id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
2,803 |
\frac{\text{d}}{\text{d}h} (-h^2 + 1) = -2 \cdot h
|
-11,838 |
3.44*0.01 = \dfrac{3.44}{100}
|
30,802 |
E = \sqrt{E} \cdot \sqrt{E}
|
27,009 |
\frac{1}{3 \cdot z^{\frac{2}{3}}} = \frac{1}{3 \cdot z^{\frac13 \cdot 2}}
|
1,452 |
\left(x - z\right)^2 = x^2 - xz*2 + z^2
|
-23,029 |
\frac{21}{49} = \tfrac{3*7}{7*7}
|
17,054 |
(z^2 + 2*(-1))*(z^2 + 3*(-1)) = z^4 - z^2*5 + 6
|
4,958 |
\frac13\cdot (-\sqrt{3} + 2) = (8 - 4\cdot \sqrt{3})/12
|
4,298 |
0 = h + g \Rightarrow h = -g
|
-15,802 |
-76/10 = 5/10 - 9\cdot 9/10
|
4,738 |
(f_1 + f_2) (f_2 + f_1) = \left(f_2 + f_1\right) f_1 + (f_2 + f_1) f_2
|
-3,056 |
-\left(4*7\right)^{\tfrac{1}{2}} + (25*7)^{\frac{1}{2}} = 175^{1 / 2} - 28^{1 / 2}
|
4,402 |
\left( \rho(x), z\right) = \left( \rho(x), \rho(\rho^{-1}(z))\right) = ( x, \rho^{-1}\left(z\right))
|
-10,466 |
2 = -5 \cdot p + 3 \cdot (-1) + 9 = -5 \cdot p + 6
|
4,213 |
\frac{2 / 3}{y + 2 \cdot (-1)} \cdot 1 - \frac{1}{y + 1} \cdot 2 / 3 = \frac{1}{y^2 - y + 2 \cdot (-1)} \cdot 2
|
4,196 |
f \cdot h + z^2 + (f + h) \cdot z = (h + z) \cdot \left(f + z\right)
|
18,824 |
Y^{2 \cdot l} = Y^l \cdot Y^l
|
3,681 |
a^\beta = b^y = (a \cdot b)^{\beta \cdot y}
|
-1,337 |
18/2 = 18*1/2/\left(2*\tfrac{1}{2}\right) = 9
|
7,867 |
2c + b + d = 1 + c \geq 2\sqrt{\left(b + c\right) (c + d)}
|
4,413 |
\frac{1}{\binom{(-1) + k}{2}}*\binom{2*(-1) + k}{2} = \dfrac{1}{k + (-1)}*(3*(-1) + k)
|
14,862 |
1/x + x = (1 + x^2)/x
|
31,971 |
4/52\cdot 3/51 = 12/2652 = \dfrac{1}{221}
|
19,845 |
\N = \left\{3, 2, 1, \ldots\right\}
|
33,029 |
\sqrt{x} \lt \sqrt{z}\Longrightarrow x = \sqrt{x}*\sqrt{x} < \sqrt{x}*\sqrt{z} = \sqrt{x*z}
|
-28,910 |
24 + K = 6 + 4 + 8 + 1 + 5 + K
|
32,913 |
x = x - x\cdot X + X\cdot x \Rightarrow \|X\cdot x\| + \|-X\cdot x + x\| \geq \|x\|
|
-12,947 |
20 + 3(-1) = 17
|
26,380 |
\frac{1}{5^2}\cdot (12 \cdot 12 - 5 \cdot 5) = \frac{1}{5^2}\cdot 13^2 + 2\cdot (-1)
|
-10,764 |
\dfrac{10}{5\times r + 10} = \frac{1}{5}\times 5\times \frac{1}{r + 2}\times 2
|
21,193 |
10 = \frac{2\cdot 5\cdot 4\cdot 3}{2(5 + 3(-1))!\cdot 3}
|
-20,734 |
64\cdot k/(k\cdot 24) = \frac{1}{3}\cdot 8\cdot 8\cdot k/\left(k\cdot 8\right)
|
22,944 |
(z + \left(-1\right))\cdot (-e^{\frac2m\cdot \pi} + z)\cdot \dotsm\cdot e^{(\left(-1\right) + m)\cdot \pi\cdot 2/m} = (-1) + z^m
|
-20,741 |
\frac{8 \cdot \left(-1\right) + x}{8 \cdot (-1) + x} \cdot \left(-3/1\right) = \dfrac{1}{x + 8 \cdot (-1)} \cdot \left(-3 \cdot x + 24\right)
|
11,386 |
x \cdot x \cdot x + (-1) + x^4 - x^3 = (-1) + x^4
|
6,800 |
-a^2 + b^2 = -c \cdot c + 2\cdot x\cdot c \Rightarrow (b^2 - a^2 + c^2)/(c\cdot 2) = x
|
17,962 |
(b^2 + a^2) \cdot (c \cdot c + h^2) = (a \cdot c + h \cdot b)^2 + (-c \cdot b + a \cdot h)^2
|
8,393 |
\pi = 3.14159 ... = 3 + \frac{1}{10} + 4/100 + 1/1000 + ...
|
20,842 |
z^4 + 4 = z^4 + 4\cdot z^2 + 4 - 4\cdot z^2 = (z \cdot z + 2) \cdot (z \cdot z + 2) - (2\cdot z)^2 = (z^2 + 2\cdot z + 2)\cdot (z^2 - 2\cdot z + 2)
|
3,312 |
E[a + b*X] = E[a] + E[b*X] = a + b*E[X]
|
25,121 |
2 - 9y^7 + 7y^9 = (1 - y)^2 \cdot (2 + 4y + 6y^2 + 8y^3 + 10 y^4 + 12 y^5 + 14 y^6 + 7y^7) \approx 63 (1 - y)^2
|
3,068 |
h^{x + t} = h^t*h^x
|
-2,406 |
\sqrt{6} \times 2 + 3 \times \sqrt{6} = \sqrt{4} \times \sqrt{6} + \sqrt{6} \times \sqrt{9}
|
23,077 |
1=\frac{6+15+10-1}{30}
|
10,714 |
F^{24} = F^8*F^{16}
|
-5,899 |
\frac{1}{4\cdot (n + 6\cdot (-1))}\cdot 2 = \frac{2}{24\cdot \left(-1\right) + 4\cdot n}
|
20,031 |
y*5 = 1 + \left(1 + p*5\right)*19 \Rightarrow y = 4 + 19 p
|
9,256 |
4 = 3^{\cos^2\left(x\right)} + 3^{\sin^2(x)} \Rightarrow 4 = 3^{1 - \cos^2(x)} + 3^{\cos^2(x)}
|
-20,682 |
\frac18 \cdot 1 = \frac{-2 \cdot q + 4}{-16 \cdot q + 32}
|
-23,663 |
\frac{3}{20} = \frac34 \cdot 1/5
|
7,610 |
0/6 + 1\cdot 2/3 + \frac{2}{6} = 2/3 + \frac13 = 1
|
29,002 |
y_2 + y_3 + y_4 = 0 \Rightarrow y_2 = -y_3 - y_4
|
-11,373 |
(x + 3 (-1)) (x + 3 (-1)) + b = \left(x + 3 \left(-1\right)\right) (x + 3 (-1)) + b = x^2 - 6 x + 9 + b
|
-2,916 |
\left(2 + 4 + 5*(-1)\right)*11^{1/2} = 11^{1/2}
|
16,597 |
4\cdot \cos{\theta} = 3^{1 / 2}\cdot \sin{\theta}\cdot \csc^2{\theta} = 3^{1 / 2}\cdot \csc{\theta}
|
22,209 |
x^2 = -x \cdot (-x)
|
25,465 |
e^{y \times 2}/2 = x^2/2 - 8 \times x + C \Rightarrow e^{y \times 2} = C \times 2 + x \times x - 16 \times x
|
29,551 |
h^4 \cdot z = z = h^3 \cdot z
|
-4,096 |
\frac{s}{s^3}*\frac{1}{72}*144 = \frac{s}{s^3*72}*144
|
-7,845 |
\frac{1}{-i - 3} \times (-1 - i \times 17) = \tfrac{-3 + i}{-3 + i} \times \tfrac{1}{-i - 3} \times \left(-1 - 17 \times i\right)
|
20,545 |
af_1 f_2 = f_1 a f_2
|
6,669 |
7^{202} = 7^2 \cdot \left(7^4\right)^{50}
|
-9,526 |
56 = 7*8
|
21,276 |
\frac1x = 0\Longrightarrow x \cdot 0 = 1
|
28,244 |
(n + 1)! = 1 \cdot 2 \cdot ... \cdot n \cdot \left(n + 1\right) = n! \cdot (n + 1)
|
1,198 |
J \cdot z = z \cdot J
|
-30,261 |
\frac{1}{y + 3}\cdot (y \cdot y - y + 12\cdot (-1)) = \dfrac{1}{y + 3}\cdot (y + 3)\cdot (y + 4\cdot (-1)) = y + 4\cdot (-1)
|
-15,171 |
\frac{t^{16}}{z^2 \cdot t^{10}} = \dfrac{1}{(t^5 \cdot z) \cdot (t^5 \cdot z) \cdot \frac{1}{t^{16}}}
|
12,553 |
E(x) E(W) = E(Wx)
|
21,355 |
\dfrac12 = 3/6\cdot \frac{3}{6} + 3/6\cdot 3/6
|
20,840 |
\sqrt{3} = \sqrt{\left(0 \cdot (-1) + 1\right) \cdot \left(0 \cdot (-1) + 1\right) + (0 \cdot (-1) + 1) \cdot (0 \cdot (-1) + 1) + (0 \cdot (-1) + 1)^2}
|
11,095 |
c^2 + 2\cdot d\cdot c + d^2 = (d + c)^2
|
19,438 |
15 \cdot 23 = \left(10 + 5\right) \cdot \left(20 + 3\right) = 20 \cdot 10 + 5 \cdot 20 + 10 \cdot 3 + 5 \cdot 3 = 200 + 130 + 15
|
25,466 |
(R^2)^2 = R^4 = R^3 \cdot R = R^2 \cdot R = R^3 = R^2
|
27,552 |
p\cdot f_T = p\cdot f_T
|
-21,013 |
\frac{-r + 1}{r \cdot 4 + 4 \cdot (-1)} = -1/4 \cdot \frac{(-1) + r}{r + (-1)}
|
17,710 |
|h\cdot a| = |a|\cdot |h|
|
4,032 |
\frac{a}{-\frac{a}{2} + 1} = 8 \Rightarrow 8 - 4*a = a
|
20,556 |
(x + 1) x \dotsm\cdot (x + k + (-1)) = x^k
|
-3,041 |
117^{\frac{1}{2}} + 52^{\frac{1}{2}} = (4\cdot 13)^{\frac{1}{2}} + (9\cdot 13)^{1 / 2}
|
-448 |
(e^{\frac{i*\pi}{4}})^{12} = e^{\pi*i/4*12}
|
29,180 |
(d + c)^2 = c^2 + d^2 + 2\times d\times c
|
7,532 |
2^{2*m} + (-1) = (2^m + 1)*((-1) + 2^m)
|
19,831 |
5 = 3^2 + 4(-1)
|
28,228 |
\frac{2}{6/10 + \frac{1}{7}\cdot 2}\cdot \frac17 = \frac{1}{31}\cdot 10
|
7,512 |
G^{1 + i} = G^i
|
-1,922 |
25/12 \pi = \pi/2 + \pi \cdot 19/12
|
40,305 |
4^{n + 1} + 5 = 4\cdot 4^n + 5 = 4^n + 5 + 3\cdot 4^n
|
-18,810 |
\theta*6/6 = \theta
|
27,078 |
\dfrac{x}{a^2} = \frac{x}{a^2}
|
-30,847 |
2\cdot (-1) + y = \frac{y^3 + y^2 - y\cdot 6}{3\cdot y + y^2}
|
48,666 |
\frac{2^4}{2^8}=\frac{1}{16}
|
12,842 |
\mathbb{E}[x] \cdot \mathbb{E}[z] = \mathbb{E}[x \cdot z]
|
-639 |
e^{5\cdot \frac76\cdot i\cdot \pi} = (e^{i\cdot \pi\cdot 7/6})^5
|
2,549 |
z^2 + 2 \cdot v \cdot z + v^2 = \left(z + v\right)^2
|
3,034 |
n \cdot n \cdot n = 12 \cdot n - 5 \cdot n^2 = 12 \cdot n - 5 \cdot (12 - 5 \cdot n) = 37 - 60 \cdot n
|
-698 |
π*4/3 = -24 π + \frac{76}{3} π
|
8,283 |
a\cdot b = \dfrac{1}{1/\left(a\cdot b\right)} = \dfrac{1}{\frac1a\cdot 1/b} = 1/(\frac1b\cdot \frac1a) = b\cdot a
|
462 |
-2/4 + 2 = \frac{3}{2}
|
28,753 |
(\psi \cdot \psi)^2 = \psi^4
|
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