id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
18,877 |
(1324 \cdot E)^2 = 1324 \cdot 1324 \cdot E = 12 \cdot 34 \cdot E = E
|
11,817 |
n^2 + n = n\cdot \left(1 + n\right)
|
-21,616 |
0 = \sin{\pi*2}
|
1,926 |
n + 1 \geq n + 1 rightarrow 1 + n = 1 + n
|
13,324 |
188\cdot \left(-1\right) + 16 + 112\cdot (-1) + 420 + 136\cdot (-1) = 0
|
-4,455 |
\frac{-x \cdot 5 + 8}{4 + x \cdot x - 5 \cdot x} = -\frac{4}{4 \cdot (-1) + x} - \frac{1}{x + \left(-1\right)}
|
179 |
100/200 = \frac12
|
15,458 |
c^Z W z = (c^Z W z)^Z = z^Z W c
|
10,837 |
1/(2*100) + \frac{1}{2*200} = \tfrac{3}{400}
|
24,645 |
\frac{1}{x}*x^{1/2} = \frac{1}{x^{1/2}*x^{1/2}}*x^{1/2} = \frac{1}{x^{1/2}}
|
9,079 |
5l + 6 = 5(l + 13 (-1)) + 71
|
-17,131 |
-6 = -6 \cdot (-2 \cdot m) - -12 = 12 \cdot m + 12 = 12 \cdot m + 12
|
18,959 |
\cos^2{\theta} - \sin^2{\theta} = 2\cdot \cos^2{\theta} + (-1) = 1 - 2\cdot \sin^2{\theta}
|
3,291 |
\left(\frac{2 z x}{x^2 + z^2} = -1 \implies 0 = \left(z + x\right)^2\right) \implies -z = x
|
3,643 |
(8 + y^2 + 1)^{-\frac12} = \left(y^2 + 9\right)^{-1/2}
|
9,545 |
1 = (y + (-1))^2 + \left(x + (-1)\right) * \left(x + (-1)\right) rightarrow 1 + (1 - \left(\left(-1\right) + x\right)^2)^{1 / 2} = y
|
36,755 |
-6/6.04 = \frac{1}{6.04 + 0 \times \left(-1\right)} \times \left(0 + 6 \times \left(-1\right)\right)
|
20,963 |
(y^2 - y + 6\cdot (-1))\cdot (y + 4) = 24\cdot \left(-1\right) + y^3 + 3\cdot y^2 - 10\cdot y
|
19,484 |
-\cos(p) = \sin\left(p - \pi/2\right)
|
17,159 |
60/100*n = n*3/5
|
-18,963 |
1/2 = \dfrac{1}{36 \pi} E_s*36 \pi = E_s
|
37,552 |
J_2 x_2 = J_2 x_2
|
3,286 |
\frac{1}{a}\cdot 1/b/c = \frac{1}{a\cdot c\cdot b}
|
13,005 |
\dfrac{r}{h - 2 \cdot R - r} = \frac{R}{h - R} \Rightarrow h = \frac{R \cdot R \cdot 2}{R - r}
|
13,207 |
\frac{\pi}{4} + 2*\pi*0 = \pi/4
|
-19,311 |
9/2 \cdot \frac79 = \frac{9}{9 \cdot \dfrac17} \cdot \frac{1}{2}
|
23,978 |
\left(-1\right) + y_4 = y_4
|
-19,677 |
9 \cdot 8/(9) = \tfrac{72}{9}
|
34,275 |
y^4 + 16*\left(-1\right) = (y^2 + 4*(-1))*\left(y * y + 4\right) = (y + 2*(-1))*(y + 2)*(y - 2*i)*\left(y + 2*i\right)
|
32,192 |
\operatorname{atan}(\sqrt{3}) \cdot 3 = \pi
|
-7,567 |
\frac{1}{34} \cdot (-6 + 24 \cdot i + 10 \cdot i + 40) = \left(34 + 34 \cdot i\right)/34 = 1 + i
|
32,413 |
\dfrac{1}{2}*(\sqrt{5} + 1) = 1/2 + \sqrt{5}/2
|
26,599 |
\cos^2{\theta} = (1 + \cos{2*\theta})/2
|
7,379 |
n + k - 2 \times k = -k + n
|
28,137 |
k_x*k_i = k_x*k_i
|
14,713 |
-\sin\left(40*\left(-1\right) + 90\right)*3^{1 / 2}/\sin(50) = -3^{\tfrac{1}{2}}
|
22,424 |
\frac{5}{3} = \frac{1}{\frac{10}{2} + 1} \cdot 10
|
25,217 |
\sigma\times x = \sigma\times x
|
20,197 |
\cos(2*\pi/3) = -1/2
|
22,802 |
\sqrt{8 \cdot 8 + 4^2 + (-8)^2} = 12
|
8,436 |
A\cdot H = H \cdot H\cdot H = H^3 = H\cdot H^2 = H\cdot A
|
-26,633 |
36 - B \cdot B = -B^2 + 6^2
|
19,752 |
\sin{3\cdot \theta} = 3\cdot \sin{\theta} - 4\cdot \sin^3{\theta}
|
20,309 |
|X\cdot g| = |-g\cdot X|
|
30,442 |
\frac{\partial}{\partial x} u^n = \frac{\partial}{\partial u} u^n \cdot \frac{\mathrm{d}u}{\mathrm{d}x}
|
26,328 |
x + q ± m = x + q ± m = x ± m + q
|
10,129 |
r\cdot X = r\cdot Y = n \Rightarrow X\cdot Y\cdot r = n
|
18,240 |
-1 = (-1)^{2 \cdot 3/2} = \left((-1)^2\right)^{3/2} = 1^{\frac{3}{2}} = 1^{1/2}
|
26,566 |
194689796301 = 21589*(3*7*11*13) * (3*7*11*13)
|
6,924 |
t_i*l_i = l_i*t_i
|
8,327 |
\left(e = e^{4 - 4\times B}\Longrightarrow 1 = 4 - B\times 4\right)\Longrightarrow \frac{1}{4}\times 3 = B
|
1,747 |
n^2 + 2 \cdot n + 3 \cdot (-1) = (3 + n) \cdot (n + (-1))
|
20,635 |
(k + x)*(i + \zeta) = \zeta*x + i*k + x*i + \zeta*k
|
-28,795 |
\dfrac{2\cdot \pi}{\tfrac{1}{3}\cdot 2\cdot \pi} = 3
|
12,466 |
\frac{z_m}{1 + z_m} = -\frac{1}{1 + z_m} + 1
|
12,638 |
\frac{\partial}{\partial x} (x\cdot \beta) = x\cdot \frac{d\beta}{dx} + \beta\cdot \frac{dx}{dx}
|
-4,730 |
\frac{1}{y + 2} - \tfrac{1}{y + \left(-1\right)}\cdot 5 = \frac{1}{2\cdot (-1) + y^2 + y}\cdot \left(11\cdot \left(-1\right) - 4\cdot y\right)
|
22,488 |
|\overline{e_j}| = |e_j|
|
-27,499 |
3 \cdot 5 \cdot n \cdot n \cdot n \cdot 2 = n^3 \cdot 30
|
45,997 |
(e^{i\pi})^2 = e^{2\pi i} = 1
|
4,874 |
2^{\frac{1}{3} \cdot (n + 1)} = 2^{1/3} \cdot 2^{\frac{n}{3}} > n \cdot 2^{\frac{1}{3}}
|
-15,945 |
-6\cdot 3/10 + 7/10\cdot 5 = \frac{17}{10}
|
16,966 |
-h^2 + a^2 = (-h + a) \cdot (a + h)
|
-2,248 |
\dfrac{3}{10} = \tfrac{1}{10}\cdot 4 - 10^{-1}
|
-6,894 |
6*4*8 = 192
|
26,097 |
2l + 1 = (l + 1)^2 - l \cdot l
|
7,298 |
df = 1 rightarrow fd = 1
|
-6,252 |
\dfrac{4}{z^2 - 3\cdot z + 18\cdot (-1)} = \frac{4}{(z + 3)\cdot (z + 6\cdot \left(-1\right))}
|
38,375 |
det\left(A\right) = 0 \Rightarrow A
|
-21,004 |
\frac{1}{10}\cdot 3\cdot \frac{9\cdot k}{9\cdot k} = 27\cdot k/(k\cdot 90)
|
-19,700 |
\dfrac{56}{9}\cdot 1 = 56/9
|
-15,960 |
5/10\cdot 6 - 10\cdot \frac{1}{10}\cdot 5 = -\frac{20}{10}
|
-1,365 |
\frac{24}{56} = \frac{3}{56 \cdot 1/8} \cdot 1 = 3/7
|
11,591 |
a + e + a\cdot e = (-1) + (e + 1)\cdot (a + 1)
|
-597 |
e^{7*i*\pi*3/2} = (e^{3*\pi*i/2})^7
|
-18,368 |
\dfrac{r \cdot r - r}{r^2 - 10 \cdot r + 9} = \frac{r}{(r + (-1)) \cdot (9 \cdot (-1) + r)} \cdot (\left(-1\right) + r)
|
-12,051 |
11/30 = \frac{1}{6 \cdot π} \cdot s \cdot 6 \cdot π = s
|
-19,463 |
\tfrac{\dfrac{1}{4} \cdot 3}{\frac19 \cdot 5} = 3/4 \cdot 9/5
|
3,664 |
\dfrac{1}{((-1) + y)*(3 + y)}*4 = \dfrac{1}{y + (-1)} - \frac{1}{3 + y}
|
-7,646 |
\frac{1}{-5 - 2 \cdot i} \cdot (4 + 19 \cdot i) \cdot \frac{-5 + i \cdot 2}{2 \cdot i - 5} = \frac{i \cdot 19 + 4}{-5 - i \cdot 2}
|
24,497 |
\dfrac{1}{\sqrt{1 + z \cdot z}} = \cos(\tan^{-1}(z))
|
32,150 |
(2 + 3 + 1)\cdot 3 = 18
|
4,958 |
(2 - \sqrt{3})/3 = (-4\sqrt{3} + 8)/12
|
-10,747 |
-\frac{30}{x\cdot 9 + 15\cdot \left(-1\right)} = -\frac{1}{5\cdot (-1) + 3\cdot x}\cdot 10\cdot 3/3
|
7,266 |
y \cdot \left(y^2 + 2 \cdot y + 1\right) = y^3 + 2 \cdot y^2 + y = 2 \cdot y^2 + y + 5 \cdot (-1)
|
28,292 |
(a + b)^2 = 100 = a^2 + 2 \cdot a \cdot b + b^2 \Rightarrow -\dfrac{1}{2} \cdot (a^2 + b^2) = a \cdot b
|
-10,431 |
\frac{4}{2*\left(-1\right) + x*2} = \frac22*\frac{2}{\left(-1\right) + x}
|
-4,323 |
\frac{1}{y^2 \cdot 5}6 = \frac{1}{y^2}6 / 5
|
41,377 |
2468/990 = \frac{1234}{495}
|
26,149 |
{31 \choose 2} = {29 + 3 + (-1) \choose (-1) + 3}
|
-1,596 |
-2*\pi + \pi*3 = \pi
|
30,231 |
15238195.2 = (484269.6 + 45340.8 + 184680)\times \tfrac{128}{6}
|
-12,359 |
45 = 3 * 3*5
|
-22,311 |
90 + y^2 - y*19 = (9*(-1) + y)*(10*(-1) + y)
|
24,416 |
\pi = 3.14159265358\cdot \cdots = 3 + 1/10 + \tfrac{1}{100}\cdot 4 + \frac{1}{1000} + \frac{5}{10000} + \cdots
|
29,282 |
z^{l + (-1)} \cdot z = z^l
|
8,628 |
286 = 78*(13 + 1 + 3*\left(-1\right))/3
|
-3,360 |
-\sqrt{12} + \sqrt{48} = \sqrt{16*3} - \sqrt{4*3}
|
-27,414 |
368 + 10\cdot (-1) = 358
|
16,739 |
F \cdot F \cdot D = -F \cdot D \cdot F = D \cdot F \cdot F
|
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