id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-12,136 |
11/12 = \frac{q}{12\cdot \pi}\cdot 12\cdot \pi = q
|
24,420 |
2*\sqrt{n + 1} - 2*\sqrt{n} = (\sqrt{n + 1} - \sqrt{n})*2
|
29,029 |
5/24 = \dfrac{1}{12} + 3/24
|
31,091 |
\tfrac{2}{3} = -1/3 + 1
|
9,966 |
\frac{1 - t^{1 + n}}{1 - t} = \frac{1 - t^{n + 1}}{1 - t}
|
13,232 |
|x^3\cdot z| = |x^2\cdot z\cdot x| \leq \left(x^2 \cdot x^2 + z^2\right)/2\cdot |x|
|
3,423 |
\cos(x + \pi) = \cos(x)*\cos(\pi) - \sin(x)*\sin\left(\pi\right) = -\cos(x)
|
-521 |
e^{5\cdot i\cdot \pi/4\cdot 3} = \left(e^{\frac54\cdot \pi\cdot i}\right)^3
|
3,723 |
\frac{1}{(x + 1)\cdot 1/2} = \dfrac{1}{1 + x}2
|
30,799 |
37 = -3 \cdot 5 \cdot 17 \cdot 19 \cdot 19 + 2^2 \cdot 7 \cdot 11 \cdot 13 \cdot 23
|
15,857 |
\frac{1}{2} + 1/3 + \frac16 = 1
|
37,563 |
2^{h \cdot g} = 2^{g \cdot h} = (2^h)^g
|
-2,184 |
-\frac{1}{11}\cdot 2 + \dfrac{3}{11} = 1/11
|
1,844 |
(7^{\frac{1}{2}} + 1)\cdot (7^{1 / 2} + (-1)) = 6
|
-20,774 |
\frac{20 - l \cdot 5}{3 \cdot l + 12 \cdot (-1)} = \frac{4 \cdot (-1) + l}{l + 4 \cdot (-1)} \cdot (-\frac53)
|
10,828 |
9^{20} = 1.215 \dots\cdot 10^{19} > 10^{19}
|
19,556 |
1 + m = (-1) + m + 2
|
-3,952 |
8/4*\frac{r^2}{r^2} = \frac{8*r^2}{r^2*4}*1
|
54,551 |
1 = {0 \choose 0}
|
11,314 |
1 - \sin^2{\frac{y}{2}}*2 = \cos{y}
|
21,614 |
\left(5\cdot u + (-1)\right)^2 = 1 + u^2\cdot 25 - u\cdot 10
|
-11,800 |
81/49 = \left(9/7\right)^2
|
44,809 |
7*\left(2^{21} + \left(-1\right)\right) = 14680057
|
-10,773 |
\dfrac{1}{y\cdot 50 + 20}\cdot (y\cdot 40 + 10\cdot (-1)) = \frac{10}{10}\cdot \frac{4\cdot y + (-1)}{5\cdot y + 2}
|
16,216 |
2*\sinh(z) = -e^{-z} + e^z
|
13,287 |
-1/a = \dfrac{1}{a \cdot \left(-1\right)}
|
-7,909 |
\frac{1}{5 + i*3}*(3*i + 5)*\dfrac{i*19 + 25}{-3*i + 5} = \frac{1}{-i*3 + 5}*(25 + i*19)
|
10,858 |
a' + x + \left( c_2, c_1\right) = ( c_2 + a', x + c_1)
|
-20,174 |
(63 + 7\cdot q)/(q\cdot (-56)) = 7/7\cdot \frac{1}{(-8)\cdot q}\cdot (q + 9)
|
15,762 |
{3 \choose 2} {3 \choose 1} \cdot 2! = 18
|
27,767 |
a*1/b/c = \dfrac{b\dfrac{a}{b}}{bc} = \tfrac{a}{bc}
|
4,860 |
(120 + 20)\cdot (x + 3\cdot \left(-1\right)) = 140\cdot (x + 3\cdot (-1)) = 140\cdot x + 420\cdot (-1)
|
-20,843 |
\tfrac{s\cdot 4}{s\cdot 4}\cdot (-4/7) = \frac{(-1)\cdot 16\cdot s}{s\cdot 28}
|
26,924 |
39 = \left(-1\right) + 10 \times 4
|
18,195 |
1 = \sqrt{1} = \sqrt{\left(-1\right) \cdot (-1)} = \sqrt{-1} \cdot \sqrt{-1} = -1
|
15,678 |
T_n = (T_{(-1) + n} + a)/2\Longrightarrow a < T_n < T_{n + \left(-1\right)}
|
4,024 |
3 > 5 - \frac{1}{y} \times 2 rightarrow 0 \gt \frac1y \times ((-1) + y) \times 2
|
28,156 |
\sqrt{2} \cdot 1/\left(\sqrt{2}\right)/(\sqrt{2}) = \frac{\sqrt{2}}{2}
|
6,270 |
S^{1/2} T S^{\frac{1}{2}} = T S
|
-29,569 |
-\frac{2*x^4}{x} = -2*x^3
|
2,294 |
4^3*2^6*3^6 = 4^3*3^4*2^5*3^2*2^1
|
11,072 |
2z_k = z_k
|
25,434 |
3/x - \frac{x}{2} = \tfrac3x - x/2
|
2,769 |
x \cdot (\gamma + \beta) = x \cdot \beta + \gamma \cdot x
|
8,729 |
(-1) + x^3 = (x + \left(-1\right)) (1 + x^2 + x)
|
32,176 |
((-1) + n) * ((-1) + n) = n^2 - n*2 + 1
|
-20,029 |
\dfrac{14 - p*63}{p*70 + 35*(-1)} = \frac{1}{10*p + 5*(-1)}*(2 - 9*p)*7/7
|
270 |
(-1) + m^2 = m^2 - m + m + (-1)
|
42,432 |
\tfrac{11!}{2!\cdot 2!\cdot 2!\cdot 2!} = 2494800
|
-30,850 |
y^2 + y\cdot 5 = \dfrac{1}{-2\cdot y + y^2}\cdot (y^4 + 3\cdot y^3 - y \cdot y\cdot 10)
|
38,755 |
\frac{1}{60}15 = 1/4
|
48,778 |
x^2 = (5 + 1 - 2*5^{1/2})/4 = \frac12*(3 - 5^{1/2}) = 1 - \frac12*(5^{1/2} + (-1)) = 1 - x
|
15,092 |
\frac{1}{a^4}b = \frac{b}{a^4}
|
1,059 |
\frac{1 - \frac{1}{t}}{t + (-1)} = 1/t
|
24,403 |
\cos{z} \cdot z^2 = 1 - \cos{z}\Longrightarrow \cos{z} = \frac{1}{z^2 + 1}
|
27,126 |
10^k \cdot 10 = 10^{k + 1}
|
9,588 |
B = B \cap K \Rightarrow \left\{B, K\right\}
|
42,114 |
\binom{6}{3} \times \binom{10}{4} = 4200
|
9,639 |
(d \cdot g)^2 = d \cdot d \cdot g^2
|
46,450 |
5 = {4 \choose 1} + {4 \choose 0}
|
-19,178 |
\frac{1}{9} \cdot 7 = \dfrac{D_p}{49 \cdot \pi} \cdot 49 \cdot \pi = D_p
|
13,908 |
2 + 3 + 4 + 5 = \frac12 \cdot (2 + 3 + 4 + 5 + 5 + 4 + 3 + 2)
|
-15,945 |
5 \cdot 7/10 - 6 \cdot \frac{3}{10} = 17/10
|
-1,526 |
5/9\cdot (-7/4) = \dfrac{1}{1/5\cdot 9}\cdot \left((-7)\cdot \tfrac14\right)
|
-4,184 |
\tfrac1611 = \frac1611
|
8,138 |
\left(x\cdot 5 + 5 = 20\Longrightarrow 15 = 5\cdot x\right)\Longrightarrow 3 = x
|
41,848 |
672 = 6! - 2 \cdot 4!
|
5,978 |
\frac32 + 1 = \dfrac{5}{2}
|
11,252 |
\pi \frac23 \cdot 2 \cdot \dfrac15/2 = 2\pi/15
|
17,877 |
\left(-h = z \implies h^l = z^l\right) \implies h^l + z^l = h^l\cdot 2
|
21,446 |
\sin(3 \pi/2) = \sin(\frac12 \pi + \pi)
|
11,411 |
e^1 = z rightarrow \cos(1) + i\sin(1) = z
|
11,609 |
1/2 = 5\cdot \frac{1}{8}/2 + 3\cdot \tfrac{1}{8}/2
|
22,897 |
\frac1n (n + 1) = 1/n + 1
|
-25,021 |
4 \cdot z - z^2 \cdot z \cdot \frac{64}{3} + z^5 \cdot 1024/5 - 16384/7 \cdot z^7 + \ldots = \tan^{-1}{4 \cdot z}
|
25,007 |
u\cdot Y = Y\cdot u
|
-1,832 |
\pi \cdot 7/12 = \pi \cdot 3/4 - \tfrac{\pi}{6}
|
-2,418 |
\sqrt{25\cdot 3} - \sqrt{9\cdot 3} = -\sqrt{27} + \sqrt{75}
|
29,826 |
{2 \cdot n \choose n} = \tfrac{1}{n!^2} \cdot (2 \cdot n)! \approx \dfrac{4^n}{\left(\pi \cdot n\right)^{1/2}}
|
27,380 |
d \cdot d^l = d^{1 + l}
|
7,176 |
8 = (a + b + c + d)/4 \Rightarrow a + b + c + d = 32
|
5,135 |
392/3 + \tfrac{1}{3}\times 1120 = \frac{1}{3}\times 1512 = 504
|
-19,044 |
\frac{5}{8} = E_x/(4\pi)\cdot 4\pi = E_x
|
14,335 |
\left(x*2 + a*2 = g \Rightarrow g*3 = 2*a + 2*x + 2*g\right) \Rightarrow g = \dfrac23*\left(x + a + g\right)
|
42,522 |
\dfrac{1}{a + \left(a^2 + (-1)\right)^{\frac{1}{2}}} = \frac{a - (a^2 + (-1))^{1/2}}{(a - (a^2 + (-1))^{1/2})\cdot (a + (a \cdot a + \left(-1\right))^{\frac{1}{2}})} = \dfrac{1}{a^2 - a^2 + (-1)}\cdot \left(a - (a^2 + (-1))^{1/2}\right) = a - (a^2 + (-1))^{1/2}
|
16,504 |
A^2 + A \cdot Y + Y \cdot A + Y^2 = (Y + A)^2
|
-5,107 |
10^{2 - 2}\cdot 8.7 = 10^0\cdot 8.7
|
4,659 |
\frac{H}{x} = H/x
|
35,069 |
\dfrac{\dfrac{1}{2}}{2} \cdot 1/2 = \frac{1}{8}
|
50,134 |
0\cdot2=2\cdot0=0
|
4,765 |
(t + 3 \times (-1))^2 + 9 \times \left(-1\right) + 8 = 8 + t^2 - t \times 6
|
-18,582 |
-1/7 = -\frac17
|
980 |
(f\cdot c/c)^2 = \frac{f}{c}\cdot c\cdot f/c\cdot c
|
-20,487 |
\frac19 \cdot (4 + q \cdot 2) \cdot 2/2 = \frac{1}{18} \cdot (4 \cdot q + 8)
|
3,064 |
56 = \left(7 + (-1)\right)\cdot 8 + ((-1) + 2)\cdot 7 + 1
|
31,953 |
x^2 - \varphi! = 2001\Longrightarrow 2001 + \varphi! = x^2
|
-12,421 |
\dfrac{15}{5} = 3
|
-1,418 |
10/14 = \frac{10\cdot 1/2}{14\cdot \dfrac12} = 5/7
|
26,118 |
(\left(-1\right) + 1) \cdot 20 + 250 = 250
|
7,421 |
-7/6 + 7 = 35/6
|
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