id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
---|---|
16,035 | -6/5 + \tfrac43 = \dfrac{1}{15}\cdot 2 |
11,392 | (c - f) (f + c) = -f f + c c |
-26,459 | \left(3 \cdot z\right)^2 = z \cdot z \cdot 9 |
10,386 | (a + f)/6 = (f + c)/7 = \frac{1}{8}\cdot (c + a) = \dfrac{1}{6 + 7 + 8}\cdot (a + f + f + c + c + a) = (a + f + c)/10.5 |
23,427 | 4\cdot 3/2 = 1 + 2 + 3 |
32,468 | \sin{x} \lt 0 rightarrow \sin{x} = -\frac{3}{\sqrt{13}} |
29,822 | \sin{w} = 2\cdot \cos{w/2}\cdot \sin{\frac{w}{2}} |
8,616 | \frac{x}{g} = \tfrac{x}{g} |
9,774 | 1 = y \cdot \frac{1}{z} \cdot y^2 \cdot z^2 = y \cdot z \cdot y^4 \cdot z \cdot y/z = y \cdot \frac{z}{z} \cdot z \cdot y^{16} \cdot y = z \cdot y^{21} |
12,953 | 11\cdot (10 + z) = z + 160 \Rightarrow 160 + z = 110 + z\cdot 11 |
-5,309 | 0.45\cdot 10^{\left(-1\right)\cdot (-1) + 5} = 0.45\cdot 10^6 |
30,968 | \operatorname{asec}(2) = \pi/3 |
33,988 | 10 + 140 - 50 + 30 \implies 70 = 10 + 60 |
33,912 | -\cos{Z}*\sin{C} + \cos{C}*\sin{Z} = \sin(-C + Z) |
19,339 | 1/6 = 1/6\cdot 2/2 |
19,671 | \sum_{k=1}^n (-k! + (k + 1)!) = \sum_{k=1}^n (1 + k)! - \sum_{k=1}^n k! |
22,161 | 0 = (1 - \tfrac{1}{a\cdot c})\cdot \left(c - a\right) = \dfrac{1}{a\cdot c}\cdot (c - a)\cdot \left(a\cdot c + \left(-1\right)\right) |
-20,896 | \frac{1}{10}\times 3\times \left(-2/(-2)\right) = -6/(-20) |
22,600 | (L + 1)/3 = L \implies \tfrac12 = L |
6,234 | (2/l + 1)^{3l} = ((1 + 2/l)^l)^3 |
7,508 | \left(x + Y\right)\cdot v = x\cdot v + Y\cdot v |
20,059 | -\sin{x} = \cos(\pi/2 + x) |
-16,498 | \sqrt{175}*2 = \sqrt{25*7}*2 |
-24,443 | 9 + 6\cdot 8 = 9 + 48 = 9 + 48 = 57 |
34,432 | \dfrac{1}{1 - \frac{b}{y}} \cdot (\frac{1}{y} \cdot b + 1) = \frac{1}{y - b} \cdot (y + b) |
10,643 | |b_n a_n - LM| = |b_n a_n - a_n M + a_n M - LM| |
-7,532 | \frac{1}{3}\cdot (-12\cdot i + 6) = -i\cdot 12/3 + \frac13\cdot 6 |
31,375 | 0 = \frac{4}{a^3} + \tfrac{2}{a} - \frac{1}{a^2} \cdot b = \frac{1}{a^3} \cdot \left(4 + 2 \cdot a^2 - b \cdot a\right) |
28,900 | 3^{n + 1} + (-1) = 3\cdot 3^n + (-1) = 2\cdot 3^n + 3^n + \left(-1\right) |
8,570 | -3^{1/2}/3 + 1 = 1 - \frac{1}{3^{1/2}} |
51,853 | 6 \Rightarrow 1 |
6,661 | v \cdot 2 \cdot 3 \cdot u = u \cdot v \cdot 6 |
1,445 | j^2 + j + 1 = 0 \Rightarrow -j = 1 + j^2 |
27,754 | r^i\cdot q\cdot r^j = q\cdot r^i\cdot r^j |
4,313 | 26*1/9/(13*1/9) = 2 = Y \Rightarrow 2 = Y |
-2,110 | -\frac{5}{3} \pi + \pi*17/12 = -\frac{\pi}{4} |
17,186 | 1 - u^2 = \left(1 - u\right) \left(u + 1\right) |
-18,369 | \frac{1}{t^2 + 10 t}\left(t^2 + t + 90 \left(-1\right)\right) = \frac{1}{(10 + t) t}(9(-1) + t) (t + 10) |
14,025 | (7 + n) \cdot \binom{n + 6}{n} = \binom{7 + n}{n} \cdot 7 |
-22,283 | y^2 - 3y - 70 = (y + 7)(y - 10) |
-25,510 | \frac{d}{dx} (\dfrac{4}{x + 2}) = -\dfrac{4}{(2 + x)^2} |
2,272 | s_n - s \lt \epsilon \Rightarrow s_n < \epsilon + s |
-9,211 | 2\cdot 5\cdot 11 - 3\cdot 3\cdot 11 l = -99 l + 110 |
44,392 | \cos(\pi - \theta) = -\cos\left(-\theta\right) = -\cos\left(\theta\right) |
14,466 | \frac{f_1}{f_1 - f_2} = \tfrac{0(-1) + f_1}{f_1 - f_2} |
10,364 | 0 = y^p + (-1) = (y + \left(-1\right))^p |
19,674 | a^2 - b*a*2 + b * b = (-b + a)^2 |
-28,950 | (3 + n)*(3*\left(-1\right) + n) = 9*(-1) + n^2 |
-6,023 | \frac{2}{(5 \cdot \left(-1\right) + n) \cdot (10 + n)} = \dfrac{2}{n^2 + 5 \cdot n + 50 \cdot (-1)} |
547 | -\frac{1}{5}2 = -\frac{2}{5} |
32,606 | x\cdot \tau = x\cdot \tau |
6,836 | \tfrac{1}{\beta \cdot x} = \frac{1}{x \cdot \beta} |
30,036 | \frac{1}{d^2} \cdot x^2 = r rightarrow x^2 = d^2 \cdot r |
18,920 | (e/2)^n = e^n\cdot (\frac12)^n |
16,601 | a^{g + c} = a^c*a^g |
12,637 | 6\cdot 5^m + 6\cdot (-1) - 5^m + 5 = \left(-1\right) + (6 + \left(-1\right))\cdot 5^m |
-20,614 | \frac{-q \times 21 + 49 \times (-1)}{28 \times (-1) - q \times 12} = \frac{1}{-3 \times q + 7 \times (-1)} \times (-q \times 3 + 7 \times \left(-1\right)) \times 7/4 |
39,091 | 800 = 6400*13\% |
-764 | 0 + \dfrac{6}{10} + 5/100 + 9/1000 + \frac{1}{10000}\cdot 0 = 6590/10000 |
-20,157 | \dfrac{z + 8}{z + 8}\cdot (-\tfrac{1}{10}\cdot 7) = \frac{56\cdot (-1) - 7\cdot z}{80 + 10\cdot z} |
40,729 | -(x - y) = -x + y |
-5,098 | \frac{6.5}{10000} = 6.5/10000 |
-10,277 | 30 = 10 t + 16 + 50 (-1) = 10 t + 34 (-1) |
30,362 | (-t + 1) \cdot (1 + t) = 1 - t^2 |
-29,363 | (y + 4) \cdot (y + 6) = y^2 + 6 \cdot y + 4 \cdot y + 24 = y^2 + 10 \cdot y + 24 |
10,592 | \frac{717}{999} - 71/99 = (717\cdot ((-1) + 100) - (1000 + (-1))\cdot 71)/(99\cdot 999) |
22,530 | E(Q - \theta) = E(Q) - E(\theta) = E(Q) - \theta |
27,807 | \dfrac{x^2 + (-1)}{x + (-1)} = \frac{\left(x + (-1)\right) (x + 1)}{x + (-1)} = x + 1 |
28,520 | 1 + z + z^2 + \dotsm*z^{m + (-1)} = \dfrac{1}{1 - z}*(1 - z^m) = \dfrac{1}{1 - z} - \frac{1}{1 - z}*z^m |
19,168 | \frac{n \cdot n}{(1 + n - l)^2} - \dfrac{1}{1 + n - l}\cdot n = \frac{n}{(n - l + 1)^2}\cdot \left(l + (-1)\right) |
5,365 | x = 16\cdot x_1^4\cdot x_2^4\cdot \ldots\cdot x_r^4 + 1 = (2\cdot x_1\cdot x_2\cdot \ldots\cdot x_r)^4 + 1 |
-5,889 | \frac{1}{4\cdot (y + 9\cdot (-1))}\cdot 3 = \frac{3}{36\cdot \left(-1\right) + 4\cdot y} |
24,908 | v\cdot w^3 = v \Rightarrow 0 = (w^3 + \left(-1\right))\cdot v |
4,824 | -(-\dfrac138 + 5)^2 + 9 = \frac1932 |
129 | \cos(13*\pi/7) = \cos\left(\pi/7\right) |
21,472 | Cov(y_1,y_2) = \mathbb{E}(y_1 \cdot y_2) - \mathbb{E}(y_1) \cdot \mathbb{E}(y_2) = \mathbb{E}(y_1 \cdot y_2) |
-2,679 | \sqrt{12} + \sqrt{75} = \sqrt{4 \cdot 3} + \sqrt{25 \cdot 3} |
31,127 | \dfrac{1}{4 \cdot n} \cdot \operatorname{Var}\left(B^2\right) = \frac{-E\left(B^2\right)^2 + E\left(B^4\right)}{n \cdot 4} |
11,841 | (-f + g) \left(g + f\right) = -f^2 + g^2 |
16,343 | 10 \cdot 10 \cdot 8 \cdot 8 \cdot 8 = 51200 |
-15,997 | 5/10 \cdot 9 - \tfrac{1}{10} \cdot 5 \cdot 7 = 10/10 |
15,199 | -\dfrac{1}{5 \cdot (\dfrac45 + (-1))} = -1/(5(-1/5)) = 1 |
-8,907 | (-3) (-3) (-3) = -3^2 * 3 |
1,234 | \alpha,x,x \geq \alpha\Longrightarrow x*\alpha = x |
32,276 | 2 \cdot 1 - 1^3 = 1 |
23,834 | 16 \cdot (z^2 + 16) = 100 \cdot z^2 \Rightarrow 256 = 84 \cdot z^2 |
18,083 | -3*(1 + 2 + 3 + 4 + 5 + \cdots) = 1/4 |
21,898 | y + (-1) = (y + (-1))\times (y + 1) \Rightarrow 1 = 1 + y |
15,324 | 2^x\times 5^y\times 6^z = 2^x\times 5^y\times 2^z\times 3^z = 2^{x + z}\times 3^z\times 5^y |
24,780 | (4^n + 2)*3 = 3*4^n + 6 |
12,782 | \frac{1}{4}(9 + 1) + \frac{1}{9}(4 + 1) = 5/2 + 5/9 \neq \mathbb{N} |
-17,274 | -\frac{48}{13} = -\frac{48}{13} |
-20,054 | \frac{81 + x\times 18}{9\times x + 9\times (-1)} = 9/9\times \tfrac{1}{x + (-1)}\times (9 + x\times 2) |
39,418 | 100 = 50 \cdot (-1) + 150 |
20,743 | \dfrac{1}{2}\cdot 6 = 3 |
10,440 | {x + 3 + (-1) \choose 3 + (-1)} = {x + 2 \choose 2} = (x + 2) (x + 1)/2 |
2,854 | (7^2)^{10*m} = (50 + (-1))^{10*m} = (1 + 50*(-1))^{10*m} |
8,275 | \dfrac{1}{i + 2} \cdot (2 \cdot i^4 + 1) = 1 = i^2 |
-20,576 | \frac{-16*n + 16}{n*10 + 10*(-1)} = \dfrac{1}{n*2 + 2*\left(-1\right)}*(2*n + 2*(-1))*(-8/5) |
15,894 | m\times g\times k'\times x = m\times g\times x\times k' |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.