id
int64 -30,985
55.9k
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stringlengths 5
437k
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14,792
|
(1 + k)!\cdot \left(k + 1 + 1\right) + (-1) = (k + 1)!\cdot (k + 1) + \left(k + 1\right)! + \left(-1\right)
|
29,355
|
a^2 + ab\cdot 2 + b^2 = (b + a)^2
|
33,417
|
\frac{\partial}{\partial z} z^n = z^{(-1) + n}\cdot n
|
40,212
|
9/30 = \frac{1}{10}\cdot 3
|
-22,209
|
8\cdot (-1) + r^2 + 7\cdot r = (r + 8)\cdot \left(r + \left(-1\right)\right)
|
18,641
|
(-1) \left(-1\right) = (-1)^2 = 1
|
-20,630
|
(2 - 6\cdot x)/\left(x\cdot (-5)\right)\cdot 8/8 = \frac{1}{(-40)\cdot x}\cdot (16 - x\cdot 48)
|
-9,153
|
-q*2*2*2*2*5 = -80*q
|
17,197
|
\dfrac{\alpha \cdot \alpha}{\bar{\alpha}\cdot \alpha} = \alpha/(\bar{\alpha})
|
11,397
|
\frac{1 - -1}{2.25 - 1.5} = 2/0.75 = \dfrac83 \approx 2.7
|
5,712
|
\left(y = -x \cdot 3 + 4 \Rightarrow y + 4 \cdot (-1) = -x \cdot 3\right) \Rightarrow x = \frac{1}{-3} \cdot (y + 4 \cdot (-1))
|
1,348
|
2^{(-1) + x}\cdot 2 - 2^{(-1) + x} = 2^{(-1) + x}
|
15,286
|
y y + \left(-1\right) = \left(y + (-1)\right) \left(y + 1\right)
|
17,035
|
\cos(2\pi + z) = \cos(z)
|
-16,005
|
-\dfrac{65}{10} = -9/10 \cdot 8 + 7/10
|
20,186
|
\int (u + (-1))\times \cos(u)\,\mathrm{d}u = \int \left(u + (-1)\right)\times f\times \sin\left(u\right)\,\mathrm{d}x = (u + (-1))\times \sin(u) - \int \sin(u\times f\times (u + (-1)))\,\mathrm{d}x
|
25,134
|
\frac{7^{1/2}\cdot 2}{3} = \frac{28^{1/2}}{3}
|
-27,357
|
153 = 525 + 372\cdot (-1)
|
8,821
|
k = \cos{\frac{\pi}{2}} + \sin{\pi/2} k
|
30,959
|
2 + y^2 - 2 \cdot y = \left(y + (-1)\right)^2 + 1
|
-66
|
21 = 5 + 16
|
7,139
|
\tfrac{x}{\sqrt{1 + x^2}} + 1 = \frac{1}{\sqrt{x^2 + 1}}\cdot (x + \sqrt{x \cdot x + 1})
|
-5,964
|
3/3\cdot \dfrac{3}{(4(-1) + t) (9(-1) + t)} = \dfrac{9}{3(4(-1) + t) (t + 9(-1))}
|
32,684
|
0 = (y + (-1))*(y * y + y + 1) = y^3 + (-1)
|
10,039
|
(1 + k)! = (1 + k)\cdot k! \Rightarrow k\cdot k! = (k + 1)! - k!
|
32,210
|
\binom{l + 2}{l + 1} = 1 + \binom{l + 1}{l}
|
2,259
|
\dfrac{6}{\frac{1}{2}6 + 1} = \frac32
|
-3,719
|
\frac{r}{r^2} \cdot 12/6 = \frac{r \cdot 12}{r^2 \cdot 6} \cdot 1
|
-17,111
|
4 = 4\cdot a + 4\cdot (-4) = 4\cdot a - 16 = 4\cdot a + 16\cdot (-1)
|
22,335
|
\frac{1}{-r + 1} = 1 + \frac{r}{-r + 1}
|
12,228
|
z \cdot z + x^2 + 4\cdot y \cdot y = z^2 + 2\cdot y^2 + x^2 + 2\cdot y^2
|
6,969
|
\dfrac{15}{16}\cdot 10 + \dfrac{1}{16}\cdot \left(-150\right) = 0
|
30,393
|
35 = 15*14/(2*3)
|
32,598
|
\dfrac{1}{2 \cdot 2} \cdot 2^1 = 2^{2 \cdot (-1) + 1}
|
2,393
|
7!/(2!*2!*1!*2!) = {1 \choose 1}*{3 \choose 2}*{5 \choose 2}*{7 \choose 2}
|
-10,544
|
\frac{1}{12}12 \left(-\frac{1}{5 + 3p}8\right) = -\frac{96}{p*36 + 60}
|
32,006
|
\dfrac{7\cdot 3 + 3}{2 + 5\cdot 3} = \frac{24}{17}
|
2,618
|
A * A - B^2 = (-B + A) (A + B)
|
-20,343
|
\frac{p}{30 (-1) + 12 p}3 = \dfrac{1}{4p + 10 (-1)}p \frac33
|
-2,015
|
3/2 \pi = \pi \cdot 23/12 - \tfrac{5}{12} \pi
|
16,385
|
\sin{a\cdot 2}/2 = \cos{a}\cdot \sin{a}
|
20,203
|
3 = 1 \cdot 5 - 2
|
2,123
|
gHf = Hg f
|
8,323
|
-77\cdot 43 + 23\cdot 144 = 1
|
18,657
|
1 = 2*K*\cos{t} \Rightarrow \cos{t} = 1/(K*2)
|
4,966
|
1 - \dfrac{1}{y_{\mu + 1} + \left(-1\right)} = \tfrac{1}{y_{\mu + 1} + (-1)} \times (y_{1 + \mu} + 2 \times (-1))
|
109
|
\frac{1}{2}\cdot (1 - \cos(z\cdot 2)) = \sin^2(z)
|
25,856
|
\dfrac{1}{z} \cdot (-4/9 - 1/3) = -\dfrac{1}{z} \cdot \frac{7}{9}
|
41,610
|
\dfrac{1}{4l} + 1/(4l) = 1/(2l) = \dfrac{2l}{4l^2}
|
26,539
|
\left(-x_0\cdot b - y_0\cdot d\right)\cdot (b\cdot x_0 - y_0\cdot d) = -b^2\cdot x_0^2 + d^2\cdot y_0 \cdot y_0
|
22,385
|
-4\cdot z^2 + 4\cdot z + 3 = -(4\cdot z^2 - 4\cdot z + 3\cdot (-1)) = -(2\cdot z + 1)\cdot (2\cdot z + 3\cdot \left(-1\right))
|
3,089
|
n \times (-h + g) = -h \times n + n \times g
|
24,821
|
A \cdot B \cdot C = C \cdot A \cdot B
|
-1,339
|
\dfrac{5}{4} \cdot (-1/4) = \dfrac{(-1) \cdot 1/4}{\dfrac15 \cdot 4}
|
-523
|
(e^{2\cdot \pi\cdot i/3})^{16} = e^{i\cdot \pi\cdot 2/3\cdot 16}
|
19,613
|
10\cdot h + h \cdot h = (5 + 5 + h)\cdot (5 + h + 5\cdot (-1))
|
19,883
|
\mathbb{E}[X_2^2 \cdot X_1] = \mathbb{E}[X_2^2] \cdot \mathbb{E}[X_1]
|
21,558
|
(-1)^n = (-1)^{n + 2*\left(-1\right)}
|
3,153
|
c \cdot x \cdot d \cdot g = d \cdot c \cdot x \cdot g
|
22,138
|
(-1)\times (-1) - 1 + 1 = 1 + 0
|
-5,253
|
10^{0 - -3}\cdot 0.61 = 0.61\cdot 10^3
|
-697
|
e^{\pi\cdot i\cdot 11/6\cdot 14} = (e^{\tfrac{11}{6}\cdot \pi\cdot i})^{14}
|
35,659
|
\left(\frac13\right)^4 = \tfrac{1}{81}
|
1,826
|
2\times \pi/8 = \dfrac{\pi}{8}\times 2 = \frac{\pi}{4}
|
11,096
|
|N| = |g*N/g| \implies N/g*g = N
|
-23,920
|
9 + \tfrac{32}{8} = 9 + 4 = 9 + 4 = 13
|
1,822
|
(1 + n)^2 = n \cdot 2^2 + ((-1) + n)^2
|
33,291
|
\dfrac{1}{2^n*\frac{1}{n}}*2^{1 + n}*\dfrac{1}{n + 1} = 2*\tfrac{1}{n + 1}*n
|
3,042
|
2\cdot \cos(t)\cdot \sin(t) = \sin(2\cdot t)
|
-26,570
|
(7 + z)\cdot (z + 7\cdot (-1)) = z^2 - 7^2
|
-2,651
|
6\cdot \sqrt{7} = \left(5 + 1\right)\cdot \sqrt{7}
|
-5,156
|
10^{-1 + 4}*16.2 = 10^3*16.2
|
15,226
|
100 + \tfrac{100}{2} (1 + 100)\cdot 2 = 100 + 10100
|
15,049
|
5 (-1) - 4 (-1) = -5 + 4 = -1
|
5,866
|
x x + 4 x + 3 = (x + 1) (x + 3)
|
3,138
|
\left(2 - n + h\right)\cdot 2 \leq h rightarrow h \leq 2\cdot n + 4\cdot \left(-1\right)
|
19,188
|
\frac{1}{\gamma^2 + 1} = \frac{\text{d}}{\text{d}\gamma} \operatorname{atan}(\gamma)
|
-4,978
|
1.58*10 = 1.58*10*10^2 = 1.58*10^2 * 10
|
-4,515
|
\frac{23\cdot (-1) + 3\cdot x}{12\cdot (-1) + x^2 + x} = \frac{5}{x + 4} - \frac{2}{3\cdot (-1) + x}
|
2,936
|
\frac{1}{2} \cdot (-f^2 + c^2) = \frac{1}{2} \cdot c \cdot c - \dfrac12 \cdot f \cdot f
|
-18,160
|
69*(-1) + 99 = 30
|
9,452
|
(x + c)^2 = x^2 + 2\cdot x\cdot c + c^2 = i + 2\cdot x\cdot c - i = 2\cdot x\cdot c
|
-5,624
|
\dfrac{1}{2*(f + 2)} = \dfrac{1}{2*f + 4}
|
28,389
|
\frac{1}{2^7}{6 \choose 1} = \frac{3}{64}
|
-30,563
|
\dfrac{3750}{750} = 750/150 = \dfrac{1}{30}\cdot 150 = 5
|
9,091
|
z\frac{1}{z}a^m = \left(z\dfrac{a}{z}\right)^m
|
18,056
|
\frac12\cdot 3 = \left(n - k + 1\right)/k = \frac{1}{k}\cdot (n + 1) + (-1)
|
15,073
|
1 = \frac{2 + 2}{2 + 2} = \frac12*2 + 2/2 = 2
|
24,250
|
0 = \lim_{l \to ∞}\left(c_l - f_l\right) \Rightarrow 1 = \lim_{l \to ∞} c_l/\left(f_l\right)
|
1,499
|
3 = \left\lceil{\dfrac{1}{16} \cdot 33}\right\rceil
|
-20,415
|
-\frac{45}{35 + p \cdot 5} = -\frac{9}{p + 7} \cdot \frac55
|
43,854
|
\frac{1}{2}*5 = \dfrac{5}{2}
|
-11,577
|
20 \cdot i - 20 + 0 \cdot (-1) = i \cdot 20 - 20
|
-20,744
|
\dfrac{1}{(-4) \cdot z} \cdot (6 \cdot (-1) + 2 \cdot z) = 2/2 \cdot \frac{3 \cdot (-1) + z}{(-2) \cdot z}
|
-7,684
|
\tfrac{1}{25}\cdot \left(-60 + 30\cdot i - 80\cdot i + 40\cdot (-1)\right) = \dfrac{1}{25}\cdot (-100 - 50\cdot i) = -4 - 2\cdot i
|
32,996
|
(1^3 + 1^3) \times \left(1^3 + 1^2 \times 1\right) = 4
|
-19,421
|
6/1*2/5 = 2*\frac{1}{5}/(\frac{1}{6})
|
26,335
|
\frac{90}{36} = 15/6 = \frac52
|
3,407
|
c^2 + (-1) = (-1) + (-c)^2
|
47,974
|
\left(2 + 3\right) \cdot \left(2 + 3\right) = 5^2 = 25
|
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