id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-5,498 |
\frac{5}{q^2 - 8q + 9\left(-1\right)}q = \frac{5}{(q + 9(-1)) \left(1 + q\right)}q
|
-1,770 |
-\frac{1}{3}\pi + \pi \tfrac{11}{6} = \pi \dfrac{3}{2}
|
-7,013 |
2 \times 10^{-1}/9 = \frac{1}{45}
|
33,160 |
A = (Y \cap A) \cup (Y' \cap A) = (Y \cup Y') \cap A
|
-24,449 |
4 + \tfrac{60}{10} = 4 + 6 = 10
|
299 |
\dfrac{1}{n}\cdot (n + 1) = 1/n + 1
|
-17,787 |
80 + 13 \cdot (-1) = 67
|
9,621 |
(x + 1) \cdot \left(x + \left(-1\right)\right) = \left(-1\right) + x \cdot x
|
-2,677 |
6^{1/2} = 6^{1/2}*(2 + 4*(-1) + 3)
|
3,952 |
99 = 11*9 = (3 * 3 + 2*1^2)*3 * 3 = (3^2 + 2*1^2) (1 * 1 + 2*2^2)
|
-12,018 |
\frac{19}{24} = \frac{1}{12 \cdot \pi} \cdot s \cdot 12 \cdot \pi = s
|
21,994 |
\dfrac{\sin\left(x\right)}{1 + \sin(x)} = \dfrac{1}{\sin(x) + 1}(1 + \sin(x) + (-1)) = 1 - \dfrac{1}{1 + \sin\left(x\right)}
|
-1,294 |
6/12 = \frac{6*\frac16}{12*\frac16} = 1/2
|
35,053 |
1328 = 3^6 \cdot 2 + 2 \cdot (-1) - 2^7
|
10,635 |
(\sin(\frac12 \cdot x) + \cos\left(x/2\right))^2 = 1 + 2 \cdot \sin\left(x/2\right) \cdot \cos(\frac12 \cdot x) = 1 + \sin(x)
|
-19,253 |
\tfrac{8}{15} = A_s/(100\cdot \pi)\cdot 100\cdot \pi = A_s
|
7,884 |
v_1 \cdot x_2 \cdot x_1 = v_1 \cdot x_1 \cdot x_2
|
-29,432 |
\frac{39}{44} = 3*13/(11*4)
|
31,607 |
60 = 3\cdot 17 + 9\Longrightarrow 60 - 3\cdot 17 = 9
|
-30,620 |
(3 + x^2) \cdot 4 = 12 + x^2 \cdot 4
|
37,932 |
58261 = 7 * 7*29*41
|
32,505 |
-\sqrt{3} + 2 = (\left(\sqrt{3} - 1\right)/\left(\sqrt{2}\right))^2
|
24,364 |
\left(1 + x\right)^{m_1}*(1 + x)^{m_2} = (x + 1)^{m_1 + m_2}
|
28,714 |
\frac{1}{f_2\cdot f_1} = 1/\left(f_1\cdot f_2\right)
|
4,192 |
\sin{\vartheta} = 1/\csc{\vartheta}
|
13,299 |
\left(-f + h\right) (h \cdot h + fh + f^2) = -f^3 + h^3
|
20,099 |
\left(x_1 + x_2\right)^2 - 2*x_1*x_2 = x_2^2 + x_1^2
|
-19,015 |
\frac{1}{20} \cdot 3 = \frac{A_s}{16 \cdot \pi} \cdot 16 \cdot \pi = A_s
|
-27,506 |
21*x^2 = 3*x*x*7
|
20,984 |
\frac{a x}{a + x} 1 = a - \frac{a^2}{a + x} = x - \tfrac{1}{a + x} x^2
|
-25,816 |
\frac{5}{6*3}*1 = \frac{5}{18}
|
9,083 |
e^{-i\cdot x} = (e^{i\cdot x})^{-1}
|
30,087 |
p \cdot x^W = p \cdot x^W
|
17,357 |
f*\tau = f*\tau
|
-598 |
e^{\frac{i}{12} \cdot \pi \cdot 15} = (e^{i \cdot \pi/12})^{15}
|
2,545 |
v - \dfrac{1}{2}*(v + 1) = ((-1) + v)/2
|
15,251 |
{20 \choose 2}^{10} = {20 \choose 2} {20 \choose 2} \ldots {20 \choose 2}
|
27,277 |
3^{4 n + 3} = 3^3 (10 + (-1))^{2 n} = 3^3 \left(1 + 10 \left(-1\right)\right)^{2 n}
|
-1,634 |
-\frac{3}{4} \cdot \pi = -\pi \cdot 7/4 + \pi
|
51,561 |
9825757^4 - 2104527924 \times 2104527924 \times 2104527924 = -137318688623
|
-1,500 |
-\dfrac{1}{9}4 \left(-\frac{1}{8}9\right) = \frac{(-9)\cdot 1/8}{\frac{1}{4} (-9)}
|
-11,602 |
22*i - 7 = 8 + 15*(-1) + 22*i
|
14,618 |
\frac{1^k + 1^k}{1 + 1} = 1^{k + (-1)}
|
24,492 |
\mathbb{E}(T Y) = \mathbb{E}(T) \mathbb{E}(Y)
|
18,662 |
a^{x + f} = a^f\times a^x
|
6,402 |
1 \leq 4\cdot x \lt 2\Longrightarrow 1 + x\cdot 4 = x\cdot 4
|
-9,360 |
60\cdot o = 2\cdot 2\cdot 3\cdot 5\cdot o
|
23,125 |
y/y = 1 = \frac{y}{y}
|
17,633 |
p^n = p^{(-1) + n} \times p
|
26,595 |
(-2 + (4 + 30)^{\dfrac{1}{2}})/2 = -1 + \dfrac{34^{\frac{1}{2}}}{2}
|
-25,049 |
\frac{5}{13}*4/12 = 20/156 = \tfrac{5}{39}
|
11,239 |
(b^{j_1})^{j_2} = b^{j_1 j_2} = b^{j_2 j_1}
|
31,435 |
\sin(z + \dfrac{1}{2}*\pi) = \cos(z)
|
-10,646 |
3/3*\frac{6}{5*\rho + 15} = \dfrac{18}{\rho*15 + 45}
|
1,914 |
fz^{-x + i} = z^{i - x} f
|
5,804 |
(y^2 + y*5 + 6)^{\frac{1}{2}} = (\left(y + 3\right)*(2 + y))^{\dfrac{1}{2}}
|
-2,607 |
-7^{1 / 2} \cdot 3 + 5 \cdot 7^{\frac{1}{2}} + 7^{1 / 2} \cdot 4 = 25^{\frac{1}{2}} \cdot 7^{\frac{1}{2}} + 16^{\frac{1}{2}} \cdot 7^{\frac{1}{2}} - 9^{\frac{1}{2}} \cdot 7^{\tfrac{1}{2}}
|
22,068 |
(4\cdot (-1) + 8)^2 + (5\cdot (-1) + 7) \cdot (5\cdot (-1) + 7) = 20
|
20,316 |
0 = (-1 - -1) + \left(0 - -1\right)*0
|
6,892 |
-3\cdot a\cdot h\cdot f + a^3 + f^3 + h^3 = \left(a \cdot a + f^2 + h \cdot h - a\cdot f - f\cdot h - h\cdot a\right)\cdot (h + a + f)
|
15,929 |
{6 \choose 2}*4! = \frac{6!}{2!*4!}*4! = \frac{6!}{2!} = 360
|
32,115 |
3 (-1) + 45 + 6 (-1) + 3 \left(-1\right) = 33
|
42,958 |
1 + 2 + 3 + \cdots + 6 = 21
|
33,196 |
i\times (i + (-1))! = i!
|
21,199 |
c^{t + s} = c^s c^t
|
7,745 |
\int \frac{1}{y}\,dy = \int 1/y\,dy
|
-3,269 |
3\cdot \sqrt{6} + 4\cdot \sqrt{6} = \sqrt{6}\cdot \sqrt{9} + \sqrt{6}\cdot \sqrt{16}
|
19,526 |
23 + c^2 = (c + 1) (c + (-1)) + 24
|
-5,539 |
\frac{1}{2 (k + 9)} = \frac{1}{2 k + 18}
|
41,840 |
3^{560}=81^{140}=(140*80*1+1)
|
11,242 |
9/48 + \frac{3}{54} = 3/16 + 1/18 = \dotsm
|
31,107 |
\tfrac13 + 1*\frac13*2/2 = \frac23
|
7,532 |
(-1) + 2^{2 \cdot m} = \left(1 + 2^m\right) \cdot (2^m + (-1))
|
3,666 |
p = y + 2 \Rightarrow y = p + 2\cdot (-1)
|
8,204 |
-3 \cdot r^2 + r \cdot 12 + 40 = (6 \cdot \left(-1\right) + r)^2 - ((-1) + r^2 - 6 \cdot r) \cdot 4
|
20,697 |
\arccos(\cos(\pi - \arccos{t})) = \arccos{-t} \Rightarrow \arccos{-t} = \pi - \arccos{t}
|
36,669 |
2^{1/2} = \dfrac{7 \cdot 1/5}{\left(-1/50 + 1\right)^{1/2}}
|
-5,490 |
\frac{6}{(q + 2) \cdot (7 + q) \cdot 2} = \tfrac12 \cdot 2 \cdot \dfrac{3}{\left(7 + q\right) \cdot (2 + q)}
|
11,020 |
z^2 + y^2 - z*2 - 2by + 8(-1) = 0 \Rightarrow \sqrt{b^2 + 9} * \sqrt{b^2 + 9} = (z + (-1))^2 + (-b + y)^2
|
-444 |
(e^{\pi\cdot i\cdot 7/12})^{15} = e^{15\cdot \frac{7}{12}\cdot \pi\cdot i}
|
14,505 |
216 = 6^3 = 2^3 \cdot 3 \cdot 3^2
|
10,305 |
\left(b\cdot a = b + a \implies 0 = -b + a\cdot b - a\right) \implies (a + (-1))\cdot (b + (-1)) = 1
|
19,927 |
(r + h)^2 = r^2 + 2 \cdot h \cdot r + h^2
|
931 |
y*e^y = x \Rightarrow e^{-y}*x = y
|
-1,820 |
\pi \cdot \dfrac{13}{6} = \pi/4 + \pi \cdot 23/12
|
30,271 |
(z + (-1)) (1 + z^2 + z) = z^3 + (-1)
|
34,793 |
20 = \frac{5!}{3!\cdot 1!\cdot 1!}
|
34,697 |
l/2 \leq k \Rightarrow \frac{l}{2} \geq l - k
|
-21,126 |
\frac{2*\frac12}{2} = 2/4
|
17,497 |
\dfrac12 = 99/100 \cdot \frac{1}{99} \cdot 49 + 1/100
|
-20,802 |
\frac{k \cdot 10 + 9}{k \cdot 10 + 9} \cdot 4/1 = \frac{40 \cdot k + 36}{10 \cdot k + 9}
|
-11,986 |
\dfrac{29}{30} = \dfrac{s}{10 \cdot \pi} \cdot 10 \cdot \pi = s
|
34 |
\lambda^{32} = \lambda^{16}\cdot \lambda^{16}
|
8,449 |
\int (-y^{\frac{3}{2}} + y^{1/2})\,\mathrm{d}y = \int \sqrt{y}\cdot (1 - y)\,\mathrm{d}y
|
12,864 |
\dfrac{1}{\dfrac{1}{\alpha}} = \alpha
|
24,242 |
1007 = \frac12 \cdot (2013 + 1)
|
-3,884 |
\dfrac{1}{y^5}*y^2*\frac39 = \dfrac{3}{9*y^5}*y^2
|
-20,001 |
\frac99*\frac{1}{6(-1) + x*10}9 = \frac{81}{x*90 + 54 (-1)}
|
-13,629 |
\frac{20}{2 + 8} = 20/10 = 20/10 = 2
|
8,479 |
-39 = 14 \cdot (-1) + (-25)
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.