id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-4,729 |
\frac{2 \cdot y + 26 \cdot (-1)}{y \cdot y - y \cdot 2 + 15 \cdot (-1)} = \frac{4}{3 + y} - \frac{2}{y + 5 \cdot \left(-1\right)}
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4,309 |
n = 3 + \dfrac{1}{2} \cdot (n + (-1)) + (n + 5 \cdot (-1))/2
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12,575 |
\operatorname{re}{\left(z\right)} = -0 \cdot 0 + (\operatorname{re}{(z)})^2 \implies (1 \pm 1)/2 = \operatorname{re}{(z)}
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25,318 |
y_2 = \operatorname{acos}(x) \Rightarrow \cos(y_2) = x
|
-4,093 |
p^3\cdot \dfrac65 = \frac{p \cdot p^2}{5}\cdot 6
|
8,583 |
\frac{1}{\left(-1\right)^{l*2}}*\left(-1\right)^l = \frac{1}{(-1)^l}
|
36,262 |
3/4 + \sqrt{33}/4 = \frac14 \cdot (\sqrt{33} + 3)
|
16,279 |
x^0 x^0/(1/x) = x^1
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31,489 |
e*G_i*k = k*G_i*e
|
-3,001 |
\sqrt{25 \cdot 13} + \sqrt{9 \cdot 13} = \sqrt{117} + \sqrt{325}
|
-1,499 |
\frac{1}{6}*7*(-\frac85) = \frac{1}{\frac{1}{7}*6}*(\left(-8\right)*\frac15)
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29,854 |
\frac{1}{\left(-1\right) + 5} = \frac{1}{4}
|
-3,410 |
(3 + (-1)) \cdot 3^{\frac{1}{2}} = 3^{\dfrac{1}{2}} \cdot 2
|
23,138 |
-\frac{{56 \choose 7}}{{60 \choose 7}} + 1 = 38962/97527
|
20,800 |
Z = (z + y) \cdot z \Rightarrow Z = z \cdot z + y \cdot z
|
3,198 |
166 = {10 + 4 + (-1) \choose 4 + (-1)} - {(-1) + 7 + 4 \choose 4 + (-1)}
|
19,423 |
t = a - t^3 + a^2 \cdot a \Rightarrow 0 = a - t + (a - t)\cdot (a^2 + a\cdot t + t \cdot t)
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34,243 |
Q^\complement^k = Q^1*...*Q^k
|
24,208 |
(D' + A' + B' + x) \cdot (F + A + G + H) = B' \cdot H + A \cdot D' + G \cdot A' + x \cdot F
|
19,668 |
\frac{\int 1\,dx}{5^{\frac13}} = \int \frac{1}{5^{1/3}}\,dx
|
-1,237 |
\dfrac{(-5) \cdot \dfrac{1}{2}}{\frac{1}{7} \cdot (-1)} = -\frac{7}{1} \cdot (-5/2)
|
-2,225 |
\frac{1}{17}9 - \frac{6}{17} = \frac{3}{17}
|
-3,143 |
5 \cdot 13^{\frac{1}{2}} = 13^{1 / 2} \cdot (1 + 4)
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23,796 |
\mathbb{E}\left[\left(H + Y\right)^2\right] = \mathbb{E}\left[H \cdot H\right] + \mathbb{E}\left[Y^2\right] + 2 \cdot \mathbb{E}\left[Y \cdot H\right]
|
-444 |
(e^{\pi*i*7/12})^{15} = e^{\pi*i*7/12*15}
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-15,423 |
\frac{1/y\cdot x^2}{(x\cdot y^3)^2}\cdot 1 = \frac{x^2\cdot \tfrac1y}{y^6\cdot x^2}
|
10,239 |
5/12 = 5 \cdot \tfrac16/2
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18,198 |
z^5 + (-1) = ((-1) + z)\cdot (1 + z^4 + z^3 + z \cdot z + z)
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-20,595 |
5/5 \cdot \frac{z}{z \cdot 5 + \left(-1\right)} \cdot 4 = \dfrac{20 \cdot z}{5 \cdot (-1) + 25 \cdot z}
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-9,831 |
0.01\cdot \left(-50\right) = -\dfrac{50}{100} = -1/2
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4,687 |
Var\left(R\right) = Var\left(R_1 + \dotsm + R_{10}\right) = Var\left(R_1\right) + \dotsm + Var\left(R_{10}\right)
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36,293 |
4*(1 + t^2) = (1 + t^2 - t*z) * (1 + t^2 - t*z) + z^2 = \left(1 + t^2\right)*(1 + (z - t)^2)
|
13,670 |
|\frac{1}{x \cdot y} \cdot (-y + x)| = |\frac{1}{x} - \frac1y|
|
40,478 |
|\rho| = |-\rho|
|
-15,769 |
-6\cdot 6/10 + 4/10\cdot 5 = -\frac{16}{10}
|
-26,469 |
x^2 + a^2 + a*x*2 = (x + a) * (x + a)
|
33,555 |
36\% = 40\% \cdot 40\% + 20\% \cdot 20\% + 40\% \cdot 40\%
|
42,893 |
(3*a + 1)/b + (3*b + 1)/a = \frac{1}{a*b}*(3*a^2 + a) + \frac{1}{a*b}*\left(3*b * b + b\right) = (3*a^2 + a + 3*b^2 + b)/(a*b) = \dfrac{1}{a*b}*(3*(-3*a + (-1)) + a + 3*(-3*b + (-1)) + b) = \dfrac{1}{a*b}*\left(-8*(a + b) + 6*(-1)\right)
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-17,482 |
99 + 43 (-1) = 56
|
-8,306 |
-1 = \left(-1\right)
|
41,734 |
x + d + a + b = b + d + a + x
|
12,100 |
-(3 + m) * (3 + m) + 2(m + 2)^2 = m^2 + m*2 + \left(-1\right)
|
7,351 |
Var(X) = \mathbb{E}(\left(X - \mathbb{E}(X)\right)^2) = \mathbb{E}(X^2) - \mathbb{E}(X)^2
|
46,380 |
0 = \arcsin{0}
|
15,475 |
\frac{7 + n}{1 + 2 n} = \frac12 + \tfrac{13}{4 n + 2}
|
28,667 |
l = n + (-1) \implies n = 1 + l
|
-20,388 |
3/10 \cdot \frac{-2 \cdot m + 7}{7 - m \cdot 2} = \frac{-m \cdot 6 + 21}{-m \cdot 20 + 70}
|
17,093 |
\left(x \lt 72\Longrightarrow x = 66\right)\Longrightarrow 78 = -x + 144
|
10,937 |
2*t^{t + (-1)} = t^{(-1) + t} + t^{\left(-1\right) + t}
|
15,422 |
\left|{X}\right| \left|{Y}\right| = \left|{XY}\right| = \left|{Y}\right| \left|{X}\right|
|
22,691 |
-\frac12 + x = \frac{1}{2}((-1) + 2x)
|
846 |
\frac{1}{1 - x} + \left(-1\right) = \frac{1 - 1 - x}{1 - x} = \dfrac{x}{1 - x}
|
-30,881 |
90 = 140 + 50\cdot (-1)
|
50,460 |
5\cdot 4\cdot 4\cdot 4\cdot 4\cdot 4\cdot 4 = 20480
|
-10,703 |
\dfrac{12}{r \cdot 4} = \dfrac144 \cdot \frac{3}{r}
|
25,152 |
\frac{1}{10}\cdot 6\cdot \frac{1}{9}\cdot 5 = 1/3
|
-22,842 |
\frac{16}{24} = \dfrac{2 \cdot 8}{3 \cdot 8}
|
25,432 |
y^3 + y^2 = 2 \times y - 2 \times y^2 + y^2 = 2 \times y - 2 \times y \times y + y^2 = 2 \times y - y^2
|
-11,273 |
(x + h)^2 = (x + h)*(x + h) = x^2 + 2*h*x + h^2
|
-20,662 |
\frac{1}{p*7 + 35}*(50*(-1) - 10*p) = \frac{p + 5}{p + 5}*(-\tfrac{1}{7}*10)
|
-28,806 |
\dfrac{2\pi}{2\pi*1/687} = 687
|
41,413 |
64 \cdot 4 + 16 \cdot 6 = 352
|
1,147 |
\tan{z} + (-1) = \frac{1}{\cos{z}} \sin{z} + \left(-1\right) = (\sin{z} - \cos{z})/\cos{z}
|
-10,392 |
-\frac{180}{z \cdot 20 + 100} = \frac{20}{20} \cdot (-\frac{1}{z + 5} \cdot 9)
|
-3,196 |
\sqrt{6}*(4 + 2*(-1)) = 2*\sqrt{6}
|
-25,051 |
\frac{4}{13}\cdot 6/12 = \dfrac{1}{156}24 = 2/13
|
12,579 |
10 = 2^{3.32 \cdot \cdots}
|
-10,630 |
\frac{5}{3*t}*5/5 = \dfrac{25}{t*15}
|
5,323 |
1 \cdot 1 \cdot 1 + 2^3 + 9^3 + 26^3 = 18314
|
22,256 |
\frac{1}{2^{1/2}} = \frac{1}{2^{1/2}\cdot 2} + \dfrac{1}{2\cdot 2^{1/2}}
|
14,137 |
x^4 + x \cdot x + 1 = (x \cdot x + 1)^2 - x^2
|
-6,428 |
\frac{5}{(y + 5\cdot (-1))\cdot 4} = \dfrac{1}{20\cdot (-1) + y\cdot 4}\cdot 5
|
7,733 |
y^m/m! = \frac{\partial}{\partial y} (\dfrac{y^{m + 1}}{\left(m + 1\right)!})
|
-3,659 |
\dfrac{1}{6} \cdot 5/t = \frac{5}{t \cdot 6}
|
27,963 |
x\cdot z\cdot y = z\cdot x\cdot y
|
9,086 |
\int_1^2 {1/(2\cdot u)}\,\mathrm{d}u = (\int_1^2 {1/u}\,\mathrm{d}u)/2
|
14,882 |
15 = {3 \choose 0} \cdot {7 + 0 \cdot (-1) + (-1) \choose 3 + (-1)}
|
27,157 |
2\cdot b^2 + a^2 - 2\cdot b\cdot a = b^2 + (-b + a) \cdot (-b + a)
|
3,162 |
\sin{r} = \sin(\pi\cdot 2 + r)
|
6,624 |
\xi^x = -1 \implies 1 = \xi^{x \cdot 2}
|
-20,964 |
9/1 \cdot \frac{7 + n}{n + 7} = \dfrac{1}{n + 7} \cdot (9 \cdot n + 63)
|
30,333 |
4/5 + 1 = \tfrac{9}{5}
|
10,937 |
p^{(-1) + p}*2 = p^{p + (-1)} + p^{p + (-1)}
|
-19,503 |
1/9\cdot 5/(8\cdot \tfrac19) = \dfrac19\cdot 5\cdot 9/8
|
29,828 |
\dfrac{n}{n \cdot 2 + 2} = \frac12 - \frac{1}{n \cdot 2 + 2}
|
30,460 |
v + y = y + v
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-9,259 |
x^2*26 = xx*2*13
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10,591 |
\frac{1}{-2 \cdot b^2 + c^2} \cdot c + 2^{\frac{1}{2}} \cdot \tfrac{b \cdot (-1)}{c^2 - 2 \cdot b^2} = \frac{1}{2^{\frac{1}{2}} \cdot b + c}
|
-7,006 |
\frac{3}{5}*3/4 = \dfrac{9}{20}
|
-20,442 |
\frac{1}{-8}\left(24 (-1) - x*28\right) = 4/4 (-x*7 + 6(-1))/(-2)
|
-22,206 |
(a + 2 \cdot (-1)) \cdot \left(10 \cdot (-1) + a\right) = 20 + a \cdot a - a \cdot 12
|
11,613 |
y \times y + 1 + y = \frac{1}{y + (-1)}\times ((-1) + y^3)
|
20,391 |
\csc(2\cdot y) - \cot\left(2\cdot y\right) = \left(1 - \cos(2\cdot y)\right)/\sin(2\cdot y) = \dotsm = \tan(y)
|
7,139 |
\frac{1}{\sqrt{x^2 + 1}}x + 1 = \frac{1}{\sqrt{x^2 + 1}}(\sqrt{x^2 + 1} + x)
|
-12,100 |
\frac{11}{18} = \frac{s}{18 \pi}*18 \pi = s
|
32,761 |
-1/a = \frac{1}{\left(-1\right) \cdot a}
|
-13,566 |
2 - 6 + 35/5 = 2 - 6 + 7 = 2 + 6\cdot (-1) + 7 = -4 + 7 = 3
|
30,621 |
a*U = U \Rightarrow U = a*U
|
21,143 |
217 = (20 \cdot z + 3) \cdot q + \left(20 \cdot z + 3 + 3 \cdot (-1)\right)/20 = \left(20 \cdot z + 3\right) \cdot (q + \frac{1}{20}) - 3/20
|
-12,071 |
\dfrac{19}{24} = \dfrac{1}{4 \cdot \pi} \cdot s \cdot 4 \cdot \pi = s
|
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