id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-10,471 |
\frac{12}{12} \cdot (-\frac{(-1) + 3 \cdot y}{2 + 5 \cdot y}) = -\tfrac{y \cdot 36 + 12 \cdot (-1)}{60 \cdot y + 24}
|
4,812 |
\sum_{l=1}^\infty \left(2l + a_l\right)^2 = \sum_{l=1}^\infty (a_l * a_l + 4a_l l + 4l^2)
|
12,330 |
5 - 0 \cdot 3 + 9/3 = \frac93 + 5 - 0 \cdot 3
|
31,662 |
\dfrac{9\cdot \frac{1}{10}}{2^5} + 1/10 = 41/320
|
1,526 |
\dfrac{4}{2 \cdot x} = -2 \cdot x = -2 \cdot e^{\frac{\pi}{2} \cdot x} = 2 \cdot e^{((-1) \cdot x \cdot \pi)/2}
|
-4,366 |
l\cdot 7/6 = \dfrac{7\cdot l}{6}
|
5,740 |
d^x = x\Longrightarrow d = x^{1/x}
|
1,097 |
0 = f \cdot z^2 + z \cdot d + h \Rightarrow z^2 + \frac{d}{f} \cdot z = -h/f
|
239 |
\frac{10!}{{5 \choose 2}}\cdot \frac{1}{1!\cdot 1!\cdot 1!\cdot 3!\cdot 2!\cdot 2!} = 15120
|
35,544 |
\dfrac{1}{E^{\dfrac12}} = E^{-\frac12}
|
22,844 |
-\rho^2 + t t = (-\rho + t) (t + \rho)
|
-23,123 |
-\frac12 \cdot 3 = -3/2
|
21,084 |
|\dfrac1D| = \frac{1}{|D|}
|
16,456 |
8! \cdot {10 \choose 2} = 10!/2!
|
30,971 |
3*1/4/4 = \frac{3}{16}
|
-12,422 |
\dfrac{1}{3} \cdot 132 = 44
|
9,892 |
\frac{-z_2 + z_1}{z_2 \cdot z_1} = 1/(z_2) - 1/\left(z_1\right)
|
-21,062 |
\frac{1}{2} \cdot 2 \cdot \frac24 = 4/8
|
16,653 |
1 = -3032\cdot 14995 + (-14995\cdot 2 + 37469)\cdot 6079
|
13,912 |
\frac{1}{12} \cdot \left(2^2 + \left(-1\right)\right) = 0.25
|
9,948 |
\frac{\partial}{\partial c} (b\times a) = 1000\times h + 100\times c + 10\times b + a = 9\times \left(1000\times a + 100\times b + 10\times c + h\right) = 9000\times a + 900\times b + 90\times c + 9\times h
|
-13,198 |
-3.6 = -\dfrac{2.52}{0.7}
|
-730 |
(e^{\frac{1}{4} \cdot \pi \cdot 7 \cdot i})^{15} = e^{15 \cdot 7 \cdot i \cdot \pi/4}
|
22,313 |
a'*d + a*b*c + a'*c = c*b + b*c*a + a'*c + d*a'
|
19,863 |
3 \times 2/2 = 3
|
-17,041 |
-5 = -5\cdot \left(-5\cdot y\right) - 40 = 25\cdot y - 40 = 25\cdot y + 40\cdot (-1)
|
-20,569 |
\frac188 \frac{5\left(-1\right) - 7S}{S \cdot 9} = \tfrac{1}{S \cdot 72}(40 (-1) - 56 S)
|
13,810 |
V_0 S_0 = S_0 V_0
|
18,362 |
g + 3(-1) = -(-g + 3)
|
7,278 |
1 = 3^l\cdot 3^k \Rightarrow k = l = 0
|
20,825 |
x + \frac13 = \left(3 x + 1\right)/3
|
-27,515 |
a \cdot a \cdot 3 \cdot 2 \cdot 2 = 12 \cdot a^2
|
26,565 |
20648 = 22^3 + 10^3 + 10^3 + 20 \cdot 20 \cdot 20
|
-7,098 |
2/5\cdot 3/6\cdot \tfrac47/4 = \tfrac{1}{35}
|
43,272 |
\binom{15}{2} = \binom{13 + 3 + (-1)}{(-1) + 3}
|
-23,895 |
\dfrac{22}{5 + 6} = \frac{22}{11} = \dfrac{22}{11} = 2
|
28,539 |
5^{6*n + 2} = 5^{6*n + 3 + (-1)} = \frac{1}{5}*5^{3*(2*n + 1)}
|
20,159 |
y^6 + (-1) = (1 + y^4 + y^2) (y \cdot y + (-1))
|
-26,137 |
-\dfrac32 - -3/1 = -1.5 + 3 = 1.5
|
22,519 |
\int f\,\mathrm{d}y \Rightarrow \int f\,\mathrm{d}y
|
-25,294 |
d/dx \frac{1}{x^6} = -\tfrac{1}{x^7}\cdot 6
|
6,877 |
0/127 = \frac{1}{127}\cdot 0
|
-20,446 |
-\frac{3}{-27} = ((-3)\cdot 1/\left(-3\right))/9
|
4,737 |
h^2 + g \cdot g = \left(h + g\right)^2 - 2 \cdot h \cdot g
|
-26,647 |
4 + 121\cdot G^4 - G^2\cdot 44 = (G^2\cdot 11 + 2\cdot (-1))^2
|
36,649 |
\sin(x) = x - \dfrac{x^3}{3!} + x^5/5! \pm \cdots \approx x
|
-1,492 |
\frac{1}{12}45 = \frac{45}{12*\frac{1}{3}}1/3 = \frac{15}{4}
|
-6,731 |
10^{-1} + \frac{1}{100} \cdot 8 = \frac{1}{100} \cdot 8 + \frac{1}{100} \cdot 10
|
-614 |
-28\cdot \pi + \pi\cdot 85/3 = \frac{\pi}{3}
|
-12,021 |
5/8 = \dfrac{s}{16 \cdot \pi} \cdot 16 \cdot \pi = s
|
-7,528 |
(a + b) \cdot (a - b) = a^2 - b^2
|
-24,617 |
9*4 + 8*\frac{1}{10}20 = 9*4 + 8*2 = 36 + 8*2 = 36 + 16 = 52
|
3,717 |
\frac{\frac{2}{3}}{1/3} \cdot 1 = 2
|
2,103 |
g^5 + g + (-1) = g^5 + g^2 - g^2 + g + (-1) = \left(g \cdot g - g + 1\right) (g^3 + g^2 + (-1))
|
1,976 |
1 - \left(1 - p_1\right)\cdot (1 - p_2) = p_1 + p_2 - p_1\cdot p_2
|
-3,788 |
\dfrac{2}{3*r * r} = \frac{2}{r^2}*1/3
|
3,122 |
\sqrt{17}*(10 + 12)/2 = \sqrt{17}*11
|
18,369 |
(2 - 2 n) \left(1 - r*((-1) + n)\right) r^{3 (-1) + n} = (1 - \left(n + (-1)\right) r) r^{3 (-1) + n} (1 - r)
|
-5,046 |
2.8\cdot 10 = 2.8\cdot 10/100 = \frac{2.8}{10}
|
18,406 |
z * z + 1 = 1 + \frac{dz}{dt}\Longrightarrow \frac{dz}{dt} = z^2
|
14,059 |
(61 - 28\cdot 3^{1/2})/37 = \frac{7 - 2\cdot 3^{1/2}}{2\cdot 3^{1/2} + 7}
|
39,577 |
e\cdot A = e\cdot A
|
-1,336 |
-\frac137*3/8 = \frac{3 / 8}{\left(-1\right)*3*1/7}1
|
5,201 |
\frac16 \cdot 3/6 = \frac{3}{36}
|
-9,113 |
\frac{84.5}{100} = 84.5\%
|
30,622 |
90 = 100 + 10 \cdot \left(-1\right)
|
11,936 |
1 - 2*\cos(z) + (-1) = 2 - 2*\cos(z) = 2*(1 - \cos(z))
|
-22,955 |
\frac{1}{24} \cdot 18 = \frac{3 \cdot 6}{6 \cdot 4}
|
-1,990 |
\pi\cdot \frac{1}{4}\cdot 5 = 3/2\cdot \pi - \pi/4
|
31,999 |
\frac{m}{s}\times m\times s = m^2 = \frac{m^3}{s}
|
13,188 |
z \cdot z - i \cdot 3 \cdot z - i \cdot 3 \cdot z + 3 \cdot i \cdot i \cdot 3 = (-3 \cdot i + z) \cdot \left(-i \cdot 3 + z\right)
|
18,687 |
1 - 1/x = \dfrac{1}{-\frac{1}{-x + 1} + 1}
|
-5,540 |
\frac{5}{3 \cdot r + 6} = \frac{5}{3 \cdot (r + 2)}
|
-10,569 |
3/(y*75) = 3*1/3/(y*25)
|
-17,677 |
21 + 29 = 50
|
12,592 |
E\{a+b\} = E\{a\}+E\{b\}
|
-5,202 |
10^{3 + 1}*8.4 = 10^4*8.4
|
-18,783 |
y = \frac{y}{4} \times 4
|
-621 |
\pi/3 = -\pi\cdot 8 + \pi \dfrac{25}{3}
|
-10,298 |
2/2*\frac{1}{k*2} 8 = \frac{16}{4 k}
|
5,547 |
(3 + x) \cdot (3 + x) - (x + 2)^2 = 5 + 2\cdot x
|
-10,703 |
\tfrac144*3/t = 12/\left(4t\right)
|
23,536 |
-u + u + w - w = u + w - w + u
|
17,529 |
{(-1) + n + q \choose q} = {n + q + (-1) \choose (-1) + n}
|
4,563 |
\dfrac{1}{(-a/z + 1)^2 \cdot z^2} = \dfrac{1}{(z - a)^2}
|
-499 |
\left(e^{\frac{\pi*i}{4}}\right)^{17} = e^{17*\dfrac{\pi*i}{4}}
|
10,999 |
\int \left(1 - e^{-y}\right) \cdot e^{e^y}\,\mathrm{d}y = \int (e^y + (-1)) \cdot e^{-y} \cdot e^{e^y}\,\mathrm{d}y = \int (e^y + (-1)) \cdot e^{e^y - y}\,\mathrm{d}y
|
24,391 |
c^2 - g^2 = (c - g) (c + g)
|
9,579 |
5/27 = 6/27*\dfrac{5}{6}
|
953 |
\left((\left(-1\right) + b^2)^{1/2} = -b i\Longrightarrow -b b = (-1) + b^2\right)\Longrightarrow b = -\dfrac{1}{2^{1/2}}
|
-2,677 |
\sqrt{6}*(2 + 4(-1) + 3) = \sqrt{6}
|
34,812 |
\sqrt{15} = \sqrt{5} \sqrt{3}
|
14,882 |
15 = \binom{7 + 0\times \left(-1\right) + (-1)}{3 + (-1)}\times \binom{3}{0}
|
31,486 |
\dfrac{1}{C K} = \frac{1}{K C} = K C = C K
|
36,427 |
(1-p)^4p + (1-p)^5 = (1-p)^4(p + 1 - p) = (1-p)^4
|
711 |
\sqrt{\frac{1 + t}{1 - t}} = \frac{1 + t}{\sqrt{1 - t^2}} = (1 + t) E[t]
|
-28,922 |
7/\left(7\cdot 1/20\right) = 7\cdot \tfrac{20}{7} = 20
|
-26,176 |
\frac14*6 + 3*7 = 1.5 + 21 = 22.5
|
21,098 |
3\cdot \frac{\sin{3\cdot x}}{x\cdot 3} = \frac{1}{x}\cdot \sin{x\cdot 3}
|
-2,345 |
9/20 - 3/20 = \frac{1}{20}*6
|
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