id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
26,427 |
-15/2 + 7 = -1/2
|
18,142 |
\frac{1}{2}*(1 + \cos{2*y}) = \cos^2{y}
|
-1,592 |
-7/6 \cdot \pi + \frac{11}{12} \cdot \pi = -\frac{\pi}{4}
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47,342 |
\tan{\frac{\pi}{4}} = 1
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17,192 |
l*x*\beta = \beta*l*x
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-4,843 |
6.30 \times 10^{-1} = {6.30 \times 10^{-1}} \times 10^{2} = 6.30\times 10^{1}
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-10,769 |
5/5 \dfrac{1}{8 (-1) + 10 q} \left(q\cdot 3 + 2\right) = \frac{1}{50 q + 40 (-1)} (15 q + 10)
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41,949 |
E_1 \cap (B \cup E_2) = (B \cap E_1) \cup (E_1 \cap E_2) = E_2 \cup \left(B \cap E_1\right)
|
-9,188 |
20 - n \cdot 24 = 2 \cdot 2 \cdot 5 - n \cdot 2 \cdot 2 \cdot 2 \cdot 3
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7,157 |
10 \cdot 32 = 320
|
293 |
20 - 24 \cdot z + 5 \cdot z = 7 \Rightarrow 20 - 19 \cdot z = 7
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19,455 |
\frac{40}{120} = \frac{1}{3} = \frac{2}{6}
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-3,096 |
3^{1 / 2}\cdot 5 + 4\cdot 3^{1 / 2} = 3^{1 / 2}\cdot 25^{1 / 2} + 16^{1 / 2}\cdot 3^{\frac{1}{2}}
|
-1,418 |
\frac{10}{14} = 10\cdot \tfrac{1}{2}/(14\cdot 1/2) = \tfrac{5}{7}
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54,688 |
\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{x+y+z}\implies \frac{1}{x^5}+\frac{1}{y^5}+\frac{1}{z^5}=\frac{1}{(x+y+z)^5}
|
3,845 |
y + 2 = 4 + y + 2(-1) = 4\left(1 + (y + 2(-1))/4\right)
|
1,477 |
4\cdot l + 2 = (2\cdot l + 1)\cdot 2 + 0
|
10,650 |
R = q^3\Longrightarrow R^{1/3} = q
|
-10,560 |
\dfrac33 \cdot (-\frac{10}{20 \cdot \left(-1\right) + z \cdot 5}) = -\frac{30}{z \cdot 15 + 60 \cdot \left(-1\right)}
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-27,503 |
2\cdot 2\cdot 3\cdot w\cdot 5 = w\cdot 60
|
45,659 |
-\frac{1}{2} + \frac{\sqrt{17}}{2} = (-1 + \sqrt{17})/2
|
17,192 |
n*\alpha*\beta = \beta*n*\alpha
|
-7,626 |
\tfrac{1}{2 - i}(i*13 - 1) \tfrac{2 + i}{i + 2} = \dfrac{-1 + i*13}{-i + 2}
|
25,684 |
\binom{a}{-b + a} = \binom{a}{b}
|
8,818 |
\frac{1}{250}\cdot 203 = \dfrac{27}{30^4}\cdot 30\cdot 29\cdot 28
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-29,565 |
\frac1z \times (4 + 2 \times z^4 + 5 \times z) = \frac4z + 2 \times z^4/z + \frac{5}{z} \times z
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28,526 |
\frac{2}{2} \times 2 = 2
|
9,535 |
(\frac{20}{5})^{\dfrac{15}{10}} = 8
|
4,040 |
(\left(-1\right) + q) \cdot \left((-1) + x\right) + (-1) = x \cdot q - x - q
|
47,401 |
2^{2 \cdot 2^2} = 256
|
30,723 |
\left(1.75 - 0.5 \cdot y = -y + 2 \implies 0.25 = 0.5 \cdot y\right) \implies y = 0.5
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-10,111 |
-\tfrac{19}{20}\cdot \left(-\frac{7}{8}\right) = ((-19)\cdot (-7))/(20\cdot 8) = \frac{1}{160}\cdot 133
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29,083 |
\dfrac{10}{x} = 20/(2x)
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23,200 |
2 \cdot 2 \cdot 2^3 = 32
|
21,481 |
f \cdot e_2 \cdot e_1 = e_2 \cdot e_1 \cdot f = e_1 \cdot f \cdot e_2
|
-20,343 |
\frac{p\cdot 3}{30\cdot (-1) + 12\cdot p} = 3/3\cdot \tfrac{1}{4\cdot p + 10\cdot (-1)}\cdot p
|
3,487 |
x\cdot (-\frac{x}{x} + 1) = 0 \implies 1 = x/x
|
16,576 |
(a + b)^3 = b \cdot b^2 + a^3 + 3\cdot a^2\cdot b + 3\cdot a\cdot b^2
|
-22,047 |
\dfrac72 = \dfrac{1}{10}*35
|
25,137 |
2 = \sqrt{(-1) + 2} \cdot 2
|
9,356 |
\cos(\theta + \alpha) = \cos{\theta}\cdot \cos{\alpha} - \sin{\alpha}\cdot \sin{\theta}
|
22,243 |
a^2 - 4 \cdot a + 4 = (a + 2 \cdot (-1))^2
|
21,862 |
\left(V \cdot A = x\Longrightarrow x/A = A \cdot V/A\right)\Longrightarrow V \cdot A/A = x/A
|
-746 |
-\pi*20 + 121/6*\pi = \pi/6
|
32,661 |
4k + 2 = 2(2k + 1)
|
-19,003 |
1/9 = \tfrac{C_x}{36 \pi}\cdot 36 \pi = C_x
|
37,743 |
1 = (1 - 2^{1 / 2})^{2 \cdot 0}
|
35,606 |
\tan{\beta} = \dfrac{\sin{\beta}}{\cos{\beta}} \implies \tan{\beta}
|
18,112 |
( a', e) \left( a, e\right) = ( aa', e)
|
20,821 |
x^2 - f^2 = (x - f) \cdot (x + f)
|
-1,755 |
\pi\cdot \tfrac{5}{4} - \dfrac{\pi}{3} = 11/12\cdot \pi
|
30,986 |
\binom{x}{t} = \binom{x}{x - t}
|
54,430 |
\sin\left(c - \dfrac{3 \pi}{2}\right) = \sin(-(\dfrac{3 \pi}{2} - c)) = -\sin(\frac{\pi}{2} 3 - c) = \cos(c) = \cos(c)
|
783 |
6!/(2!\cdot 3!) = {3 \choose 2}\cdot {1 \choose 1}\cdot {6 \choose 3}
|
12,787 |
f^2 = \left(6 + f\right) \left(12 + f\right)\Longrightarrow f = -4
|
-28,407 |
x^2 - 14 \cdot x + 58 = x^2 - 14 \cdot x + 49 + 9 = (x + 7 \cdot (-1))^2 + 9 = \left(x \cdot (-7)\right)^2 + 3^2
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-11,977 |
26/45 = G/(18\cdot \pi)\cdot 18\cdot \pi = G
|
29,847 |
16^{\frac{3}{4}} = (16^3)^{\tfrac14} = (2^{4^3})^{\frac14} = 2^3
|
2,785 |
5 \cdot \pi \cdot r^2 = 9 \cdot \pi \cdot r^2 - 4 \cdot r^2 \cdot \pi
|
-4,445 |
-\tfrac{2}{1 + z} - \frac{1}{4 + z}\cdot 3 = \frac{1}{z^2 + z\cdot 5 + 4}\cdot (11\cdot (-1) - 5\cdot z)
|
29,937 |
49 = ( a + d, a + d) = 16 + 2 \cdot ( a, d) + 25
|
-11,527 |
-12 i - 16 + 0(-1) = -16 - 12 i
|
28,581 |
\frac{k + \left(-1\right)}{k + 1} = \frac{k + 1 + 2*(-1)}{k + 1} = 1 - \frac{1}{k + 1}*2
|
-21,025 |
\tfrac{15 \cdot y + 21 \cdot (-1)}{-y \cdot 3 + 18 \cdot (-1)} = \dfrac{1}{6 \cdot (-1) - y} \cdot (y \cdot 5 + 7 \cdot (-1)) \cdot 3/3
|
-20,448 |
\dfrac{12 \cdot (-1) + 4 \cdot z}{z \cdot 4 + 12} = \frac44 \cdot \dfrac{z + 3 \cdot (-1)}{z + 3}
|
-6,556 |
\frac{1}{z^2 - 12 \cdot z + 27} \cdot 3 = \frac{3}{\left(3 \cdot \left(-1\right) + z\right) \cdot \left(9 \cdot (-1) + z\right)}
|
-4,519 |
\frac{20\cdot (-1) + 8\cdot z}{z^2 - 6\cdot z + 5} = \dfrac{1}{5\cdot (-1) + z}\cdot 5 + \dfrac{3}{z + (-1)}
|
5,943 |
(10^3 - 9^2 * 9*2 + 8^3)/6 = 9
|
-21,161 |
\dfrac{1}{4} = \dfrac{2}{8}
|
6,199 |
k + (-1) = k\cdot 2 - k + (-1)
|
26,764 |
2\sqrt{3} = p/r + (-1) = \left(p - r\right)/r
|
33,955 |
1/28 + 1/14 + \frac{1}{7} + 1/4 + \dfrac{1}{2} = \frac{1}{28}(1 + 2 + 4 + 7 + 14) = 1
|
11,097 |
\tan^3(\tan^{-1}(x)) = \tan(\tan(\tan(\tan^{-1}(x)))) = \tan(\tan(x)) = \tan^2(x)
|
6,612 |
w_1*x + w_2*e + w_3*f = (w_3 + w_1 + w_2)*f + w_1*(-f + x - e + f) + (e - f)*(w_1 + w_2)
|
966 |
5 \cdot (z + 2 \cdot (-1)) = 10 \cdot (-1) + 5 \cdot z
|
26,155 |
\tan{f} = -\tan(\pi - f)
|
8,790 |
4 \cdot (x - d)^2 = 4 \cdot d^2 - d \cdot x \cdot 8 + 4 \cdot x \cdot x
|
-28,869 |
0.01\cdot 20/(60\cdot 0.01) = \frac{1}{3}
|
11,095 |
x^2 + a^2 + x \cdot a \cdot 2 = (a + x)^2
|
390 |
\frac{\mathrm{d}}{\mathrm{d}z} (e^{2*z + (-1)} + 1) = 2*e^{z*2 + (-1)}
|
31,280 |
W = X \implies W = X
|
31,497 |
\N = \left\{2, 0, 1, \dots\right\}
|
38,435 |
\sqrt{124} = \sqrt{2^2\cdot 31} = \sqrt{2^2} \sqrt{31} = 2\sqrt{31}
|
16,481 |
(1 + x)^2 + 24 = 25 + x^2 + 2 \cdot x
|
21,932 |
x^5 = n\times x^2 - m\times x^3 = n\times x^2 - m\times n + m \times m\times x
|
2,280 |
(-z + y)^2 = z^2 \cdot z \implies 4 - z^3 + y^2 - 2zy = 0
|
21,978 |
\left(a + b \times i\right) \times (m + n \times i) = a \times m - b \times n + (a \times n + b \times m) \times i = a \times m - b \times n + i
|
21,270 |
2 \times (-1) + x_2 = x_2
|
11,563 |
x*2 + y*3 + 4*\beta = 24 \Rightarrow y*3 = -\beta*4 + 24 - x*2
|
5,122 |
\tan{x} = \frac{\sin{x}}{\cos{x}} = \sqrt{1 - \cos^2{x}}/\cos{x}
|
-5,159 |
0.81 \times 10^4 = 10^{6 + 2 \times (-1)} \times 0.81
|
-20,071 |
\frac{36 + 32\cdot y}{27 + y\cdot 24} = \frac{y\cdot 8 + 9}{8\cdot y + 9}\cdot 4/3
|
-22,283 |
70 (-1) + y^2 - 3y = (y + 7) (y + 10 \left(-1\right))
|
-29,877 |
d/dy y^l = y^{(-1) + l} l
|
51,372 |
2 + 2 + 2 + 2 + 2 + 4 = 14
|
21,961 |
\left\{1, 3, 27, 5, 4, 0, 2, \dotsm\right\} = \mathbf{Z}_{28}
|
-10,628 |
-\frac{30}{100 + q\cdot 60} = \frac{10}{10}\cdot (-\frac{3}{q\cdot 6 + 10})
|
-1,646 |
13/12 \times \pi = 0 + 13/12 \times \pi
|
22,688 |
n! = n*(n + (-1))! = n*(n + (-1)) \left(n + 2(-1)\right)!
|
-20,024 |
\tfrac{r\cdot 18 + 72}{-r\cdot 4 + 16\cdot \left(-1\right)} = \dfrac{1}{8\cdot (-1) - 2\cdot r}\cdot (-2\cdot r + 8\cdot (-1))\cdot (-\frac{1}{2}\cdot 9)
|
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