id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
30,285 |
\operatorname{acos}(0) = \operatorname{acos}\left(\frac{-1^2 + 1}{1^2 + 1}\right)
|
7,255 |
(1 + x^2 - x)\cdot \left(1 + x^2 + x\right) = 1 + x^4 + x \cdot x
|
18,137 |
\frac{12\cdot 3}{2} = 18
|
-24,697 |
\sqrt{42\cdot x^4\cdot b^6} = \sqrt{(x^2)^2\cdot (b^3)^2\cdot 2\cdot 3\cdot 7} = \sqrt{(x^2)^2}\cdot \sqrt{\left(b^3\right)^2}\cdot \sqrt{42} = x^2\cdot b \cdot b \cdot b\cdot \sqrt{42} = x^2\cdot b^3\cdot \sqrt{42}
|
6,490 |
(p^2 + q^2)\cdot \left(x \cdot x + s^2\right) = (p\cdot x + q\cdot s) \cdot (p\cdot x + q\cdot s) + (q\cdot x - p\cdot s) \cdot (q\cdot x - p\cdot s) = \left(p\cdot x - q\cdot s\right)^2 + (p\cdot s + q\cdot x) \cdot (p\cdot s + q\cdot x)
|
-12,937 |
3/21 = \dfrac17
|
12,991 |
4 * 4*2 + 2^2 = 3^2*4
|
9,340 |
\sqrt{(\frac{1}{\sqrt{2}})^2 + (1/\left(\sqrt{2}\right))^2} = \sqrt{\frac{1}{2} + 1/2} = 1
|
-20,345 |
\frac{8 + 4*q}{18*q + 16} = \frac{2}{2}*\dfrac{4 + 2*q}{8 + 9*q}
|
5,162 |
\left(I\times x\right)^2 = I^2\times x = I\times x
|
26,332 |
6 = (1 + 1) \cdot (1 + 2)
|
22,121 |
\frac{1}{6 * 6^2}*(27 + 6*3 + 3) = \frac{48}{216} = 2/9
|
-8,954 |
\dfrac{119.2}{100} = 119.2\%
|
-27,037 |
\sum_{n=1}^\infty \dfrac{(1 + 5)^n}{n\cdot 6^n}\cdot (n + 2) = \sum_{n=1}^\infty \frac{6^n}{n\cdot 6^n}\cdot (n + 2) = \sum_{n=1}^\infty (n + 2)/n
|
25,968 |
z*0.04 = z*4\%
|
11,837 |
\sin(C_2 + C_1) = \sin{C_1}\cdot \cos{C_2} + \sin{C_2}\cdot \cos{C_1}
|
16,628 |
e\cdot y = e\cdot y
|
14,998 |
0 = 3\cdot (8\cdot p^3 - 36\cdot p \cdot p + 42\cdot p + 15\cdot (-1)) - (2\cdot p + 3)\cdot (12\cdot p \cdot p - 36\cdot p + 25) = 76\cdot p + 78\cdot (-1)
|
16,359 |
-\sin{B} \cos{A} + \sin{A} \cos{B} = \sin(-B + A)
|
-3,127 |
\sqrt{13}*3 + \sqrt{13} = \sqrt{13}*\sqrt{9} + \sqrt{13}
|
10,510 |
0 = 2^2 - 4\cdot 1
|
-19,461 |
\frac{1}{2}*7/\left(1/8*9\right) = \frac127*\dfrac198
|
13,034 |
(J + 1)^2 + (-1) = J^2 + J*2
|
-1,637 |
-\pi\cdot 7/6 = -\pi \frac145 + \frac{\pi}{12}
|
-26,546 |
1 + x\cdot 2 + x \cdot x = 1^2 + 2\cdot x + x^2
|
43,922 |
\left(3\cdot 5\cdot 11\right)^2\cdot 61 = 1660725
|
14,326 |
\dfrac13\cdot (1 - h) = \frac13 \Rightarrow h = 0
|
40,076 |
\pi = 3.14 \cdot \dotsm
|
7,787 |
1/(\sqrt{k}) = \frac{1}{\sqrt{k} + \sqrt{k}} 2 \lt \dfrac{2}{\sqrt{k} + \sqrt{k + (-1)}}
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-2,026 |
-\pi\cdot 11/6 + \dfrac16\cdot 11\cdot \pi = 0
|
-6,697 |
7/10 + 5/100 = \frac{1}{100}\cdot 5 + \tfrac{1}{100}\cdot 70
|
32,713 |
3 + \chi^2 + (-1) = 2 + \chi^2
|
-2,455 |
\sqrt{2} \cdot (5 + 3) = 8 \cdot \sqrt{2}
|
7,674 |
x^n + x n x^{n + \left(-1\right)} = x^n + n x^n = \left(n + 1\right) x^n = \left(n + 1\right) x^{n + 1 + (-1)}
|
12,431 |
0 = 0 (-1) = \left(1 - 1\right) (-1) = (-1) - -1 = -1 - -1
|
23,908 |
\sinh^2(y) = \left(e^y - e^{-y}\right)^2/4 = \frac14 (e^{2 y} + e^{-2 y} - 2 e^0)
|
12,926 |
0 = (2 \cdot x + (-1)) \cdot 2 \Rightarrow \frac12 = x
|
29,081 |
0/0 = \dfrac{1}{0}*0 = 1
|
5,473 |
\frac17\cdot 16 = 4\cdot \frac{8}{14}
|
10,589 |
2 \cdot x + (-1) = -\cos(2 \cdot \operatorname{asin}(\sqrt{x})) = 2 \cdot \sin^2(\operatorname{asin}\left(\sqrt{x}\right)) + \left(-1\right) = 2 \cdot x + (-1)
|
-12,548 |
156 + 112 (-1) = 44
|
14,691 |
\left(-1\right) + \cos^2(x)\cdot 2 = \cos\left(x\cdot 2\right)
|
10,378 |
\frac{1}{1! \cdot 0!} \cdot 1! \cdot \frac{3!}{1! \cdot 2!} \cdot \dfrac{7!}{3! \cdot 4!} = \dfrac{7!}{1! \cdot 2! \cdot 4!}
|
-19,425 |
\frac{5\cdot \frac16}{1/4\cdot 9} = \frac49\cdot \frac56
|
13,398 |
-1/2\cdot z + z\cdot 3/4 = z\cdot 1/4
|
-16,892 |
-7 = -7 \cdot (-4 \cdot i) - -35 = 28 \cdot i + 35 = 28 \cdot i + 35
|
46,789 |
793 \cdot 793^2 + 854 \cdot 854 \cdot 854 = 183^4
|
2,823 |
1/\left(x\cdot 5\right) = 1/(5\cdot x)
|
-19,346 |
\frac{9 / 5}{9 \cdot 1/2} \cdot 1 = 9/5 \cdot 2/9
|
-26,222 |
\frac{\text{d}}{\text{d}x} e^{-7\times x^2 + x\times 6} = \left(-x\times 14 + 6\right)\times e^{-x^2\times 7 + 6\times x}
|
-10,123 |
-3/4 = -\dfrac{15}{20}
|
-6,961 |
66 = 11\cdot 2\cdot 3
|
-19,424 |
\dfrac{1}{8}*9/(1/6*7) = 9/8*\frac{1}{7}*6
|
-20,504 |
\tfrac{1}{9 \cdot x + 27 \cdot (-1)} \cdot (-8 \cdot x + 24) = \frac{x + 3 \cdot (-1)}{3 \cdot (-1) + x} \cdot (-8/9)
|
-6,969 |
48 = 2\cdot 4\cdot 6
|
-11,468 |
8\cdot i + 0 + 6\cdot (-1) = -6 + i\cdot 8
|
-18,309 |
\frac{k}{(7 \cdot (-1) + k) \cdot (2 \cdot (-1) + k)} \cdot (k + 7 \cdot (-1)) = \frac{-7 \cdot k + k^2}{k^2 - 9 \cdot k + 14}
|
-8,536 |
\frac{8}{12} - 2/4 = \tfrac{8}{12} - 2*3/\left(4*3\right) = \frac{1}{12}*8 - \frac{6}{12} = (8 + 6*(-1))/12 = \frac{2}{12}
|
5,588 |
10 \cdot h^2 - 7 \cdot f \cdot h + f^2 = (f - h \cdot 5) \cdot (f - h \cdot 2)
|
5,380 |
a^{m + (-1)} \cdot a = a^m
|
5,149 |
1/z - \frac1x = \frac{x - z}{z \cdot x}
|
10,851 |
\sqrt{n} = n^{1/2} = n^{1 - \frac12} = \frac{n}{n^{\frac12}}
|
21,614 |
(5\cdot w + \left(-1\right))^2 = 25\cdot w \cdot w - w\cdot 10 + 1
|
29,238 |
\dfrac{m + 1}{m^{s \cdot 2}} = \dfrac{1}{m^{2 \cdot s}} + \frac{1}{m^{2 \cdot s}} \cdot m
|
20,269 |
(i + 1)! = i! \cdot (i + 1) \lt 2^i \cdot \left(i + 1\right)
|
-4,461 |
-\frac{1}{y + 3*\left(-1\right)}*2 - \tfrac{3}{y + 4} = \dfrac{-y*5 + 1}{12*(-1) + y^2 + y}
|
338 |
l = 2*l/2 = (2*l + 1)/2
|
18,798 |
3 = 3 * 3 * 3/3 - 2*3
|
-4,703 |
-\dfrac{4}{(-1) + z} - \frac{1}{2(-1) + z} = \frac{1}{2 + z^2 - 3z}(9 - 5z)
|
14,544 |
x^5 - 10\cdot x + 12 = 12 + (-2\cdot x + x^2 \cdot x)\cdot (2 + x^2) - 6\cdot x
|
17,074 |
17^2 + 5^2 + 7^2 + 11 \cdot 11 + 13^2 = 653
|
-26,061 |
\frac15*(-2 - 16*i + i + 8*(-1)) = (-10 - 15*i)/5 = -2 - 3*i
|
30,270 |
1 + 2^{10} = (1 + 2 \cdot 2)\cdot (1 + 2^8 - 2^6 + 2^4 - 2^2)
|
21,522 |
\frac{\partial}{\partial z} z^k = z^{(-1) + k}\cdot k
|
1,659 |
\cos{x \cdot 2} = 2 \cdot \cos^2{x} + (-1)\Longrightarrow \cos^2{x} = (\cos{2 \cdot x} + 1)/2
|
15,794 |
15^2 + 20^2 = 25 \cdot 25 = 7 \cdot 7 + 24 \cdot 24
|
24,667 |
\mathbb{E}\left[X \cdot X\right] = \mathbb{E}\left[X\right] \mathbb{E}\left[X\right]
|
-10,441 |
-\frac{10}{9*(-1) + 3*t}*2/2 = -\frac{20}{18*(-1) + 6*t}
|
32,918 |
20/3 = \dfrac{5}{3}\cdot 4
|
10,106 |
(4\cdot n + n^2\cdot 4)/4 = n^2 + n
|
-16,518 |
6\cdot \sqrt{25}\cdot \sqrt{11} = 6\cdot 5\cdot \sqrt{11} = 30\cdot \sqrt{11}
|
-7,846 |
\frac15 \cdot (-11 - 3 \cdot i - 22 \cdot i + 6) = \frac15 \cdot (-5 - 25 \cdot i) = -1 - 5 \cdot i
|
-13,078 |
-1.6384 \div 0.04 = -40.96
|
-26,556 |
\left(x + 1\right)^2 = x^2 + 1^2 + x \cdot 2
|
22,153 |
\frac{1}{(-y + 1)^3} = (1 + y + y^2 + \cdots)^3
|
13,309 |
a^2 - x^2 = \left(-x + a\right)\cdot \left(x + a\right)
|
34,793 |
20 = \frac{5!}{3!\times 1!\times 1!}
|
14,621 |
(-3*17 + 60)*2 + 17 (-1) = 2*60 - 7*17
|
-3,859 |
d^2/2 = \frac{d^2}{2}
|
-19,272 |
5/3 \cdot 6/7 = \frac{\frac{5}{3}}{\frac{1}{6} \cdot 7} \cdot 1
|
31,355 |
\cos{π \cdot 4/5} = \cos{\dfrac15 \cdot π \cdot 6}
|
45,807 |
\dfrac{5}{14}*56 = 20
|
36,914 |
u = 1/u
|
24,629 |
m + n + \left(-1\right) = 2 + m + (-1) + n + 2*(-1)
|
34,643 |
r + l/x = \left(x \times r + l\right)/x
|
6,204 |
0.3 = \dfrac{0.4\cdot 0.3}{0.4}
|
5,842 |
\frac{1}{10} \cdot (100 + 110 + 120 + 130 + ... + 190) = 145
|
22,611 |
7(2*4 + (-1)) * (2*4 + (-1)) = 2\left((-1) + 2*7\right)^2 + \left(2 + (-1)\right)^2*5
|
35,509 |
3 \cdot \frac{1}{6} \cdot 5 = 15/6 = 5/2
|
15,148 |
2 \times x_0 = x_0 - -x_0
|
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