 2 \cdot n + 2 + (-1) = n^2 - 4 \cdot n + 2
|
44,647 |
1024169717 + 1024169712 (-1) = 5
|
5,976 |
\left(9 + 1\right) \cdot \log_e(9 + 1) + 9 \cdot (-1) = 10 \cdot \log_e(10) + 9 \cdot (-1) = 10 + 9 \cdot (-1) = 1
|
26,744 |
x = \dfrac{1 - t^2}{t^2 + 1}\Longrightarrow x x = \frac{\left(-t^2 + 1\right)^2}{(1 + t^2)^2}
|
-6,341 |
\dfrac{4}{(x + 3)\cdot \left(x + 10\cdot (-1)\right)} = \tfrac{1}{x \cdot x - 7\cdot x + 30\cdot (-1)}\cdot 4
|
1,793 |
k_1*h_1*h_2*k_2 = k_1*k_2*h_1*h_2
|
3,570 |
3^n - 3^{n + 2(-1)} = 3^{n + 2\left(-1\right)} (9 + (-1))
|
15,264 |
\frac{1}{9}*7 = 1 - \frac19*2
|
20,594 |
\left(x - V\right) (x + V) = x - V^2 = (x + V) \left(x - V\right)
|
-3,614 |
\frac{1}{q \cdot q \cdot 4} \cdot 16 \cdot q^5 = \dfrac{1}{q \cdot q} \cdot q^5 \cdot 16/4
|
29,500 |
\sqrt{3} + 2 = \dfrac{1 + \sqrt{3}}{\sqrt{3} + (-1)}
|
5,255 |
\frac{1}{4}*(3^5 + 3^9 + 2*3^3) = 4995
|
13,465 |
\left(t \cdot 2 + 1 = 0 rightarrow t \cdot 2 = -1\right) rightarrow -\dfrac{1}{2} = t
|
29,193 |
(2 \cdot c)^2 - (2 \cdot f) \cdot (2 \cdot f) \cdot m = (c^2 - m \cdot f^2) \cdot 4
|
27,892 |
\dfrac1x = c + x\cdot b \Rightarrow x^2\cdot b + c\cdot x + (-1) = 0
|
12,637 |
(6 + \left(-1\right)) \cdot 5^i + (-1) = 5^i \cdot 6 + 6 \cdot (-1) - 5^i + 5
|
-6,894 |
192 = 6\cdot 4\cdot 8
|
25,331 |
(\frac{16}{54})^{\frac13} = (\dfrac{8}{27})^{1/3} = 2/3
|
15,955 |
1/405 = \frac{4}{180}\times \frac19
|
33,795 |
16*25*34 = 13600
|
-9,341 |
x\cdot 11 + 77 \left(-1\right) = -7\cdot 11 + x\cdot 11
|
16,071 |
1/4 + \frac{1}{4}*2 = 3/4 \lt 1
|
19,484 |
-\cos(x) = \sin(-\pi/2 + x)
|
32,187 |
4\cdot 126 = 504
|
12,636 |
(d + b) \cdot (d + b) = d^2 + b \cdot d \cdot 2 + b^2
|
6,528 |
Y \cdot (1 + o^2 + (-1)) = Y + (o^2 + (-1)) \cdot Y
|
-1,728 |
\pi \frac32 + \frac{1}{2}3 \pi = \pi*3
|
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