id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
3,848 |
|h_m\times a_m - a\times h| = |a_m\times h_m - a_m\times h + a_m\times h - h\times a|
|
11,500 |
\frac{1}{\Omega^{1/2} \cdot \Omega^{\frac12}} = \frac{1}{\Omega}
|
43,275 |
c = (1 + 1/4)\times \dfrac{p}{4} rightarrow \frac{5}{16}\times p = c
|
10,658 |
42 = \left((-1) + 7\right) \cdot 7
|
24,843 |
(7 + a) \times (7 + a) - 17 \times \left(a + 4\right) = a \times a - 3 \times a + 19 \times \left(-1\right)
|
33,788 |
h*H = H*h
|
35,539 |
\sin(g + b) = \sin{g} \cos{b} + \cos{g} \sin{b}
|
10,384 |
\sqrt{2} \approx 1.41\times \cdots < 1.44 = 1.2^2 = (5/4)^2
|
24,098 |
2^2 + 4^2 = 2^4 + 2^2
|
15,286 |
x^2 + \left(-1\right) = ((-1) + x) (1 + x)
|
6,505 |
h \cdot h + h\cdot g = d \cdot d \implies d^2 - h^2 = g\cdot h
|
21,695 |
120 \cdot (75 + 30 \cdot \left(-1\right)) = 5400
|
-3,659 |
5\times 1/6/p = 5/(p\times 6)
|
1,760 |
( -(2 \cdot a - x) + 2 \cdot b, z) = \left( (-a + b) \cdot 2 + x, z\right)
|
10,703 |
1/(2) + 1/(2\cdot 3) + \ldots + \frac{1}{(n + 1)\cdot n} = -\frac{1}{1 + n} + 1
|
11,781 |
1415934836 = 84\cdot 256 \cdot 256^2 + 101\cdot 256^2 + 256^1\cdot 115 + 256^0\cdot 116
|
-12,117 |
\dfrac{1}{6} = \tfrac{t}{6 \cdot \pi} \cdot 6 \cdot \pi = t
|
-4,146 |
8n^2 = n * n*8
|
39,255 |
2^4 \cdot 2 \cdot 2 = 2^3 \cdot 2^3
|
-20,174 |
\frac77 \frac{1}{(-8) q} (9 + q) = \frac{1}{q\cdot (-56)} (63 + q\cdot 7)
|
-6,140 |
\dfrac{1}{(s + 1) \cdot 2} = \frac{1}{2 + 2 \cdot s}
|
-3,882 |
\frac{1}{t^5} t^4 = \dfrac{t t t t}{t t t t t} = 1/t
|
10,056 |
\frac{1}{3}(3m + 3\left(-1\right)) + (3m^2 + 3m + 1)/3 = \frac{1}{3}\left(3m^2 + 6m + 2(-1)\right) = m^2 + 2m - 2/3
|
36,336 |
20 = 5 \cdot A \Rightarrow A = 4
|
8,422 |
\dfrac49 = 2/3 \cdot \frac13 \cdot 2
|
5,889 |
\pi\cdot 3/2 = \dfrac{\pi\cdot (-1)}{2} + \pi\cdot 2
|
6,191 |
12 \cdot \left(725760 + 986400 + 985824 + 967680\right) = 43987968
|
21,571 |
d = d \cdot x = x \Rightarrow d = x
|
-18,269 |
\frac{1}{-3 \cdot n + n^2} \cdot (15 \cdot (-1) + n^2 + 2 \cdot n) = \tfrac{\left(n + 5\right) \cdot (n + 3 \cdot (-1))}{n \cdot (3 \cdot \left(-1\right) + n)}
|
15,562 |
\frac{1}{x \cdot z} = \frac{1/z \cdot z}{x \cdot z}
|
39,242 |
1 = -\sin\left(\frac{\pi}{2}*3\right)
|
-10,281 |
\dfrac{\frac{1}{6}}{4*x + 2*(-1)}*6 = \frac{1}{24*x + 12*(-1)}*6
|
25,655 |
4^{100} - 3^{100} = 100 \cdot d^{99} = \dfrac{100}{d} \cdot d^{100}
|
15,364 |
1 + 3 + 3^2 + 3^3 + \dotsm + 3^k = \frac{1}{2} \times ((-1) + 3^{k + 1})
|
24,988 |
\frac{1}{(n + 1)^2} \cdot ((n + 1) \cdot (n + 1) + 1) = \dfrac{1}{(n + 1)^2} + 1
|
-5,935 |
\dfrac{1}{27*(-1) + y*3}*2 = \frac{2}{3*(y + 9*(-1))}
|
23,069 |
y^3 - 3y + 2(-1) = \left(y + 2(-1)\right) (y^2 + 2y + 1) = \left(y + 2(-1)\right) (y + 1)^2
|
-4,602 |
\frac{z \cdot 2 + 14 \cdot (-1)}{z^2 + 2 \cdot z + 15 \cdot (-1)} = -\frac{1}{z + 3 \cdot (-1)} + \frac{3}{5 + z}
|
-20,164 |
(-t\cdot 4 + 5)/(-7)\cdot \dfrac33 = \left(15 - 12\cdot t\right)/(-21)
|
29,500 |
\sqrt{3} + 2 = \frac{1}{\sqrt{3} + (-1)}(1 + \sqrt{3})
|
32,354 |
(x + y)^3 = (x + y) \cdot \left(x + y\right) \cdot \left(x + y\right) = \left(x + y\right) \cdot (x^2 + 2 \cdot x \cdot y + y^2)
|
21,126 |
8\cdot \left(2r \cdot r + 3r + 1\right) + 1 = 16 r^2 + 24 r + 9 = (4r + 3)^2
|
-1,165 |
\frac{1}{9}\cdot 5\cdot (-\frac98) = \dfrac{5\cdot 1/9}{\frac{1}{9}\cdot (-8)}
|
31,971 |
\frac{4}{52} \cdot 3/51 = 12/2652 = \dfrac{1}{221}
|
-11,908 |
\frac{1}{100} \cdot 1.601 = 1.601 \cdot 0.01
|
3,354 |
\dfrac{1}{\sqrt{2\cdot n} + \sqrt{2\cdot n + 2}} = \dfrac{\frac{1}{\sqrt{2\cdot n + 2} - \sqrt{2\cdot n}}}{\sqrt{2\cdot n} + \sqrt{2\cdot n + 2}}\cdot (\sqrt{2\cdot n + 2} - \sqrt{2\cdot n}) = (\sqrt{2\cdot n + 2} - \sqrt{2\cdot n})/2
|
560 |
(-1) + y^3 = (\left(-1\right) + y)*(y^2 + y + 1)
|
24,150 |
0 = m^2 - x \implies m = x^{1 / 2}
|
-18,968 |
\frac{9}{10} = \frac{D_t}{100 \cdot \pi} \cdot 100 \cdot \pi = D_t
|
4,358 |
(n + 2*(-1))! + (n + (-1))! + n! = n * n*(n + 2*(-1))!
|
6,598 |
z^2 - y^2 = 4 \cdot x^5 rightarrow (y + z) \cdot (z - y) = 4 \cdot x^5
|
21,576 |
a \cdot z = \frac12 \cdot (a \cdot z + z \cdot a) = z \cdot a
|
36,858 |
2^{3.14} = 2^{\frac{1}{100} \cdot 314} = \left(2^{314}\right)^{\tfrac{1}{100}}
|
4,850 |
\left(\frac{36}{100} = \frac4z \Rightarrow 400 = 36 \cdot z\right) \Rightarrow z = 11.11
|
26,168 |
x\cdot 2 \gt -x + 3\Longrightarrow 1 < x
|
-23,516 |
0.23\cdot 0.053 = 0.23\cdot 0.23\cdot 0.23 = 0.23 \cdot 0.23 \cdot 0.23
|
2,249 |
\dfrac{1}{(-1) + 1}*(1 + 1) = 2/0
|
5,711 |
b\cdot \lambda + a = b\cdot \lambda + a
|
11,476 |
\left(90 \cdot k = 9 \cdot (x - p) \implies -p + x = 10 \cdot k\right) \implies x = p + 10 \cdot k
|
-27,499 |
30 \cdot n^3 = 3 \cdot n \cdot n \cdot n \cdot 5 \cdot 2
|
11,522 |
2\cdot (-1) + H^3 = (H + 2)\cdot (H^2 - H\cdot 2 + 4) - 2\cdot 5
|
7,375 |
(c + b)/2 + y = \dfrac{1}{2}(c + b + 2y)
|
10,592 |
\frac{1}{99 \cdot 999} \cdot (((-1) + 100) \cdot 717 - 71 \cdot \left(1000 + (-1)\right)) = -\frac{71}{99} + 717/999
|
1,041 |
(g^n)^{12} = 1\Longrightarrow g^n
|
29,085 |
\left(1 + x\right)*\left(1 + x^2 - x\right) = x^3 + 1
|
14,217 |
n\cdot \left(m + 1\right) = n\cdot m + n
|
26,853 |
\sin(\pi/12) = \sqrt{(-\cos\left(\frac{\pi}{6}\right) + 1)/2}
|
14,637 |
\frac{1}{|z|^n + (-1)} = \frac{1}{(|z|^n + (-1)) \cdot |z|^n} + \frac{1}{|z|^n}
|
-3,040 |
-\sqrt{11} + \sqrt{25\cdot 11} = -\sqrt{11} + \sqrt{275}
|
-16,449 |
7 \cdot 4^{\frac{1}{2}} \cdot 7^{\frac{1}{2}} = 7 \cdot 2 \cdot 7^{1 / 2} = 14 \cdot 7^{1 / 2}
|
-10,093 |
0.875 = \frac{1}{8}7
|
37,816 |
0\times 0 = 0^2 = 0
|
-30,909 |
(32 - k)\cdot 470 = (-k + 32)\cdot 470
|
19,157 |
\int\limits_{-\pi}^\pi \sin^2(n \cdot x)\,\mathrm{d}x = \pi = \int\limits_{-\pi}^\pi \cos^2(n \cdot x)\,\mathrm{d}x
|
21,428 |
\frac{\sin\left(\frac{f}{3^k}\right)}{\frac{1}{3^k}} = 3^k \cdot \sin\left(\frac{f}{3^k}\right)
|
-20,893 |
\frac{1}{10 - k} \cdot (-k + 10) \cdot (-\frac12 \cdot 5) = \tfrac{1}{20 - k \cdot 2} \cdot (5 \cdot k + 50 \cdot (-1))
|
20,516 |
\cos{B}\cdot \sin{F} + \cos{F}\cdot \sin{B} = \sin(F + B)
|
2,752 |
(\left(-1\right) + n)/n = \frac{1}{n!} \times \left(-(n + (-1))! + n!\right)
|
30,842 |
\frac{a^2}{2} = a\cdot a/2
|
-5,319 |
10^{4 + 3} \cdot 7.8 = 7.8 \cdot 10^7
|
7,853 |
\tan\left(g\right) = \frac11*\tan(g)
|
-16,061 |
8\times 7\times 6\times 5 = \frac{8!}{(8 + 4\times (-1))!} = 1680
|
30,894 |
\mathbf{R} = \left]-\infty, \infty\right[
|
6,556 |
\left(4/3\right)^3 = \frac{4^3}{3^3} = \dfrac{64}{27}
|
239 |
\frac{1}{{5 \choose 2}}\cdot \frac{1}{2!^2\cdot 3!\cdot 1!^3}\cdot 10! = 15120
|
-12,099 |
1/36 = r/(12*π)*12*π = r
|
7,929 |
\left(3n\right)^2 = n \cdot n\cdot 9
|
-3,988 |
k^2\cdot 35/(k\cdot 30) = 35/30\cdot k^2/k
|
-19,064 |
1/5 = \frac{A_s}{25 \cdot \pi} \cdot 25 \cdot \pi = A_s
|
27,710 |
\frac{x + 1}{(x^2)^{1 / 2}} = \frac{x + 1}{(-1) \cdot x} = -1 - 1/x
|
16,840 |
(-p^2 + p^3)/2 = p^2 \cdot (p + (-1))/2
|
17,164 |
3/6\cdot 4/6/6 = 1/18
|
9,802 |
\frac{1}{-t^l + 1}*\left(1 - t^{2*l}\right) = 1 + t^l
|
32,878 |
(-1) + y^2 = (\left(-1\right) + y)\cdot (1 + y)
|
13,806 |
( t', x')*\left( t, x\right) \coloneqq t'*(-t) + x'*x
|
18,307 |
0 = D^2\Longrightarrow 0 = D
|
12,930 |
\tfrac{\left(-2\right)\cdot \pi}{3} = \pi/3 - \pi
|
25,647 |
300 - 90 + 180 \implies 300 + 280*(-1) = 20
|
-1,617 |
\pi \cdot 19/12 = 43/12 \cdot \pi - 2 \cdot \pi
|
-2,884 |
7^{1/2} = 7^{1/2}\cdot (2 + (-1))
|
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