id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-18,665 |
2\cdot n + 2 = 6\cdot \left(n + 3\right) = 6\cdot n + 18
|
-9,598 |
0.01 (-37) = -37.5/100 = -3/8
|
20,841 |
0 = c_1 - 1/2 + 5/2\Longrightarrow c_1 = -2
|
15,429 |
\left(u \cdot 3 - v\right)^2 + (-v + 3 \cdot u) \cdot (-u + v) - \left(v - u\right)^2 = -v^2 + 5 \cdot u^2
|
33,863 |
(1 + 1/n)^n*(1 - \frac{1}{n})^n = \left(1 - \frac{1}{n^2}\right)^n \gt 1 - \frac{1}{n}
|
14,491 |
\frac{2^9\cdot 66}{2^{12}} = 8.25
|
2,169 |
Y\cdot F\cdot t = t\cdot F\cdot Y
|
-4,797 |
1\cdot 10^4 = 1.0\cdot 10^{(-1)\cdot (-1) + 3}
|
-9,371 |
-n \times 2 \times 2 \times 2 = -8 \times n
|
7,970 |
\left((-1) + x\right)^3 = x \cdot x^2 - 1 + x \cdot 3 - 3 \cdot x \cdot x
|
22,539 |
s z - s \cdot 2 = 5 \left(-1\right) + 2 z + t \Rightarrow -s \cdot 2 - t + 5 = (s + 2 (-1)) z
|
28,472 |
|\rho_1| = |\rho_2| = q \Rightarrow q = |\rho_2\cdot \rho_1|
|
-22,768 |
36/60 = \frac{3}{5\cdot 12}\cdot 12
|
1,162 |
(2\cdot \left(5\cdot x + 2\right))^2 + 2\cdot (5\cdot x + 2) = 100\cdot x \cdot x + 80\cdot x + 16 + 10\cdot x + 4 = 10\cdot (10\cdot x^2 + 9\cdot x + 20)
|
31,502 |
\frac1y\times (y \times y + y) = 1 + y
|
8,356 |
-(-g + b) = g - b
|
-4,382 |
\frac{z^2}{z^5} = \frac{z \cdot z}{z \cdot z \cdot z \cdot z \cdot z} = \frac{1}{z^3}
|
25,121 |
2 - 9 \cdot y^7 + 7 \cdot y^9 = \left(1 - y\right)^2 \cdot (2 + 4 \cdot y + 6 \cdot y^2 + 8 \cdot y^3 + 10 \cdot y^4 + 12 \cdot y^5 + 14 \cdot y^6 + 7 \cdot y^7) \approx 63 \cdot (1 - y)^2
|
-1,738 |
\frac34*\pi = \pi*4/3 - \pi*\dfrac{7}{12}
|
18,795 |
l \cdot x^{l + \left(-1\right)} = \frac{\partial}{\partial x} x^l
|
20,353 |
5^2\cdot 6 \cdot 6\cdot 8\cdot 7 = 50400
|
32,071 |
60 = \dfrac{1}{2! \cdot 3!} 6!
|
-6,682 |
9/100 + \frac{1}{100}\times 20 = \frac{9}{100} + 2/10
|
-4,127 |
\frac18 \cdot 7 = \tfrac{7}{8}
|
-4,654 |
-\frac{1}{y + 2}3 - \frac{1}{y + 1}3 = \dfrac{-6y + 9(-1)}{y * y + 3y + 2}
|
23,623 |
367 \cdot (-1) + 3120 = 2753
|
3,751 |
y + 8 - 6*\sqrt{y + \left(-1\right)} = y + (-1) - 6*\sqrt{y + \left(-1\right)} + 9 = (\sqrt{y + \left(-1\right)} + 3*(-1))^2 = \left(3 - \sqrt{y + (-1)}\right)^2
|
44,277 |
\left(4^2\cdot 8 - 2^2\cdot 2\cdot 3\right)\cdot \frac{\pi}{3} = \pi\cdot 104/3
|
34,879 |
(a - x)/4 = -x/4 + \frac{1}{4} \cdot a
|
6,313 |
t + q + (-1) = -((-1) + q) \cdot (\left(-1\right) + t) + q \cdot t
|
12,046 |
\frac{76!}{76! - 75!} = \dfrac{76*75!}{75! (76 + (-1))} = 76/75
|
21,419 |
16 = (3 + 1) \cdot (3 + 1)
|
231 |
x\cdot 2 + \omega = \frac{1}{\omega}\cdot ((x + \omega) \cdot (x + \omega) - x^2)
|
22,585 |
h^{f \cdot g} = (h^f)^g = (h^g)^f
|
-22,907 |
5*3/(5*5) = \frac{15}{25}
|
8,283 |
a \cdot b = \frac{1}{\dfrac{1}{a \cdot b}} = \tfrac{1}{1/a \cdot \frac1b} = \frac{1}{\frac{1}{b} \cdot 1/a} = b \cdot a
|
15,516 |
e^y*e^x = e^{x + y}
|
25,872 |
0 = w\cdot u\cdot w = w\cdot \left(c\cdot u + b\cdot w\right) = c\cdot u\cdot w + b\cdot |w|^2
|
27,057 |
\frac{1}{e^{(-1) \times \left((-2) \times 1.0 \times 10^{-10}\right) \times 1000}} \times 2 = 2 \times 0.999999 = 1.99999
|
52 |
\dfrac{x}{40}\cdot 40 = x\cdot \frac{1}{40}\cdot 40 = x = x
|
19,857 |
\alpha * \alpha \beta^2 = \alpha^2 \beta * \beta
|
-6,928 |
24 = 2*4*3
|
18,416 |
\sin(4\left(y + \pi\right)) = \sin(y*4)
|
3,571 |
1 + \alpha^4 = 1 + 2\cdot \alpha^2 + \alpha^4 - 2\cdot \alpha \cdot \alpha = (1 + \alpha^2)^2 - (\sqrt{2}\cdot \alpha)^2
|
35,503 |
\frac{1}{1 + x^2}\cdot \left(x^6 + 1\right) = x^4 - x^2 + 1
|
-11,742 |
(\frac198)^2 = 64/81
|
11,884 |
1 + y + 2*y^2 + 3*y^3 + \cdots = 1 + \frac{1}{(-y + 1)^2}*y
|
15,413 |
\binom{x_1 + x_2}{x_1} = \frac{1}{x_1! \cdot x_2!} \cdot (x_1 + x_2)!
|
19,664 |
b_n^{m + (-1)}\cdot b_{(-1) + n}\cdot a_m\cdot m = a_m\cdot b_{n + (-1)}\cdot b_n^{\left(-1\right) + m}\cdot {m \choose 1}
|
-9,188 |
-24*i + 20 = -2*2*2*3*i + 2*2*5
|
18,132 |
|\Re{(x)}| \leq |x|\Longrightarrow 0 \leq -\left(\Re{(x)}\right)^2 + |x|^2
|
-18,385 |
\frac{a\times (a + 6)}{(a + 7\times (-1))\times \left(6 + a\right)} = \frac{1}{a^2 - a + 42\times (-1)}\times (a^2 + 6\times a)
|
3,339 |
\mathbb{E}\left[Bv\right] = B^2 v = Bv = Bv
|
17,214 |
4^2/12 = 16/12 = 4/3
|
19,950 |
J\cdot 3\cdot i = i\cdot 3\cdot J
|
-17,720 |
10 = 12 + 2*(-1)
|
23,971 |
\frac{-X^{m + 1} + 1}{-X + 1} = 1 + X + X \cdot X + ... + X^m
|
15,760 |
\frac{1}{2} = \dfrac{1}{24}\cdot 12
|
20,999 |
\sqrt{z}\cdot e^{z\cdot 3} = \frac{\sqrt{z}}{e^{-z\cdot 3}}
|
204 |
x \cdot x \cdot 9 = (x \cdot 3) \cdot (x \cdot 3)
|
-20,311 |
\tfrac{1}{7}*(x + 4)*\frac{1}{5}*5 = \frac{1}{35}*\left(20 + x*5\right)
|
11,002 |
1 + y + y^2 + \dots = \dfrac{1}{-y + 1}
|
-8,428 |
8 = \left(-1\right)\cdot (-8)
|
17,118 |
\left(k + (-1)\right)\cdot \left(k + 1\right) = k^2 + (-1)
|
-16,026 |
46/10 = 10\cdot 7/10 - 8\cdot \frac{1}{10}3
|
33,866 |
K \cdot 9 = K \cdot 25 = K
|
2,136 |
z^4 - N^4 = (z^2 + N * N) (z^2 - N^2)
|
6,311 |
\sin(v+w) = \sin(v)\cos(w)+\cos(v)\sin(w)
|
1,678 |
(p - z*2) * (p - z*2) = p^2 - 4*p*z + 4*z^2
|
17,071 |
\dfrac{1}{2 \left(-1\right) + 1} = -1
|
19,964 |
x^2 + x^2 + 1 = x x + x + x + x x = x^2 + x + x + x^2 + 1
|
28,232 |
\left(z^m + a^m \Leftrightarrow a + z = 0\right) \Rightarrow 0 = z^m + a^m
|
-11,613 |
0 + 20*(-1) + i*20 = -20 + 20*i
|
19,922 |
40/7 = 5 + \tfrac{5}{7}
|
20,302 |
n!/i! = {n \choose i}*\left(n - i\right)!
|
1,310 |
\frac{1}{x + \left(-1\right)} \cdot (x \cdot x + (-1)) = \frac{1}{x + \left(-1\right)} \cdot \left(x + 1\right) \cdot \left(x + \left(-1\right)\right) = x + 1
|
4,216 |
c^2\cdot d = d = d\cdot c \cdot c
|
7,670 |
-(i + (-1)) + k + 2\cdot (-1) = k + 2\cdot \left(-1\right) - i + 1
|
41,341 |
-\sin(z) = \sin\left(\pi + z\right)
|
5,288 |
1 + 3 + \cdots + 2 \cdot n + (-1) + 2 \cdot (n + 1) + (-1) = n^2 + 2 \cdot n + 1 = (n + 1) \cdot (n + 1)
|
-2,444 |
(2 + 3 + 4)\times \sqrt{7} = 9\times \sqrt{7}
|
-4,482 |
(2*(-1) + x)*(3*(-1) + x) = x^2 - 5*x + 6
|
-6,132 |
\frac{1}{2*\varphi + 20*\left(-1\right)}*3 = \frac{1}{2*(10*(-1) + \varphi)}*3
|
31,397 |
x/x = x\cdot x/x/x = (\frac{x}{x})^2
|
16,663 |
{6 \choose 3}*{3 \choose 2}*{2 \choose 1}*{3 \choose 1} = 6*5*4*3
|
9,936 |
(8 + 1)\cdot (1 + 4)\cdot (1 + 1)\cdot (1 + 1)\cdot \left(1 + 1\right) = 360
|
12,312 |
d\cdot x\cdot E^2 = d\cdot E^2\cdot x
|
-16,360 |
8*16^{1 / 2}*5^{1 / 2} = 8*4*5^{\dfrac{1}{2}} = 32*5^{1 / 2}
|
23,222 |
a^U \cdot x^l = x^l \cdot a^U
|
23,424 |
10 = (1 + 1)\cdot (1 + 4)
|
11,103 |
(10 + (-1))/3 = (18 + 3\cdot (-1))/5 = \left(2 + 26\cdot (-1)\right)/(-8)
|
15,745 |
B \cdot Y = x\Longrightarrow x = B \cdot Y
|
28,296 |
\overline{M} + \overline{z} = \overline{M + z}
|
9,485 |
4^k \frac{2}{k + 2} = \frac{1}{k + 2} 2^{1 + k\cdot 2}
|
-5,904 |
\dfrac{5}{(p + 3\times (-1))\times (p + 2\times (-1))} = \frac{5}{6 + p \times p - p\times 5}
|
8,946 |
2^{1 + k} + 2*(-1) = (2^k + (-1))*2
|
13,260 |
(y^6)^{36} + \left(-1\right) = \left(-1\right) + y^{216}
|
-22,294 |
(7 (-1) + a) (9 (-1) + a) = a^2 - 16 a + 63
|
7,006 |
4 + x^2 - 4*x = \left(x + 2*(-1)\right)^2
|
-1,951 |
-π/6 + \frac{π}{12} = -π/12
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.