id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
25,753 |
\frac{s\cdot (-10)}{(s^2 + 1)\cdot \left(s \cdot s + 2\right)} = \frac{s\cdot 10}{s^2 + 2} - \dfrac{10\cdot s}{s^2 + 1}
|
-9,233 |
11 \cdot n^2 = 11 \cdot n \cdot n
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28,879 |
\frac{2}{1.5 + 2} = \frac17\cdot 4
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31,621 |
(x*G + Z*G + Z*x)/\left(Z*G*x\right) = \frac{1}{x} + 1/Z + \frac1G
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-26,654 |
3\cdot y^2 - 20\cdot y + 7\cdot (-1) = (y\cdot 3 + 1)\cdot (y + 7\cdot (-1))
|
19,605 |
1/\left(b\cdot d\right) = 1/(d\cdot b)
|
3,089 |
xg_2 - xg_1 = (g_2 - g_1) x
|
17,979 |
\tfrac{f - b - c}{c + f - b} = \frac{1 - \frac{1}{f - b}*c}{1 + \frac{c}{f - b}}
|
9,164 |
2 = x^{15} \Rightarrow x^{45} = 8
|
23,344 |
y-x+1=y-(x-1)
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-2,237 |
7/12 - \dfrac{5}{12} = \frac{2}{12}
|
-4,266 |
\frac25 \times n = 2 \times n/5
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-2,731 |
\sqrt{16 \cdot 5} - \sqrt{4 \cdot 5} = \sqrt{80} - \sqrt{20}
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20,465 |
540 = \binom{3}{2} \binom{1}{1} \binom{4}{2} \binom{2}{2}*3! \binom{5}{1}
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16,852 |
4^{m + 1} + (-1) = 4*4^m + (-1) = 3*4^m + 4^m + (-1)
|
6,912 |
\sin(v\cdot 2) = 2\cdot \sin(v)\cdot \cos(v)
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-20,378 |
\frac{1}{k*(-36)} (-k*30 + 12 (-1)) = \left(-k*5 + 2 (-1)\right)/\left((-6) k\right)*6/6
|
30,415 |
\cos{x} \sin{z} + \cos{z} \sin{x} = \sin(x + z)
|
31,052 |
1 + x^6 = (x^4 + 1 - x^2) \cdot (x^2 + 1)
|
39,136 |
-6 - 9*9*3 + 2*3 + 3*27 = 27 (-9) + 3*27 = 27 (-6) = -162
|
17,212 |
3 \cdot y^2 + 2 = 3 \cdot (y \cdot y + (-1)) = 3 \cdot \left(y + (-1)\right) \cdot (y + 1) = 3 \cdot (y + (-1)) \cdot (y + 4 \cdot (-1))
|
-30,238 |
\frac{1}{x + (-1)} \cdot (x^2 - 2 \cdot x + 1) = \dfrac{1}{x + (-1)} \cdot (x + \left(-1\right)) \cdot (x + \left(-1\right)) = x + (-1)
|
6,055 |
xzR \Rightarrow zRx
|
9,711 |
720 = 2^4*5*3^2
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-21,039 |
(5*\left(-1\right) + a)/8*\frac{7}{7} = \frac{1}{56}*\left(7*a + 35*(-1)\right)
|
2,014 |
(-z + y) (y + z) (z^2 + y^2) = y^4 - z^4
|
9,079 |
71 + 5*(n + 13*(-1)) = n*5 + 6
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-3,407 |
-\sqrt{11} + \sqrt{11}\cdot 3 = -\sqrt{11} + \sqrt{11} \sqrt{9}
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-20,218 |
\frac{1}{5p + 8\left(-1\right)}(\left(-1\right) - p \cdot 5) \cdot 7/7 = \frac{7\left(-1\right) - p \cdot 35}{56 (-1) + 35 p}
|
17,440 |
\left(e^x\right)^2 = e^{2 \cdot x}
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-24,649 |
3/12 = -\dfrac13*2 + 3/4 + 1/6
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1,444 |
12 = C_3*3 \implies C_3 = 4
|
12,552 |
y^2 = (y + 0\cdot (-1))\cdot (0\cdot (-1) + y)
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34,321 |
(z + I)\cdot (z + 1 + I) = z^2 + z + I = z^2 + 1 + z + \left(-1\right) + I = z + 1 + I
|
5,388 |
3/(2*y) + 1/2 = \tfrac{1}{y*2}*\left(y + 3\right)
|
20,266 |
1^r=\frac{1^r}{1^r}
|
27,483 |
1 - 25/36 = \frac{1}{36}\cdot 11
|
28,990 |
\frac{1}{i!\cdot (n - i)!}\cdot n! = {n \choose i}
|
6,250 |
\mathbb{E}[D_2]\cdot \mathbb{E}[D_1] = \mathbb{E}[D_2\cdot D_1]
|
2,403 |
(d + 2)^2 = d^2 + 4 + 4 \cdot d
|
644 |
\frac{\partial}{\partial z} \left(a*z^n\right) = a*\frac{\partial}{\partial z} z^n = a*n*z^{n + (-1)}
|
-2,831 |
\sqrt{2} \cdot \sqrt{9} - \sqrt{2} = -\sqrt{2} + \sqrt{2} \cdot 3
|
31,895 |
\cos(2\cdot z) = \cos^2(z)\cdot 2 + (-1)
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-4,176 |
x^4 \cdot 2 = x^4 \cdot 2
|
8,716 |
\sin\left(x_2 + x_1\right) = \cos{x_2}*\sin{x_1} + \sin{x_2}*\cos{x_1}
|
2,036 |
\frac{\partial}{\partial x} (8*s*x) = 8*s*\frac{\mathrm{d}x}{\mathrm{d}x} + 8*\frac{\mathrm{d}s}{\mathrm{d}x}*x
|
10,938 |
(z + 1)^2 = (z + 4 + 3\cdot \left(-1\right)) \cdot (z + 4 + 3\cdot \left(-1\right)) = \left(z + 4\right)^2 - 6\cdot (z + 4) + 9
|
-30,839 |
312.5 = \frac{25^2}{2}
|
16,265 |
\operatorname{acos}\left(\frac12\right) = \pi/3
|
-20,214 |
4/4 \cdot (-\dfrac{2}{-x \cdot 7 + 6 \cdot (-1)}) = -\frac{8}{-x \cdot 28 + 24 \cdot (-1)}
|
-10,773 |
\frac{10 (-1) + x*40}{x*50 + 20} = \frac{10}{10} \frac{\left(-1\right) + 4 x}{2 + 5 x}
|
44,310 |
{8 \choose 2} = {\left(-1\right) + 6 + 3 \choose \left(-1\right) + 3}
|
13,091 |
\tan{\chi} = \frac{\sin{\chi}}{\cos{\chi}}
|
23,231 |
\frac{a}{b} = 1/(\frac1a*b)
|
21,540 |
0.25 = (0.5 - 0.25)
|
-26,083 |
\dfrac{-2 + i}{-2 + i} \dfrac{1}{-2 - i}(i*8 + 1) = \frac{8i + 1}{-2 - i}
|
-9,623 |
0.01 (-96) = -\dfrac{96}{100} = -24/25
|
14,599 |
(n^4*2 - 2*n^2 + 1) * (n^4*2 - 2*n^2 + 1) + \left(n^5 - 2*n^2 * n + 2*n\right)^2 = n^{10} + 1
|
20,941 |
(x + \left(-1\right)) \cdot (x + \left(-1\right)) + 1 = 2 + x^2 - 2x
|
23,288 |
1 + \tfrac{1}{\frac{1}{1^{-1} + 1} + 1} = \frac53
|
20,031 |
5y = (q*5 + 1)*19 + 1\Longrightarrow y = q*19 + 4
|
47,671 |
71.5 = \frac{1}{2}*13*11
|
2,336 |
10/24 = \dfrac{1}{24}*(6 + 4)
|
9,935 |
{n \choose m}/n = \dfrac{1}{m! \cdot (n - m)!} \cdot (n + (-1))! = \tfrac{1}{m} \cdot {n + \left(-1\right) \choose m + \left(-1\right)}
|
18,749 |
b\cdot D/b\cdot b = D\cdot b
|
13,244 |
\frac{19!}{24!}\cdot 22!\cdot 1/17! = \frac{18\cdot 19}{23\cdot 24} = 0.6196
|
-7,108 |
\frac{6}{14}\cdot 6/15 = 6/35
|
16,179 |
2 - \frac{1}{w + \left(-1\right)}\cdot w = \frac{1}{w + \left(-1\right)}\cdot \left(2\cdot w + 2\cdot (-1) - w\right) = \frac{1}{w + (-1)}\cdot \left(w + 2\cdot (-1)\right)
|
11,786 |
\sin\left(\arcsin(y)\right) = y
|
8,067 |
4 \cdot p \cdot q \cdot r + p^3 + q^3 + r^3 = -3 \cdot q \cdot r \cdot (r + q) + p^3 + (r + q) \cdot (r + q)^2 + 4 \cdot p \cdot r \cdot q
|
35,210 |
n - i = 1\Longrightarrow i = (-1) + n
|
29,046 |
\frac{0.6\cdot 0.3}{0.3\cdot 0.6}\cdot 0.3 = 0.3
|
34,972 |
\sqrt{3} \cdot 2 + 3 \cdot \left(-1\right) = -3 + 2 \cdot \sqrt{3}
|
-9,638 |
12\% = 12/100 = 3/25
|
15,938 |
\cos{2\cdot \theta} = 1 - 2\cdot \sin^2{\theta}
|
10,218 |
\left(y \times y \times 3 = y^4 \Leftrightarrow 1 + y^2 = \left(y^2 + (-1)\right)^2\right) \Rightarrow 3^{1 / 2} = y
|
-15,659 |
\frac{1}{q^4\cdot \dfrac{1}{q^{20}\cdot \dfrac{1}{x^5}}} = \tfrac{1}{q^4\cdot \frac{1}{q^{20}}\cdot x^5}
|
34,740 |
\frac{4 \cdot {9 \choose 5}}{{52 \choose 5}} \cdot 1 = 3/15470
|
-7,652 |
\frac{5i + 5}{-1 - 2i} = \frac{1}{-1 + i*2}(-1 + i*2) \dfrac{i*5 + 5}{-1 - i*2}
|
-4,561 |
(2 + z) \cdot \left(z + 3 \cdot \left(-1\right)\right) = z^2 - z + 6 \cdot (-1)
|
-20,189 |
\dfrac44\cdot (-\frac{2}{x + 1}) = -\frac{8}{x\cdot 4 + 4}
|
30,006 |
(2 \cdot 3^x)^2 = 3^{2 \cdot x} + 3^{x \cdot 2 + 1}
|
-7,392 |
3/8 = 1/4\cdot 3/2
|
14,418 |
27^{\frac23} = (27^{1/3})^2 = 3^2 = 9
|
5,651 |
\sqrt{\frac{a^3b}{c^4}}=\frac{a^{3/2}b^{1/2}}{c^2}=a^{3/2}b^{1/2}c^{-2}
|
35,204 |
43^2 = 1 + 24\cdot 77
|
37,570 |
49 * 49^2 = 343^2 = 117649
|
11,208 |
\left(\sin{\pi} \cdot i + \cos{\pi}\right) = -1
|
1,909 |
3 \cdot \left(k + 1\right) \cdot \left(k + 1\right) = 4 \cdot k + 3 + k^2 \cdot 3 - 1 + 2 \cdot k + k \cdot 4 + 1
|
-20,837 |
-3/4*\dfrac{x + 9}{9 + x} = \frac{1}{x*4 + 36}*(-3*x + 27*(-1))
|
37,372 |
2^m = (2 + 1)^2 + (-1) = 2^3 \Rightarrow m = 3
|
12,099 |
N \cdot 2 - 2 \cdot N^5 = 0 rightarrow (-N^4 + 1) \cdot N = 0
|
30,892 |
\left(2^{10500}\right)^{1/2} = 2^{\frac{1}{2}\cdot 10500} = 2^{5250}
|
-4,770 |
\tfrac{3}{\left(-1\right) + x} + \tfrac{1}{x + 4 \cdot \left(-1\right)} \cdot 3 = \frac{1}{x^2 - x \cdot 5 + 4} \cdot \left(15 \cdot (-1) + 6 \cdot x\right)
|
23,995 |
\int\limits_c^f k\,\mathrm{d}x = \int\limits_c^f k\,\mathrm{d}x
|
-10,781 |
-\frac{12}{50\cdot q + 40\cdot (-1)} = \frac22\cdot (-\dfrac{1}{q\cdot 25 + 20\cdot (-1)}\cdot 6)
|
10,940 |
\frac{1}{\sqrt{n}} (-n + 2 X_n) = (-\frac{n}{2} + X_n)/(\sqrt{n} \dfrac{1}{2})
|
-25,026 |
-\frac{1}{-z + 1} = -1 - z - z \cdot z - z \cdot z \cdot z - z^4 - \ldots
|
12,700 |
16^l + 16 \cdot \left(-1\right) = 16 \cdot \left((-1) + 16^{(-1) + l}\right)
|
-18,497 |
-37/35 = -\frac{1}{35}37
|
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