id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
29,067
|
6/13 = \dfrac{1}{130}*60
|
39,134
|
x/3*3 = x
|
22,395
|
\frac{1}{l \cdot m} = \frac{1}{l \cdot m}
|
24,290
|
\frac{X''}{X} = -k_y^2 rightarrow X'' + X\cdot k_y^2 = 0
|
4,006
|
E[X_1 + ... + X_k] = E[X_1] + ... + E[X_k]
|
-20,288
|
-8/3*4/4 = -32/12
|
-9,285
|
-8 t + 40 = -2*2*2 t + 2*2*2*5
|
-12,008
|
\frac19 = s/(12\cdot \pi)\cdot 12\cdot \pi = s
|
23,131
|
(x + 4\left(-1\right))^2 + (3 + \frac12x)^2 = \left(\frac{1}{2}x + 5(-1)\right)^2 + x^2
|
31,805
|
z \cdot y \cdot z = \tfrac{1}{z} \cdot 1/y/y = y^2 \cdot z^2 \cdot y^2
|
3,399
|
z \cdot 87\% = z \cdot 24\% + z \cdot 63\%
|
21,590
|
a + b = (a + b) \cdot (a + b) = a^2 + a\cdot b + b\cdot a + b \cdot b = a + a\cdot b + b\cdot a + b
|
5,200
|
\omega = \dfrac{2^{1/3}*\omega}{2^{1/3}}
|
-15,588
|
\dfrac{{(rx^{5})^{-4}}}{{(r^{3}x^{-4})^{-3}}} = \dfrac{{r^{-4}x^{-20}}}{{r^{-9}x^{12}}}
|
-18,942
|
\dfrac{1}{3} = \frac{A_s}{16 \cdot \pi} \cdot 16 \cdot \pi = A_s
|
-2,983
|
2 \cdot \sqrt{2} + 5 \cdot \sqrt{2} = \sqrt{2} \cdot \sqrt{4} + \sqrt{2} \cdot \sqrt{25}
|
50,448
|
16! = 2!\times 2!\times 2!\times 2!\times 15!
|
-20,069
|
\frac{15 \cdot x}{24 \cdot x + 27} = 3/3 \cdot \frac{5 \cdot x}{x \cdot 8 + 9}
|
-20,519
|
6/1 \cdot \frac{1}{9 \cdot (-1) + 3 \cdot z} \cdot (9 \cdot (-1) + 3 \cdot z) = \frac{z \cdot 18 + 54 \cdot (-1)}{9 \cdot \left(-1\right) + 3 \cdot z}
|
-10,418
|
5/5 (-\frac{5}{n \cdot 4}) = -\frac{25}{20 n}
|
-8,447
|
(-3)*\left(-6\right) = 18
|
-24,980
|
3π/2*4 = 6π
|
15,301
|
\cos^{-1}{z} = X \implies z = \cos{X}
|
14,870
|
d/dz \cos(-z) = -\sin(-z)*\frac{d}{dz} \left(-z\right) = \sin(-z) = -\sin(z)
|
15,894
|
e*j*k'*x = x*k'*e*j
|
1,118
|
c + d + h + 3 + s + 4 = 13 \Rightarrow s + c + d + h = 6
|
-29,318
|
-7\cdot i + 6 = 4 + 2 - i\cdot 7
|
10,556
|
4 = 4!/(3!\cdot 1!)
|
-20,404
|
\frac{1}{8} \cdot 1 = \frac{1}{72 \cdot (-1) - 72 \cdot y} \cdot (9 \cdot (-1) - y \cdot 9)
|
-12,133
|
\frac{44}{45} = \frac{s}{6\cdot \pi}\cdot 6\cdot \pi = s
|
1,824
|
n\cdot 7 + 32 = -n\cdot 3^2 + 4^2\cdot (2 + n)
|
-1,844
|
\frac16*\pi - 7/4*\pi = -\frac{1}{12}*19*\pi
|
27,799
|
\dfrac{1}{\left(-x^2 + 1\right)^{\frac{1}{2}}} = d/dx \arcsin{x}
|
50,898
|
33^2 + 88^2 = 8833
|
21,966
|
b \cdot v \lt v \cdot 0\Longrightarrow v \cdot b \lt 0
|
-25,864
|
\frac{1}{y^2}*y^5 = y^{5 + 2*(-1)} = y^3
|
1,911
|
\frac{1}{2}\cdot 17/2\cdot 84\cdot 2/17 = 42
|
3,646
|
f^2 + (-1) = \left(f + (-1)\right)\cdot (f + 1)
|
33,877
|
-5 \cdot (2 \cdot (-5) + 7) = \left(-5\right) \cdot \left(-3\right) \gt 0
|
15,889
|
-\frac{3}{32} + \frac{1}{16}\cdot 9 + \frac{3}{8} = \dfrac{27}{32}
|
8,880
|
3^{2\cdot l + 1} + 3\cdot (-1) = 3\cdot (3^l + (-1))\cdot \left(1 + 3^l\right)
|
10,209
|
N \times k = k \times N
|
4,334
|
2 \cdot \tfrac{1}{3}/3 = 2/9
|
10,854
|
\frac{10*8*6}{10!}*7! = \frac{8*6}{8*9} = 2/3
|
6,468
|
\frac{\mathrm{d}}{\mathrm{d}t} e^Y = Y e^Y = e^Y Y
|
2,944
|
\frac{1}{2} + 1/(2) = 1
|
30,223
|
\dfrac{1}{2} \cdot (5 + 15) = 10
|
12,532
|
\frac{3}{64} - \tfrac{2}{512} = \frac{22}{512}
|
40,101
|
2014 + 4 = 2018
|
-6,129
|
\dfrac{1}{5 \cdot (4 + z)} \cdot 2 = \frac{2}{20 + 5 \cdot z}
|
24,959
|
\frac{\dfrac{\sqrt{3}}{2}*\sqrt{3}}{2} = \frac34
|
11,117
|
\sin^2{z} = (-\cos{2*z} + 1)/2
|
-18,331
|
\frac{1}{t \cdot (4 \cdot (-1) + t)} \cdot \left(t + 8\right) \cdot (4 \cdot (-1) + t) = \frac{32 \cdot (-1) + t^2 + 4 \cdot t}{t^2 - t \cdot 4}
|
-6,188
|
\frac{1}{(2 + t) \cdot 2} \cdot 2 = \frac{1}{t \cdot 2 + 4} \cdot 2
|
14,815
|
0 < y \cdot y \cdot 3 + 12 \cdot y + 9 \Rightarrow 0 \lt y^2 + y \cdot 4 + 3
|
13,072
|
\sum_{p=1}^m p - \sum_{p=1}^{a + (-1)} p = \sum_{p=a}^m p
|
-22,283
|
(10\cdot (-1) + z)\cdot \left(7 + z\right) = z^2 - z\cdot 3 + 70\cdot (-1)
|
41,676
|
0.73 \cdot 24 = 17.52
|
26,019
|
x \cdot (n + 1)/n = \frac{x^{n + 1}}{x^n \cdot n} \cdot (n + 1)
|
10,288
|
{14 \choose 2} = 91 = \frac{182}{2}\cdot 1
|
43,396
|
0 = \dots + (-1)
|
8,897
|
0 \gt n \implies 2 |n| = |n| - n
|
16,933
|
\frac1x = \frac{1}{x^{\frac{1}{2}} \cdot x^{1/2}}
|
22,525
|
x^3 = \left((-1) + x + 1\right)^3
|
20,781
|
x\frac{1}{x^2 + 1}x = \frac{1}{x^2 + 1}x^2
|
11,623
|
4 - (x^2 - 4 \times x + 4) \times 7 = -x^2 \times 7 + 28 \times x + 24 \times (-1)
|
13,416
|
3 + 4 \cdot i = (c_2 + c_1 \cdot i) \cdot (c_2 + c_1 \cdot i)\Longrightarrow c_2^2 - c_1 \cdot c_1 + 2 \cdot c_2 \cdot i \cdot c_1 = i \cdot 4 + 3
|
-10,347
|
4/4 \cdot (-\frac{1}{9 \cdot k} \cdot \left(3 \cdot \left(-1\right) + 4 \cdot k\right)) = -\frac{1}{k \cdot 36} \cdot (12 \cdot (-1) + 16 \cdot k)
|
-18,368
|
\frac{1}{x \cdot x - x\cdot 10 + 9}\cdot (x^2 - x) = \frac{x}{(x + (-1))\cdot \left(x + 9\cdot (-1)\right)}\cdot (x + (-1))
|
2,616
|
\frac{1}{6 \cdot 6 \cdot 6} \cdot (6 + 54 + 18) = 78/216 = \frac{1}{36} \cdot 13 \approx 0.361
|
-10,627
|
\frac{1}{40*x}*45 = \dfrac{1}{5}*5*9/(x*8)
|
-1,586
|
\dfrac{23}{12}\cdot \pi + \dfrac{\pi}{3} = \pi\cdot 9/4
|
15,765
|
\left(4 - 9/2\right)^2 = (-\frac{9}{2} + 5)^2
|
-2,155
|
\frac{1}{3} \cdot 7 \cdot \pi = \frac{11}{6} \cdot \pi + \frac{1}{2} \cdot \pi
|
-3,343
|
\sqrt{16\cdot 2} + \sqrt{9\cdot 2} - \sqrt{2} = -\sqrt{2} + \sqrt{32} + \sqrt{18}
|
-30,586
|
9\cdot (z^2 + 2\cdot (-1)) = 18\cdot \left(-1\right) + z^2\cdot 9
|
5,843
|
|l \cdot e^z + (-1)| = |l \cdot e^z - e^z + e^z + \left(-1\right)| \leq e^z \cdot |l + (-1)| + |e^z + (-1)|
|
23,994
|
\mathbb{E}(\max{Y_1\wedge ...\wedge Y_l}) = \max{\mathbb{E}(Y_1)\wedge ...\wedge \mathbb{E}(Y_l)}
|
19,158
|
\frac{b \cdot b}{f^2 z^2}(-z + x) = \frac{\partial}{\partial x} (\frac{xb \cdot b\cdot \left(-1\right)}{f \cdot f z})
|
23,178
|
\frac{1}{100} \cdot 86 \cdot 114/100 = 9804/10000 < 1
|
5,373
|
\sqrt{\frac{x}{v}} = \sqrt{x^2/(x*v)} = x/(\sqrt{x*v})
|
-8,940
|
40.8\% = \dfrac{40.8}{100}
|
14,449
|
4 \cdot x + (-1) = 0 \Rightarrow x = 1/4
|
-3,117
|
\sqrt{13}\cdot \left(1 + 3 + 2\right) = 6\cdot \sqrt{13}
|
10,552
|
1 + \dfrac{6}{5(-1) + n} = \frac{n + 1}{5(-1) + n}
|
-186
|
\frac{8!}{5!*\left(8 + 5*\left(-1\right)\right)!} = {8 \choose 5}
|
-9,378
|
-r*70 + 110*\left(-1\right) = -r*2*5*7 - 2*5*11
|
-10,006
|
0.01 (-30) = -30/100 = -\dfrac{3}{10}
|
47,205
|
\alpha + x = x + \alpha
|
-15,318
|
\tfrac{i^4}{\dfrac{1}{i^6} \cdot \dfrac{1}{r^{10}}} \cdot \frac{1}{r} = \frac{i^4}{\frac{1}{i^6}} \cdot \frac{1}{r \cdot \frac{1}{r^{10}}} = i^{4 - -6} \cdot r^{-1 - -10} = i^{10} \cdot r^9
|
29,890
|
\dfrac{1}{((-1) + z)^2} \cdot ((-1) + z) = \frac{1}{\left(-1\right) + z}
|
-11,530
|
6 + 0 \cdot (-1) - i \cdot 12 = -12 \cdot i + 6
|
20,998
|
-g^2 + f^2 = (f - g) \left(f + g\right)
|
19,521
|
720 = {5 + (-1) \choose (-1) + 3}*5!
|
-6,932
|
720 = 10*12*6
|
-1,805
|
-\dfrac{\pi}{6} = \dfrac{1}{12}7 \pi - \pi \dfrac34
|
-1,952
|
\pi \cdot \frac{37}{12} - 2 \cdot \pi = \dfrac{13}{12} \cdot \pi
|
7,693
|
\sin{x} = x - x^2/2! - x^3/3! - x^4/4! - x^5/5! - ...
|
-4,693
|
\frac{1}{z + 3\times (-1)} + \frac{1}{5 + z} = \frac{2 + z\times 2}{15\times (-1) + z^2 + 2\times z}
|
-22,908
|
\frac{1}{24} \cdot 40 = \frac{5 \cdot 8}{8 \cdot 3}
|
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