id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
22,650 |
\left(f + d\right)^2 = d^2 + d \cdot f \cdot 2 + f^2
|
4,194 |
1/27*4/\left(8*\pi\right) = 1/(\pi*54)
|
-1,868 |
-\pi \cdot \frac{19}{12} + \pi \cdot \frac{19}{12} = 0
|
42,649 |
1000 = 0 + 0(-1) + 1000
|
-11,641 |
-10 + 10\cdot i = -4 + 6\cdot \left(-1\right) + 10\cdot i
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28,396 |
\frac{36}{120} = \frac{1}{10} 3
|
3,734 |
i = s*h*e = s*e*h
|
23,698 |
\frac{1}{6^3} \cdot \binom{6}{3} = \tfrac{20}{216} = \frac{5}{54}
|
2,053 |
\arcsin{-a} = -\arcsin{a}
|
-24,755 |
\cos{\pi \cdot 7/12} = \frac14 \cdot (-6^{1 / 2} + 2^{\frac{1}{2}})
|
18,637 |
c*2 + \frac23*a \Rightarrow a = -c*3
|
-28,967 |
3 = 15 \times (-1) + 18
|
172 |
(S + 2(-1)) (1 + S) = 2(-1) + S^2 - S
|
20,051 |
R^2*X = R^2*X
|
15,206 |
z^2 + 72 - 13\cdot n^2 = 6\cdot 2^{1/2}\cdot n \cdot n + 12\cdot 2^{1/2}\cdot z = 2^{1/2}\cdot (6\cdot n^2 + 12\cdot z)
|
-5,923 |
\frac{1}{4 \cdot (6 \cdot (-1) + k)} \cdot 3 = \tfrac{3}{24 \cdot \left(-1\right) + 4 \cdot k}
|
-425 |
(e^{7i\pi/4})^{13} = e^{i\pi \cdot 7/4 \cdot 13}
|
12,925 |
\dfrac{a}{y} = \tfrac{a}{y}
|
8,456 |
(-8\cdot a + 1)\cdot (1 + a)^2 = 1 - 8\cdot a^3 - 15\cdot a \cdot a - 6\cdot a
|
34,586 |
m \cdot m/m! = \tfrac{1}{((-1) + m)!}\cdot m
|
21,015 |
ce - cb = c*(e - b)
|
26,424 |
2\times (1 + 2^n\times \left((-1) + n\right)) = 2 + 8 + 24 + 64 + \dotsm + 2^n\times n
|
25,073 |
0 + \gamma^2 = \gamma^2
|
11,623 |
4 - 7*(y^2 - y*4 + 4) = -y^2*7 + y*28 + 24*(-1)
|
-17,035 |
3 = 3(-4p) + 3 = -12 p + 3 = -12 p + 3
|
14,651 |
\tfrac{1}{k \cdot z^k} \cdot z^{k + 1} \cdot (k + 1) = (k + 1) \cdot z/k = \left(1 + \tfrac{1}{k}\right) \cdot z
|
23,497 |
\frac{1}{1}2 = 2 + \dfrac110
|
23,318 |
\int\limits_0^\pi \cos^{2\cdot k + 1}{t}\,dt = 0 = \int\limits_0^{2\cdot \pi} \cos^{2\cdot k + 1}{t}\,dt
|
-8,573 |
\dfrac{2}{3} - \dfrac{4}{12} = {\dfrac{2 \times 4}{3 \times 4}} - {\dfrac{4 \times 1}{12 \times 1}} = {\dfrac{8}{12}} - {\dfrac{4}{12}} = \dfrac{{8} - {4}}{12} = \dfrac{4}{12}
|
-22,371 |
(7 \cdot (-1) + p) \cdot \left(p + 6\right) = 42 \cdot (-1) + p^2 - p
|
-6,430 |
\tfrac{1}{t\cdot 3 + 27}\cdot 5 = \frac{5}{3\cdot (t + 9)}
|
12,659 |
|x - z| = z - x = \frac{z^2 - x^2}{x + z} \lt \frac{1}{2 \cdot x} \cdot (z \cdot z - x^2)
|
6,101 |
\tfrac13*2/3 = \frac29
|
26,907 |
14.7 = \frac{6}{6} + 6/5 + \tfrac64 + 6/3 + 6/2 + \dfrac11 \times 6
|
9,111 |
(x + c) \cdot (x + c) + d = c^2 + d + x^2 + 2\cdot x\cdot c
|
2,156 |
\dfrac{64^{1 / 2}}{8^{1 / 2}} = (\dfrac18 \cdot 64)^{\dfrac{1}{2}} = 8^{1 / 2} = 2 \cdot 2^{\frac{1}{2}}
|
-19,226 |
1/45 = \frac{1}{36\cdot \pi}\cdot A_s\cdot 36\cdot \pi = A_s
|
323 |
(i \cdot 16)^{-1} = (4 \cdot i)^{-1} - \frac{3}{16 \cdot i}
|
-6,396 |
\tfrac{1}{12 + 2\cdot p} = \frac{1}{2\cdot (6 + p)}
|
36,918 |
3^7 + 3\cdot (-1) = 2184
|
16,756 |
\frac{1}{n}*x = x/n
|
24,936 |
x^2 = (x + \left(-1\right) + 1)^2 = \left(x + \left(-1\right)\right)^2 + 2*(x + \left(-1\right)) + 1
|
28,461 |
26 = 5 * 5 + 1^2 = 4^2 + 3^2 + 1^2 = 3^2 + 3^2 + 2^2 + 2^2
|
36,626 |
|f - g| = -(f - g) = g - f
|
24,030 |
\dfrac{h}{c} \coloneqq h/c
|
11,177 |
\frac{1}{z^2 - z + 2\cdot (-1)}\cdot 2 = \frac{2}{(z + 2\cdot (-1))\cdot (z + 1)}
|
17,242 |
(1 + 1)\cdot \left(1 + 1\right)\cdot (1 + 2)\cdot \left(7 + 1\right) = 96
|
35,942 |
Y^2 + Y = 3*Y - I = Y^3 + I
|
-6,693 |
\frac{3}{100} + \frac{1}{10} \cdot 8 = \frac{80}{100} + \tfrac{1}{100} \cdot 3
|
18,247 |
\frac{\partial}{\partial y} \left(y^p G\right) = Gy^{\left(-1\right) + p} p
|
2,333 |
F = FF^0
|
-27,766 |
d/dz \left(3\tan(z)\right) = 3d/dz \tan(z) = 3\sec^2(z)
|
-22,083 |
\dfrac{6}{6}=1
|
21,467 |
x^2 + x \cdot k \cdot 2 + k^2 = (x + k) \cdot (x + k)
|
17,021 |
\cos{4 b} = \cos(b \cdot 3 + b)
|
24,678 |
-(-\cosh(x) + \sinh(x))*\left(\sinh(x) + \cosh(x)\right) = 1 \implies 1 = 5*(\cosh\left(x\right) + \sinh(x))
|
23,091 |
\left(n^3 - n^2 + n^2 - n + 1\right) \cdot (n^2 + n + 1) = (n^2 + n + 1) \cdot (1 + n \cdot n \cdot n - n)
|
49,422 |
(a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\geq \frac{3(a+b+c)}{\sqrt[3]{abc}}=\frac{2(a+b+c)}{\sqrt[3]{abc}}+\frac{(a+b+c)}{\sqrt[3]{abc}}\geq\frac{2(a+b+c)}{\sqrt[3]{abc}}+3
|
30,281 |
3^{20*j} = ((3^3)^6*3^2)^j = (27^6*9)^j
|
13,304 |
2\times \left(-1\right) + (\frac{1}{\xi} + \xi)^2 = \frac{1}{\xi^2} + \xi^2
|
48,542 |
8 = {8 \choose 1}
|
-10,396 |
-3/d \dfrac{4}{4} = -\frac{1}{4 d} 12
|
-9,614 |
30\% = 30/100 = 0.3
|
-22,636 |
\dfrac{1}{3} \times - \dfrac{5}{8} = \dfrac{1 \times -5}{3 \times 8} = \dfrac{-5}{24} = -\dfrac{5}{24}
|
13,216 |
4 \cdot 2 \cdot 3 + 5 \cdot 0 = 24
|
6,133 |
\left(-n + m\right)\cdot 3 = -3n + 3m
|
25,237 |
(\tfrac16*5)^2 = \dfrac{1}{6}*5*\frac56
|
23,708 |
l!*(1 + l) = (1 + l)!
|
-24,879 |
\frac{11}{12} = \frac{1}{12}\cdot s\cdot 12 = s
|
40,162 |
4 + x = 3 + x + 1 = 3\cdot (1 + (x + 1)/3)
|
-10,470 |
\frac{3}{3}\cdot \frac{1}{5\cdot q}\cdot 3 = \dfrac{9}{15\cdot q}
|
-4,127 |
\frac18\cdot 7 = \frac{1}{8}\cdot 7
|
2,067 |
\psi^4 + 4 = \psi^4 + 4\cdot \psi^2 + 4 - 4\cdot \psi^2 = \left(\psi^2 + 2\right)^2 - 4\cdot \psi^2 = (\psi^2 - 2\cdot \psi + 2)\cdot (\psi^2 + 2\cdot \psi + 2)
|
13,713 |
7 = 7/2 \times 2
|
18,672 |
Sy = yS + Sy
|
-3,052 |
10^{1 / 2} \cdot (1 + 4 + 5) = 10^{\tfrac{1}{2}} \cdot 10
|
-5,225 |
0.64*10^{10 + 5 (-1)} = 10^5*0.64
|
13,973 |
2 + 3^{1 / 2} = ((2^{1 / 2} + 6^{\frac{1}{2}})/2)^2
|
-6,169 |
\frac{1}{k * k + 5k + 36 (-1)}5 = \frac{1}{(k + 9) (4(-1) + k)}5
|
5,720 |
x_2/(x_1) \cdot x_1^2 = x_1 \cdot x_2
|
6,347 |
\left(x^2 + x + 1\right) \cdot (x + (-1)) = (-1) + x^2 \cdot x
|
17,103 |
(C' \times x/x)^3 = \frac{x}{x} \times C'^3
|
-28,785 |
\int z \cdot z\,\mathrm{d}z = \frac{1}{2 + 1} \cdot z^{2 + 1} + X = z^3/3 + X
|
-6,748 |
\frac{1}{100}\cdot 4 + 50/100 = 4/100 + \dfrac{5}{10}
|
13,364 |
48 = 50 + 3\cdot \left(-1\right) + 1
|
7,466 |
\sin{2\cdot \pi} + \sin{4\cdot \pi} = \sin\left(\pi\cdot 4 + \pi\cdot 2\right)
|
836 |
\left(2^5 + 5^6\right)^2 = 5^{12} + 2^{10} + 2\cdot 2^5\cdot 5^6
|
30,275 |
c + g_1 + g_2 = g_1 + g_2 + c
|
21,960 |
(3^{\left(-1\right) + x} + (-1))/2 = (3^{x + \left(-1\right)} + 3(-1))/2 + 1
|
818 |
\left(-X\cdot n + X\cdot n\right)/n = X - n\cdot X/n
|
403 |
T/I \times z = \dfrac{T}{I} \times z
|
-3,661 |
\frac{108}{60}*\tfrac{k^3}{k^5} = \frac{108*k^3}{60*k^5}
|
-29,096 |
(-2)*(-6) = 12
|
-3,988 |
k \cdot k\cdot 35/(k\cdot 30) = k \cdot k/k\cdot 35/30
|
-23,348 |
\dfrac{1}{9}*4*3/4 = \frac13
|
17,942 |
9^{91} \gt 9^{90} = (9^9)^{10} > \left(7^{10}\right)^{10} = 7^{100} \gt 7^{94}
|
33,121 |
h \cdot m = h_1 \cdot m_1 \Rightarrow h_1/h = \frac{m}{m_1}
|
18,146 |
\frac37 = \dfrac{9}{21}
|
-3,256 |
(4 + 2)\cdot 3^{1/2} = 6\cdot 3^{1/2}
|
13,471 |
8 = 4*k*j - k + j \Rightarrow \left(4*j + (-1)\right)*k + j = 8
|
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