id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
9,347 |
\sin{2^{n + 1}} = 2 \cdot \cos{2^n} \cdot \sin{2^n}
|
234 |
D^2 \cdot D := D \cdot D^2
|
53,286 |
1 = (-1)^2
|
12,737 |
(y + 1) (4y^2 - 4y + 3\left(-1\right)) = 4(y^2 - y - 3/4) \left(y + 1\right)
|
11,860 |
\frac{H}{r + 1} + \frac{A}{(-1) + r} = \frac{1}{((-1) + r)*(1 + r)} \Rightarrow 1 = r*(H + A) + A - H
|
10,431 |
x^{k + (-1)} = \dfrac{d\cdot x^{k + (-1)}}{d + x} + \frac{x}{d + x}\cdot x^{k + (-1)} = \dfrac{d}{d + x}\cdot x^{k + (-1)}
|
-20,715 |
\frac{6 + 27 m}{m \cdot 24} = (2 + m \cdot 9)/\left(8m\right) \cdot 3/3
|
5,147 |
(x \cdot 3 + 1)^4 \cdot (18 \cdot x + 1) = (1 + 3 \cdot x)^4 \cdot (15 \cdot x + 1 + 3 \cdot x)
|
21,038 |
\left(2\cdot (2\cdot (-1) + z) + z + 1 - z + 3\cdot (z + \left(-1\right)) = z + 2 \Rightarrow z + 2 = 5\cdot z + 6\cdot (-1)\right) \Rightarrow z = 2
|
30,781 |
b_1 + d + b_2 = d + b_2 + b_1
|
-4,082 |
\frac{1}{3}\cdot 2\cdot y^4 = \tfrac{2\cdot y^4}{3}\cdot 1
|
3,858 |
1728 = (2 \sqrt{3})^6
|
-19,079 |
\frac{1}{15}2 = \frac{B_t}{100 \pi}*100 \pi = B_t
|
-262 |
\dfrac{8!}{(3 \cdot (-1) + 8)!} = 8 \cdot 7 \cdot 6
|
9,121 |
-\tfrac{b}{f_2 \cdot 2} = -\frac{1}{f_2 \cdot 4} \cdot (-4 \cdot f_1 \cdot f_2 + b^2) \implies 4 \cdot f_2 \cdot f_1 = b \cdot b - 2 \cdot b = (b + (-1))^2 + (-1) \geq -1
|
-7,738 |
\dfrac{1}{-4 - 4\cdot i}\cdot (4 - 4\cdot i)\cdot \frac{4\cdot i - 4}{-4 + 4\cdot i} = \dfrac{4 - 4\cdot i}{-4\cdot i - 4}
|
5,912 |
10^2 \cdot 10 \cdot 10^2 \cdot 10 = 10^6
|
7,780 |
2*y*x + x^2 + y^2 = \left(y + x\right)^2
|
27,626 |
\int\limits_{-1}^3 f\,dx = \int\limits_{-5}^{-1} f\,dx
|
35,587 |
(2(0+1))^n=2^n
|
7,412 |
4 \cdot z^4 + 4 \cdot z^3 + z \cdot z = 4 \cdot z^4 + 2 \cdot z^3 + z^3 \cdot 2 + z^2
|
-1,079 |
6/63 = \frac{6\cdot \frac{1}{3}}{63\cdot 1/3} = \dfrac{2}{21}
|
1,593 |
3 = |i \times b + a| \Rightarrow \sqrt{a^2 + b^2} = 3
|
-406 |
e^{2 \cdot \pi \cdot i} = e^{\pi \cdot i} \cdot e^{\pi \cdot i} = (-1)^2 = 1
|
-10,611 |
-\dfrac{1}{15\cdot \left(-1\right) + 5\cdot r}\cdot 30 = 5/5\cdot (-\frac{1}{r + 3\cdot (-1)}\cdot 6)
|
6,121 |
z = \frac{c_2}{w} + c_1 w \Rightarrow 0 = w^2 c_1 - wz + c_2
|
10,873 |
\tfrac35 \cdot \frac35 = 9/25
|
33,257 |
120 = 2^3\times 3\times 5
|
25,910 |
b^2 + a^2 = \sqrt{(a^2 - b^2)^2 + (2 \cdot a \cdot b)^2} = 25 \implies b^2 = 16\wedge a^2 = 9
|
27,173 |
\dfrac{1}{\dfrac{1}{y^2}} = y^2 = \frac{1}{1} \cdot y \cdot y
|
10,530 |
\frac{1}{2^{1 + x}}\cdot (x + 1)! = \left(x + 1\right)/2\cdot \dfrac{1}{2^x}\cdot x!
|
31,305 |
2^{\frac62} = 8
|
-11,587 |
-4 - i*2 = -4 + 0 \left(-1\right) - 2 i
|
8,230 |
K = (d \times K)^x = d^x \times K
|
3,323 |
z\cdot 6 - y\cdot 4 = z\cdot 6 - y\cdot 3 - y
|
-5,694 |
\frac{1}{z \cdot z + 8z + 7}2z = \frac{2z}{\left(z + 1\right) (7 + z)}
|
10,010 |
d\cdot d\cdot h = d\cdot d\cdot h
|
-11,515 |
i \cdot 13 - 3 + 12 = 13 \cdot i + 9
|
1,443 |
c/d + 1 = \tfrac1d(c + d)
|
13,610 |
2^{5/12} = 1.334839 \cdot \dots \approx \frac{1}{3} \cdot 4
|
-7,766 |
\frac{-3*i - 3}{3 + 3*i} = \frac{1}{i*3 + 3}*(-3 - i*3)*\frac{-i*3 + 3}{3 - 3*i}
|
23,870 |
3z + 1 = (1 + (z + 4)^{\frac{1}{2}})^2 = 1 + 2(z + 4)^{1 / 2} + z + 4
|
-22,840 |
\frac{16}{20} = \frac{4\cdot 4}{4\cdot 5}
|
8,123 |
n^2 * n^2 * n^2 = n^6
|
20,697 |
\operatorname{acos}(\cos(-\operatorname{acos}(t) + \pi)) = \operatorname{acos}(-t) \Rightarrow \operatorname{acos}(-t) = \pi - \operatorname{acos}(t)
|
-3,021 |
\sqrt{2}*\sqrt{25} - \sqrt{2}*\sqrt{4} = 5*\sqrt{2} - 2*\sqrt{2}
|
25,235 |
0.5 + 0*0.5 = 1/2
|
23,611 |
6 + 8\cdot n = 2\cdot (3 + 4\cdot n)
|
30,462 |
\operatorname{E}(X^2) = \operatorname{E}((X + 1)^1) = \operatorname{E}(X + 1)
|
-7,534 |
\frac{1}{3 - i*5}*\left(-i*19 - 9\right) = \frac{3 + 5*i}{3 + 5*i}*\frac{-9 - i*19}{3 - 5*i}
|
-20,160 |
\frac44 \cdot \frac{6}{-y \cdot 3 + 9 \cdot \left(-1\right)} = \frac{24}{36 \cdot (-1) - 12 \cdot y}
|
-26,397 |
1/(46656\cdot \tfrac{1}{7776}) = 6^{-6 - -5} = \tfrac16
|
18,488 |
y^2 + y + 1 = (-y + 2\cdot \left(-1\right))\cdot (-y + 1) + 3
|
14,303 |
15/79\cdot 16/80 = \frac{3}{79}
|
-26,600 |
3x * x + 147 \left(-1\right) = 3(x^2 + 49 \left(-1\right)) = 3(x + 7) (x + 7\left(-1\right))
|
-7,364 |
2/5 = \frac{\dfrac{4}{5}}{2}1
|
31,260 |
C_2 C_1 = \begin{array}{rl}1 & -1\\0 & 1\end{array} = \frac{1}{C_1 C_2}
|
2,592 |
xy = \Im{(xy)} = \Im{(yx)} = yx = -x y
|
32,745 |
1/35 = 3/7 \cdot 2/6/5
|
22,061 |
2 \times a^1 \times x^1 + a^2 \times x^0 + x \times x \times a^0 = \left(a^1 + x^1\right)^2
|
-19,700 |
\frac{7}{9}*8 = \dfrac{1}{9}*56
|
2,442 |
x^6 + z^6 = (x^2)^3 + \left(z^2\right)^3 = (x^2 + z^2)\cdot (x^4 - x^2\cdot z^2 + z^4)
|
18,577 |
4 + 3 < 5 + 6\Longrightarrow 3\cdot 4 \lt 5\cdot 6
|
24,556 |
z^6 + (-1) = (z + (-1))*(z^0 + z^5 + z^4 + z^3 + z^2 + z^1)
|
-18,405 |
\frac{1}{6*r + r^2}*\left(6 + r^2 + 7*r\right) = \frac{(r + 6)*(1 + r)}{(6 + r)*r}
|
27,282 |
\pi/3 = -\dfrac{7}{12} \cdot \pi + 11 \cdot \pi/12
|
10,168 |
\frac{1}{42} + \frac{1}{42} + \frac{1}{42} + \dfrac{1}{42} + \frac{1}{42} + 1/42 + \frac{1}{42} = 7/42 = \tfrac16 \approx 0.167
|
30,226 |
y/\|y\| \cdot \|y\| = y
|
25,466 |
(T \cdot T)^2 = T^4 = T^3 \cdot T = T^2 \cdot T = T^3 = T^2
|
40,349 |
N + 4 = 3 + N + 1
|
14,213 |
{10 \choose 6}*2 = {12 \choose 7} - {10 \choose 5} - {10 \choose 3}
|
834 |
3 \cdot (n \cdot 7 + m \cdot 5) = n \cdot 21 + 15 \cdot m
|
22,437 |
2 + n + 3\cdot (-1) = (-1) + n
|
7,739 |
6*y + z = 5 \Rightarrow z = 5 - 6*y
|
23,147 |
-4*i = 4*(\cos\left(-\frac12*\pi\right) + i*\sin(-\frac12*\pi)) = -4*i
|
27,146 |
\sin{\dfrac{m}{x} \cdot \pi} = \operatorname{im}{\left(y\right)} \Rightarrow y = e^{i \cdot m \cdot \pi/x}
|
32,146 |
150/255 = \frac{1}{17}10
|
23,689 |
x^{-w} = \frac{1}{x^w}
|
-3,852 |
q^2*2/7 = q^2*\dfrac27
|
10,755 |
f\cdot x + \left(f - x\right)^2 = x \cdot x + f \cdot f - x\cdot f
|
35,281 |
5*\frac{1}{36}16 - 5*\dfrac{1}{36}20 = -\frac{20}{36} = -\frac{1}{9}5
|
13,812 |
\sin{\theta} = \frac{\tan{\theta/2}*2}{1 + \tan^2{\tfrac{\theta}{2}}}*1
|
18,258 |
8*x*y = \left(x + 2*y\right)^2 - (x - 2*y)^2 = 1 - \left(x - 2*y\right) * \left(x - 2*y\right)
|
898 |
\left(-(-Y + C) * (-Y + C) + (C + Y)^2\right)/4 = C*Y
|
39,025 |
-l = l \Rightarrow l = 0
|
28,047 |
6 = \frac{4}{2} \cdot 3
|
-20,147 |
\frac{7 - 3m}{-3m + 7} \cdot \dfrac{3}{7} = \frac{21 - 9m}{49 - m \cdot 21}
|
21,273 |
31 = 961^{1 / 2}
|
25,522 |
2\cdot g_2\cdot g_1 + g_1 \cdot g_1 + g_2 \cdot g_2 = (g_1 + g_2)^2
|
23,839 |
2*(\frac{8}{3} + \tfrac43) = 8 = 2^3
|
15,023 |
\frac{1}{-y \cdot y + x^2}\cdot (x - y) = \frac{1}{x + y}
|
-15,945 |
\dfrac{1}{10} \cdot 17 = 5 \cdot \frac{1}{10} \cdot 7 - \frac{1}{10} \cdot 3 \cdot 6
|
-2,670 |
3^{\dfrac{1}{2}} + 75^{1 / 2} = 3^{\frac{1}{2}} + (25*3)^{1 / 2}
|
46,818 |
7 \cdot 8 \cdot 9 \cdot 10 = 7!
|
19,063 |
\tfrac{1}{(-x + w)^2} = \frac{1}{-x + w}
|
31,793 |
y^3 + x^3 = (x + y)\cdot (x^2 - y\cdot x + y^2)
|
3,257 |
(D^2 + D\cdot 5 + 4)\cdot x = 4\cdot x + x\cdot D^2 + 5\cdot x\cdot D
|
4,796 |
(b\cdot \frac{x}{b})^2 = b\cdot x\cdot b\cdot x/b/b = b\cdot x^2/b
|
33,300 |
a = \left(a^2\right)^{1 / 2} \leq \frac12*a^2
|
30,840 |
5^2\cdot 3^2\cdot 2^5 = 7200
|
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