id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
14,841
|
(3^3 - 3*(2^3 + 2\left(-1\right)) + 3(-1))/6 = (27 + 18 \left(-1\right) + 3(-1))/6 = 1
|
19,174
|
10^{1/2}*2 + 2 = 2*(10^{1/2} + 1)
|
-15,426
|
\frac{1}{y^4\cdot \frac{1}{q^2}}\cdot y \cdot y \cdot y = \frac{y^3}{(y^2/q) \cdot (y^2/q)}
|
-1,133
|
-6/56 = \frac{\left(-6\right)\cdot 1/2}{56\cdot 1/2} = -3/28
|
30,872
|
X < 2^X \leq X^X \implies X^X \leq 2^{X \cdot X} \leq X^{X^2} = X^X
|
-22,356
|
16 (-1) + d^2 - d*6 = (d + 2) \left(8(-1) + d\right)
|
31,250
|
9 \times 81 = 729
|
36,137
|
\binom{1 + x}{x} = 1 + x
|
2,006
|
\frac{y^x + (-1)}{y + (-1)} = \tfrac{1}{y + (-1)}\cdot (y + (-1))\cdot (1 + y + ... + y^{x + (-1)}) = 1 + y + ... + y^{x + (-1)}
|
4,388
|
1/d - \frac1b = b/(db) - d/\left(db\right) = \frac{1}{db}(b - d)
|
9,603
|
d/dx e^{i \times x} = i \times e^{x \times i}
|
16,267
|
2 \cdot (-1) + x = -(2 - x)
|
-1,242
|
\frac{2}{3} (-5/4) = \dfrac{1/4 (-5)}{3*1/2}
|
16,904
|
7^{10*427 + 5} = (7^{10})^{427}*7^5
|
18,092
|
\sin^{26}(x) - \sin^{24}(x) = \sin\left(6\cdot x + 4\cdot x\right)\cdot \sin(6\cdot x - 4\cdot x) = \sin\left(2\cdot x\right)\cdot \sin\left(10\cdot x\right)
|
14,963
|
(-1) + x^{\omega + (-1)} = (x^{\dfrac12((-1) + \omega)} + 1) (x^{\frac{1}{2}\left((-1) + \omega\right)} + (-1))
|
-7,683
|
\frac{-2 - i \cdot 6}{-i \cdot 3 - 1} \cdot \frac{1}{3 \cdot i - 1} \cdot (-1 + 3 \cdot i) = \frac{-2 - i \cdot 6}{-i \cdot 3 - 1}
|
17,489
|
0\cdot (0 - -1 + (-1)) + \left(-1 - -1 + (-1)\right) = 1
|
13,153
|
(-1) + \frac{5!}{2!\cdot 3!} = 9
|
16,752
|
x + I + h - c = I + h - c + x
|
6,515
|
-\frac{2}{z^5} = \frac{z}{-z^6\cdot 1/2}
|
-579
|
e^{5\pi i/3 \cdot 16} = \left(e^{\frac{5}{3}i\pi}\right)^{16}
|
33,595
|
29^2 = 21 \cdot 21 + 20 \cdot 20
|
1,963
|
(I*x_j - A)*(I*x_\mu - A) = \left(I*x_j - A\right)*(-A + I*x_\mu)
|
22,012
|
2 \cdot (-1) + 2^{k + 1} = ((-1) + 2^k) \cdot 2
|
-24,392
|
8 + 9 \cdot 9 = 8 + 9\cdot 9 = 8 + 81 = 89
|
-7,329
|
\frac{1}{5 \cdot 4} = \frac{1}{20}
|
22,272
|
x_1 \cdot x_2 \cdot \dots \cdot x_N = x_1 \cdot x_2 \cdot \dots \cdot x_N
|
6,979
|
\frac{\mathrm{d}}{\mathrm{d}w} \arcsin{w} = \frac{1}{\sqrt{1 - w^2}}
|
31,420
|
G_2 - G_2 - G_1 = G_2 \cap G_2 \cap G_1^\complement^\complement = G_2 \cap (G_1 \cup G_2^\complement) = G_1 \cap G_2
|
9,137
|
328350 = 100\cdot 99/2 + \frac{98}{3}\cdot 99\cdot 100
|
1,888
|
w\cdot z\cdot y = y\cdot w\cdot z
|
38,611
|
\frac{1}{\frac{1}{5}\cdot 6} = \frac{5}{6}
|
20,806
|
a + c = ( a, c) \cdot ( 1, 1) \leq (a^2 + c^2)^{\frac12}
|
35,199
|
251 \cdot 501 \cdot 250/6 = 5239625
|
19,845
|
\left\{2, 3, \ldots, 1\right\} = \N
|
-15,180
|
\dfrac{{n^{5}x^{25}}}{{n^{6}x^{-6}}} = \dfrac{{n^{5}}}{{n^{6}}} \cdot \dfrac{{x^{25}}}{{x^{-6}}} = n^{{5} - {6}} \cdot x^{{25} - {(-6)}} = n^{-1}x^{31}
|
28,252
|
\cos(2*z + 2*\left(-1\right)) = \cos{2*((-1) + z)}
|
-4,432
|
-\frac{3}{y + 5\left(-1\right)} - \frac{2}{5 + y} = \tfrac{-y\cdot 5 + 5(-1)}{25 (-1) + y \cdot y}
|
-721
|
e^{2*\dfrac{\pi*i}{2}} = \left(e^{i*\pi/2}\right)^2
|
8,567
|
6 \cdot (6 \cdot x \cdot k + x + k) + 1 = (1 + 6 \cdot k) \cdot \left(x \cdot 6 + 1\right)
|
-4,419
|
\frac{11*\left(-1\right) - y}{y^2 - y*6 + 5} = -\frac{4}{y + 5*\left(-1\right)} + \frac{1}{\left(-1\right) + y}*3
|
4,143
|
\dfrac{1}{\dfrac{2^m}{2}} = \dfrac{2}{2^m}
|
-1,076
|
\frac{10}{56} = \dfrac{10 \cdot \frac12}{56 \cdot 1/2} = 5/28
|
-3,922
|
66/30*\dfrac{1}{a^5}*a^2 = \frac{66}{30*a^5}*a^2
|
6,863
|
1 - \frac{1}{x + 1}*x = \dfrac{1}{x + 1}
|
34,186
|
84 = 3\cdot \binom{(-1) + 6 + 3}{(-1) + 3}
|
11,652
|
x = (\left(-1\right) + k\cdot 3)^{1/3} \implies 1 + x^3 = k\cdot 3
|
18,860
|
\tfrac{63}{80} = \frac{64}{80}\cdot 63/64 = 4/5\cdot 63/64
|
20,367
|
1 \lt e^{1/l} < 3^{\frac{1}{l}} = (1 + 2)^{\frac{1}{l}} \lt 1 + 2/l
|
28,980
|
2^x/x! = \dfrac{\frac{\frac112*2}{2}*2/3*2}{4\cdots} \leq 2(\dfrac{2}{3})^{x + 2\left(-1\right)}
|
6,712
|
50 \cdot 0 + C_4 = 0\Longrightarrow C_4 = 0
|
-20,163
|
\frac{8}{5 - q \cdot 8} \cdot q \cdot 9/9 = \frac{q \cdot 72}{-72 \cdot q + 45}
|
9,178
|
a+b= 1 \implies a-b=16
|
-18,415
|
\frac{1}{k^2 + 9\cdot k}\cdot \left(k^2 + k\cdot 17 + 72\right) = \dfrac{1}{k\cdot (9 + k)}\cdot (9 + k)\cdot (k + 8)
|
20,176
|
-d^2 = -d\cdot d
|
25,362
|
( a, c, g) = ( c, g, a) = ( g, a, c)
|
-6,247
|
\frac{t}{45*(-1) + t * t + t*4} = \tfrac{t}{\left(t + 5*(-1)\right)*(t + 9)}
|
-19,472
|
7/4 \cdot \frac{2}{5} = \frac{7 \cdot \frac14}{5 \cdot \frac{1}{2}}
|
23,579
|
y_2^{y + y_1} = y_2^y\cdot y_2^{y_1}
|
5,702
|
x^g x^{-g} = x^{g - g} = x^0 = 1 \Rightarrow x^{-g} = \dfrac{1}{x^g}
|
-1,911
|
-\pi = \pi/4 - \pi*5/4
|
14,317
|
a^3 + b^3 + c^3 - 3 \cdot c \cdot b \cdot a = (-a \cdot c + a^2 + b^2 + c \cdot c - b \cdot a - c \cdot b) \cdot (c + a + b)
|
-1,504
|
\frac{1}{72} \cdot 36 = \frac{1}{72 \cdot \frac{1}{36}} \cdot 1 = 1/2
|
-20,192
|
\dfrac77*\frac{7*(-1) + 8*y}{-10*y + 7*(-1)} = \frac{1}{-70*y + 49*\left(-1\right)}*(y*56 + 49*(-1))
|
-7,076
|
\dfrac{2*\frac{1}{11}}{10} = \dfrac{1}{55}
|
-10,583
|
12/12\cdot (-\frac{7}{25\cdot a^3}) = -\dfrac{84}{a \cdot a \cdot a\cdot 300}
|
12,421
|
\pi^2 \cdot t \cdot t \cdot R \cdot 2 = 2 \cdot \pi \cdot R \cdot \pi \cdot t^2
|
10,786
|
16 - 2 \cdot 4 \cdot \frac{9}{2} = 25 - 9/2 \cdot 2 \cdot 5
|
1,053
|
2zK + z^2 + K * K = (z + K)^2
|
22,057
|
\alpha*r = \alpha*r
|
-18,417
|
\frac{1}{n \cdot n - n\cdot 7 + 10}\cdot (4\cdot \left(-1\right) + n \cdot n) = \frac{1}{(2\cdot (-1) + n)\cdot (5\cdot (-1) + n)}\cdot (n + 2)\cdot (2\cdot (-1) + n)
|
1,434
|
\cos\left(z*999 + z\right) = \cos{1000*z}
|
32,928
|
0 = n^2 - n + 56 (-1) = (n + 8(-1)) (n + 7)
|
-25,892
|
0.4 = \dfrac25
|
6,154
|
\frac{\partial}{\partial x} x^Q = Q \times x^{\left(-1\right) + Q}
|
-9,588
|
0.01\cdot \left(-87\right) = -87.5/100 = -\dfrac{7}{8}
|
24,430
|
2^l = 2^l\cdot i + 1 \gt 2^l\cdot i
|
16,107
|
2000 = 100 \cdot 20 \cdot 15/15
|
-23,051
|
-7/8 = (\left(-7\right)*1/4)/2
|
20,262
|
2\cdot \cos^2(\theta/2) + (-1) = \cos(\theta)
|
1,449
|
1/9 + \frac{1}{9} + 1/9 = \frac19 \cdot 3 = 1/3
|
18,051
|
h d - b e - d + h + 1 = ((-1) + d) ((-1) + h) - b e
|
28,060
|
\frac{4}{3}\cdot 8 + 1/3 = 11
|
37,586
|
5^2\cdot 3\cdot 2 = 150
|
-25,226
|
-\frac{9}{x^{10}} = \frac{d}{dx} \frac{1}{x^9}
|
24,897
|
h \cdot d \cdot c = h \cdot d \cdot c
|
12,993
|
t = 2\cdot r\Longrightarrow t/2 = r
|
5,796
|
det\left(X\right) = det\left(E\right)*det\left(X\right) = det\left(E*X\right)
|
-19,422
|
5/2 \times 9/7 = \dfrac{\frac{9}{7}}{2 \times 1/5} \times 1
|
22,305
|
6y = 0 \Rightarrow y = 0
|
18,685
|
(m^2 - l * l) * (m^2 - l * l) + (2ml)^2 = m^4 + 2m^2 l^2 + l^4 = (m^2 + l * l)^2
|
-1,449
|
\dfrac{\frac{1}{4}*3}{\tfrac12*(-1)} = -2/1*3/4
|
16,285
|
\frac{n!}{(n + \left(-1\right))!} = n
|
14,835
|
\frac{1}{x}x^{\tfrac13} = x^{1/3 + (-1)} = x^{-2/3} = \frac{1}{x^{2/3}} = \frac{1}{x^{\frac{2}{3}}}
|
-6,381
|
\frac{5}{3 \cdot x + 15} = \frac{5}{(x + 5) \cdot 3}
|
-28,776
|
1 - 2 \cdot \sin^2{x} = \cos{2 \cdot x}
|
4,458
|
\tfrac{g_2}{\sigma} g_1 \sigma = \frac{g_1}{\sigma} \sigma \sigma g_2/\sigma
|
-6,247
|
\frac{t}{\left(9 + t\right)\cdot (5\cdot (-1) + t)} = \tfrac{t}{45\cdot (-1) + t^2 + 4\cdot t}
|
22,786
|
(n + (-1)) \times \left(2 \times \left(-1\right) + n\right) \times (2 \times (-1) + n)! = \left(n + 2 \times (-1)\right) \times ((-1) + n)!
|
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