id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
12,618
|
\sqrt{x - g} \dfrac{x - g - x - h}{\left(-h + x\right) (-g + x)} = \dfrac{-g + h}{\sqrt{-g + x} (x - h)}
|
4,392
|
(a^2 - g^2) \cdot u = (a + g) \cdot (-g + a) \cdot u
|
10,543
|
x^2 = -(x + 3 \times (-1)) \times (-x + 5) - 4 \times (8 - 2 \times x) + 17
|
8,295
|
\left(6 + 20^{1 / 2}\right)^{1 / 2} = \left(5^{1 / 2} \cdot 2 + 6\right)^{\dfrac{1}{2}}
|
12,995
|
(c - d)^2 = d^2 + c^2 - cd \cdot 2
|
33,375
|
(2\cdot (-1) + z\cdot 3)\cdot (5 + z) = 10\cdot (-1) + z^2\cdot 3 + 13\cdot z
|
-657
|
(e^{\dfrac{7}{4} \cdot i \cdot \pi})^3 = e^{3 \cdot \frac14 \cdot \pi \cdot 7 \cdot i}
|
-9,092
|
138\% = \frac{138}{100}
|
-7,426
|
9/91 = \frac{6}{14} \cdot \frac{3}{13}
|
-6,707
|
\frac{1}{100}\cdot 30 + \dfrac{5}{100} = \frac{5}{100} + \frac{3}{10}
|
36,087
|
17 + 4 \cdot (-4) = 1
|
-10,385
|
\frac{40 + s \cdot 4}{60 \cdot s + 40 \cdot (-1)} = \frac{s + 10}{10 \cdot (-1) + 15 \cdot s} \cdot \frac{1}{4} \cdot 4
|
-7,627
|
(-2 + 26 i - i + 13 (-1))/5 = (-15 + 25 i)/5 = -3 + 5i
|
31,459
|
\int\limits_g^f \cot{z}\,\mathrm{d}z = \int\limits_g^f \cot{z}\,\mathrm{d}z
|
21,892
|
(2 + (-1) + 2\cdot x + (-1))/2 = x
|
23,425
|
2\cdot \sin{u}\cdot \sin{v} = \cos(-u + v) - \cos(v + u)
|
36,075
|
-\frac{1}{27} = \dfrac{1}{-27}
|
7,351
|
\mathbb{Var}\left(Q\right) = \mathbb{E}\left((Q - \mathbb{E}\left(Q\right))^2\right) = \mathbb{E}\left(Q^2\right) - \mathbb{E}\left(Q\right)^2
|
-14,002
|
10\cdot 7 + 2\cdot 24/3 = 10\cdot 7 + 2\cdot 8 = 70 + 2\cdot 8 = 70 + 16 = 86
|
24,872
|
3 = y\cdot 4 - 2\cdot (1 - y) \Rightarrow 5/6 = y
|
36,721
|
\sqrt{f'^2 + f \cdot f} = \sqrt{f^2 + f'^2}
|
12,149
|
\frac{-x + 1}{3\times (x^2 + 2)} + \frac{1}{3\times \left(1 + x\right)} = \dfrac{1}{(x \times x + 2)\times (x + 1)}
|
15,390
|
\sqrt{0.5 \cdot 2} = 1
|
-25,807
|
\tfrac{2}{7\cdot 6} = 2/42
|
-25,689
|
d/dz (\frac{4}{z + 2}) = -\frac{4}{(2 + z)^2}
|
-11,563
|
-4 + 15 (-1) + i*4 = i*4 - 19
|
-18,358
|
\dfrac{(6*(-1) + t)*t}{(1 + t)*\left(t + 6*(-1)\right)} = \frac{-t*6 + t^2}{t^2 - 5*t + 6*\left(-1\right)}
|
-18,403
|
\frac{f^2 + f}{f^2 - 3*f + 4*(-1)} = \tfrac{1}{(f + 1)*(f + 4*(-1))}*f*(1 + f)
|
-22,315
|
(9 + s)\cdot (4 + s) = s^2 + s\cdot 13 + 36
|
-6,049
|
\frac{y\cdot 8}{8\cdot (y + 6\cdot (-1))\cdot (y + 9\cdot (-1))} = \frac{y}{(6\cdot (-1) + y)\cdot (y + 9\cdot (-1))}\cdot \frac{1}{8}\cdot 8
|
33,138
|
D_x\cdot D_i = D_x\cdot D_i
|
53,788
|
\frac{(n-1)^{n-1}}{n^{n-2}} = (n-1)\left(1-\frac{1}{n}\right)^{n-2} = (n-1)\left(1-\frac{1}{n}\right)^n \left(1-\frac{1}{n}\right)^{-2} \\ = \frac{n^2}{n-1} \left(1-\frac{1}{n}\right)^n
|
2,974
|
(1 + 6)\times (4 + 1)\times (2 + 1) = 105
|
-1,715
|
\pi*5/6 + \pi \tfrac134 = \pi*13/6
|
8,189
|
1 = z^3 + z - y^2 \implies z^3 + z + (-1) = y * y
|
6,658
|
(-1) + 2 \cdot \cos^2{Z} = \cos{2 \cdot Z}
|
16,784
|
I' + I*\lambda = \left(I' + \lambda*I\right)^2
|
4,828
|
-\frac{\pi}{4} \cdot 7 = -\dfrac{\pi}{2} \cdot 3 - \frac{1}{4} \cdot \pi
|
8,189
|
z^3 + z - y \cdot y = 1 \Rightarrow (-1) + z^3 + z = y^2
|
32,915
|
\eta^z + \left(-1\right) = (\eta + (-1))\times (\eta^{(-1) + z} + \eta^{2\times (-1) + z} + ... + \eta + 1)
|
-17,142
|
2 = 2\cdot 2\cdot q + 2\cdot (-6) = 4\cdot q - 12 = 4\cdot q + 12\cdot (-1)
|
25,426
|
(1 + n)^4 = 1 + n^4 + n * n^2*4 + 6n * n + n*4
|
587
|
\cot{y} - 8 \cdot \cot{8 \cdot y} = \cot{y} - 8 \cdot \cot{8 \cdot y} = \cot{y} - 8 \cdot \dfrac{1}{2 \cdot \cot{4 \cdot y}} \cdot (\cot^{24}{y} + (-1))
|
-16,624
|
8 = 8\cdot (-5\cdot t) + 8\cdot (-1) = -40\cdot t - 8 = -40\cdot t + 8\cdot (-1)
|
3,329
|
10^{n + m} = 10^n \cdot 10^m
|
17,710
|
|c h| = |c| |h|
|
16,299
|
x_1 + x_2 + v_1 + v_2 = v_2 + x_2 + v_1 + x_1
|
3,670
|
\binom{4}{2} = \tfrac{4!}{2!*(4 + 2*(-1))!} = 6
|
23,089
|
2^{1 + k} - 1 + 2^k + 1 = 2^k
|
7,858
|
(t + t_2 + t_1)^2 - t^2 + t_2^2 + t_1^2 = 2\cdot (t_2\cdot t_1 + t\cdot t_1 + t\cdot t_2)
|
21,772
|
\frac{xg}{hf}1 = \dfrac{\dfrac1h g}{1/x f}1
|
13,052
|
\frac{5}{13} = (10*9 + 2*10)/(\binom{13}{3})
|
28,002
|
y = z + 2 \Rightarrow y + 2 \left(-1\right) = z
|
2,223
|
-(4 + 1 + 2 + 3) = 16 \cdot (-1) + 1 + 4 \cdot (-1) + 9
|
-22,153
|
30/50 = \dfrac15\cdot 3
|
17,559
|
2^{k + 3} + 2^{2 + k} + 2^{1 + k} + 2^k + 2^k = 2^{k + 4}
|
9,215
|
1 + \frac{1}{k \cdot k} - 2/k = (1 - 1/k) \cdot (1 - 1/k)
|
11,422
|
3 \cdot \left(5 \cdot (-1) + 2 \cdot y\right)^2 \cdot 2 = \left(2 \cdot y + 5 \cdot \left(-1\right)\right) \cdot \left(2 \cdot y + 5 \cdot \left(-1\right)\right) \cdot 6
|
6,924
|
l_k\times p_k = l_k\times p_k
|
-2,313
|
\dfrac{8}{19} - \dfrac{2}{19} = \dfrac{6}{19}
|
36,915
|
\alpha_x = \alpha_x
|
13,049
|
-4\cdot (1 + z^2) + 4 = -4\cdot z^2
|
3,942
|
|z_2 + z_1 + \varphi| = |z_2 + z_1 + \varphi|
|
-5,491
|
\frac{z*2}{(z + 1) (z + 2(-1))} = \frac{2z}{z^2 - z + 2(-1)}
|
7,847
|
7(-100) + 11 \cdot 67 = 37
|
-30,291
|
\tfrac12\cdot (0 + 4) = 4/2 = 2
|
-12,810
|
7 = 15 + 8 (-1)
|
39,283
|
3*(12 + 6 (-1)) = 18
|
-7,618
|
\frac{-6 + i\cdot 8}{-1 - 2\cdot i} = \tfrac{-1 + 2\cdot i}{-1 + i\cdot 2}\cdot \frac{i\cdot 8 - 6}{-2\cdot i - 1}
|
11,449
|
-\sin{π/6} - -\sin{\frac56\cdot π} = 0
|
-11,999
|
4/15 = \frac{s}{6\pi}*6\pi = s
|
24,838
|
\mathbb{E}[Y \cdot V] = \mathbb{E}[Y] \cdot \mathbb{E}[V]
|
15,441
|
z^{50} = z^{16} \cdot z^2 \cdot z^{32}
|
31,468
|
e^{-i y} = \cos(-y) + i \sin(-y) = \cos(y) - i \sin(y)
|
25,876
|
-\left(2 (-1) + x_n^2\right)/(x_n*2) + x_n = \frac12 \left(x_n + 2/\left(x_n\right)\right)
|
-9,925
|
0.82 = 8.2/10 = \dfrac{1}{50} \cdot 41
|
11,396
|
20/4 = 2^1*5/2
|
21,075
|
\frac{8}{24} - 21/24 = \left(8 + 21\times (-1)\right)/24 = -13/24
|
19,134
|
280 = (20 \cdot \left(-1\right) + 120) \cdot 3 + 20 \cdot (-1)
|
4,552
|
\dfrac{1}{x^3}(x^3 - 7x) = 1 - \frac{7}{x \cdot x}
|
31,466
|
2 + \sqrt{3} = e^{-i*x} = \cos(x) - i*\sin(x)
|
55,574
|
10 = \binom{5}{3}
|
-22,804
|
\frac{54}{4 \cdot 18} \cdot 1 = 54/72
|
34,545
|
\dfrac{p}{n} \cdot \tfrac{p + \left(-1\right)}{n + (-1)} = \tfrac{1}{-n + n^2} \cdot (p^2 - p)
|
-22,199
|
(9 \cdot (-1) + q) \cdot (6 + q) = q \cdot q - q \cdot 3 + 54 \cdot (-1)
|
18,918
|
\frac{z^2}{z^2 + (-1)}*2 = 2 + \dfrac{1}{z^2 + (-1)}*(z + 1 - z + (-1)) = 2 + \frac{1}{z + (-1)} - \dfrac{1}{z + 1}
|
1,704
|
u \cdot D^1 = D^{\frac12} \cdot u \cdot D^{\dfrac{1}{2}}
|
-6,689
|
0/100 + \frac{1}{100}*7 = 0/10 + \frac{1}{100}*7
|
16,162
|
\frac{42}{2}1 + 14 \left(-1\right) = 7 < 14
|
10,012
|
\dfrac{x^{4i}}{A_i^4} = x^l \Rightarrow x^{i\cdot 4 - l} = A_i^4
|
-11,595
|
-2 + 4 - 9*i = 2 - 9*i
|
-17,837
|
8\left(-1\right) + 39 = 31
|
-11,611
|
-12 + 12 i = 0 + 12 (-1) + 12 i
|
-3,810
|
2\times 3\times 7 = 42
|
26,721
|
13/27 = \frac{1}{3} + \dfrac{2}{9} \cdot 2/3
|
-11,794
|
\frac{1}{16} \cdot 9 = \left(3/4\right)^2
|
51,352
|
\lim_{n \to \infty} \|\frac{\left(n + 1\right)!}{(n + 1)^{n + 1}} n^n/n!\| = \lim_{n \to \infty} \|\frac{\left(n + 1\right) n!}{(n + 1)^{n + 1}} n^n/n!\| = \lim_{n \to \infty} \|\frac{n + 1}{\left(n + 1\right)^{n + 1}} n^n\|
|
53,756
|
2^{2012} = (2^4)^{503} = (-1 + 17)^{503}
|
-1,247
|
\dfrac{30}{35} = \dfrac{30 \times 1/5}{35 \times \frac{1}{5}} = 6/7
|
29,554
|
3^{n + 1} \gt 3n = n + 2n > n + 1
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.