id
int64 -30,985
55.9k
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-30,254 |
\frac{1}{y + 4}\cdot (y^2 + 16\cdot (-1)) = \frac{1}{y + 4}\cdot (y + 4)\cdot (y + 4\cdot \left(-1\right)) = y + 4\cdot (-1)
|
6,356 |
\frac{1}{(-\frac{1}{2} + p)^4} = -p + \frac{1}{2} \implies (p - 1/2)^5 = -1
|
22,651 |
\binom{n}{1 + l} + \binom{n}{l} = \binom{n + 1}{1 + l}
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-12,638 |
40 = 156 \times (-1) + 196
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19,330 |
\frac{1}{2 + 2\cdot z^2 - 5\cdot z}\cdot \left(z\cdot 5 + 4\cdot (-1)\right) + 2 = \dfrac{4\cdot z^2 - 5\cdot z}{z^2\cdot 2 - z\cdot 5 + 2}
|
9,233 |
(2 \cdot (-1) + x) \cdot (x + 2) = x^2 + 0 \cdot x + 4 \cdot (-1)
|
-7,227 |
\frac{1}{70} = \frac15 \frac{1}{14}
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33,528 |
2/3 = \dfrac19\cdot 6
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-24,407 |
3 + \frac17 \cdot 70 = 3 + 10 = 3 + 10 = 13
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-1,219 |
\frac{3}{\frac{1}{2}*3}\dfrac15 = 2/3*3/5
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27,211 |
A = 2\cdot (63 - A) - 2\cdot (2A + 63 (-1)) = -6A + 252
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-18,284 |
\frac{1}{(1 + j)\cdot j}\cdot \left(j + 1\right)\cdot (2\cdot (-1) + j) = \frac{1}{j^2 + j}\cdot (2\cdot (-1) + j \cdot j - j)
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32,470 |
\frac34\times s + \frac14 = (-s + 1)/4 + s
|
5,031 |
{(-1) + k \choose 2} = \frac12 \cdot (k + 2 \cdot (-1)) \cdot \left(k + (-1)\right)
|
32,881 |
(-1)\cdot 0.2 + 1 = \frac{1}{1 + 0.25}
|
3,513 |
x\cdot \beta\cdot \alpha = x\cdot \beta\cdot \alpha
|
26,996 |
9^1 = 9^{\frac{1}{2}}*9^{1/2}
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21,380 |
|\dfrac{1}{n + 1}\cdot (n + (-1)) + (-1)| = |-\frac{1}{n + 1}\cdot 2| = \frac{2}{|n + 1|}
|
22,331 |
2520 = 10!/(2!*3!*5!)
|
24,071 |
0 = V \cdot T \cdot \sin{\beta} - \frac{b}{2} \cdot T^2\Longrightarrow V \cdot \sin{\beta} \cdot 2/b = T
|
19,260 |
\tfrac{84}{1 + 49 \cdot (-1)} = -7/4
|
20,880 |
l - x + T + Q = 0 + T + Q = 0 + T + 0 + Q = l + T - x + Q
|
427 |
E(Z_1 Z_2) = E(Z_2) E(Z_1)
|
10,999 |
\int (1 - e^{-\alpha})\times e^{e^\alpha}\,\mathrm{d}\alpha = \int (e^\alpha + \left(-1\right))\times e^{-\alpha}\times e^{e^\alpha}\,\mathrm{d}\alpha = \int (e^\alpha + (-1))\times e^{e^\alpha - \alpha}\,\mathrm{d}\alpha
|
-10,530 |
-\tfrac{1}{z + 5} \cdot (10 \cdot \left(-1\right) + z) \cdot \frac{1}{4} \cdot 4 = -\frac{1}{20 + z \cdot 4} \cdot (4 \cdot z + 40 \cdot (-1))
|
14,394 |
u * u = \dfrac{u^{12}}{u^{10}}
|
18,632 |
f^{l_1 + l_2} = f^{l_1} \cdot f^{l_2}
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12,392 |
2^{1/2} = \frac{1}{2}8^{1/2}
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15,629 |
\left\lceil{\frac{10}{5 + (-1)}}\right\rceil = \left\lceil{\frac{1}{4}*10}\right\rceil = \left\lceil{2.5}\right\rceil = 3
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27,025 |
\frac{S - \dfrac{m}{2}}{\sqrt{\frac14 \cdot m}} = (S \cdot 2 - m)/(\sqrt{m})
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-14,125 |
\dfrac{2}{10 + 9 \cdot (-1)} = \frac11 \cdot 2 = 2/1 = 2
|
36,447 |
c\cdot g = g\cdot c
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16,263 |
1 = \frac1h + \dfrac{1}{h + b} + \frac{1}{h + b + c} \geq \dfrac{1}{h + b + c}\cdot 3
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29,011 |
180 = 2 \cdot 2\cdot 3 \cdot 3\cdot 5
|
30,811 |
\dfrac{1}{2} \times \frac{2}{3} = 1/3
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18,306 |
\frac12 = 2/4 = 50/100
|
15,486 |
\left(l \cdot 12 + 11\right)/4 = l \cdot 3 + 2 + 3/4
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9,189 |
-2\cdot \int u^{-\dfrac{1}{3}}\,du = ((-6)\cdot u^{\frac13\cdot 2})/2 = -3\cdot u^{\frac23}
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38,810 |
b = 15 \cdot b \cdot l = 1.2 \cdot b \cdot l
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-29,240 |
0 = 5*0 + 0*(-1)
|
20,889 |
f_3 \cdot z^2 \cdot f_2 \cdot f_1 = z \cdot f_3 \cdot z \cdot f_2 \cdot f_1
|
9,873 |
\mathbb{N}_{n} := \left\{n, 1, \dotsm\right\}
|
5,514 |
h^2 + 2dh + d^2 = \left(h + d\right)^2
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4,107 |
\dfrac{1}{X_j^2} + X_j \cdot X_j + 2 = (1/(X_j) + X_j)^2
|
-439 |
\pi\cdot \tfrac{1}{4}\cdot 3 = -8\cdot \pi + \frac{35}{4}\cdot \pi
|
1,358 |
\left(15 + 84 - 2 \cdot x = x \Rightarrow x \cdot 3 = 99\right) \Rightarrow 33 = x
|
5,848 |
1/(c*g) = \frac{1}{c*g}
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-18,382 |
\frac{1}{n^2 - 8\cdot n}\cdot (8\cdot (-1) + n \cdot n - n\cdot 7) = \frac{1}{n\cdot \left(n + 8\cdot (-1)\right)}\cdot \left(1 + n\right)\cdot (8\cdot (-1) + n)
|
4,086 |
(x \times y)^3 = y^3 \times x \times x \times x
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16,012 |
(\frac{1}{1 + 5/13}*2)^{\frac{1}{2}} = \dfrac{13^{\dfrac{1}{2}}}{3}
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-10,000 |
35\% = \dfrac{35}{100} = \frac{7}{20}
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-11,615 |
-18 - 2\cdot i = -2\cdot i - 8 + 10\cdot (-1)
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26,520 |
\left(-z_1 + z_2\right)*(z_2 * z_2 + z_1^2)*(z_2 + z_1) = z_2^4 - z_1^4
|
9,973 |
x \times x + y^2 + z^2 = 2 \times x^2 + 1 = 2 \times x \times y \times z + 1
|
-6,423 |
\frac{2}{\left(r + 1\right) \cdot 2} = \frac{2}{r \cdot 2 + 2}
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-27,006 |
\sum_{n=1}^\infty \frac{1}{n^2 \cdot 3^n} \cdot (5 + 2 \cdot \left(-1\right))^n = \sum_{n=1}^\infty \frac{3^n}{n^2 \cdot 3^n} = \sum_{n=1}^\infty \dfrac{1}{n^2}
|
22,285 |
n + (-1) + n + 2 \cdot (-1) = 3 \cdot \left(-1\right) + n \cdot 2
|
42,554 |
e^{\log_e(c)} = c
|
14,552 |
\dfrac{1}{\cos{E} (1 + \sin{E})}\left(2 + 2\sin{E}\right) = 2/\cos{E} = 2\sec{E}
|
-12,126 |
\frac{2}{9} = s/(12 \pi) \cdot 12 \pi = s
|
-20,000 |
\frac{-7 \cdot z + 5 \cdot (-1)}{-z \cdot 7 + 5 \cdot (-1)} \cdot 9/8 = \frac{45 \cdot (-1) - z \cdot 63}{40 \cdot (-1) - 56 \cdot z}
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29,025 |
3 (n^2 - (n + (-1))^2) - 2 (n - n + (-1)) = 3*(2 n + (-1)) + 2 \left(-1\right) = 6 n + 5 (-1)
|
26,153 |
(g - y)/g = 1 - \frac{y}{g}
|
29,713 |
\frac{1}{((-1) + j)!} \cdot l + \dfrac{1}{(j + (-1))!} \cdot m = \frac{l + m}{((-1) + j)!}
|
6,244 |
2 + 1 + \dfrac{1}{100}\cdot \left(74 + 1\right) = 3.75
|
8,194 |
\left(t^2 - 2\cdot t + \left(-1\right) = 0 \Rightarrow -t\cdot 2 = 1 - t \cdot t\right) \Rightarrow -1 = \frac{t}{-t^2 + 1}\cdot 2
|
-25,801 |
\dfrac{1}{18} \cdot 5 = 1/6 \cdot 5/3
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-28,794 |
\frac{\pi*2}{\dfrac{1}{365}*2*\pi} = 365
|
-22,311 |
(x + 9\cdot (-1))\cdot \left(x + 10\cdot (-1)\right) = 90 + x^2 - 19\cdot x
|
16,841 |
2 \times \left(-1\right) + 5^{3 \times 0} + 2 \times 5^{2 \times 0} - 5^0 = 0
|
3,471 |
f_1/\left(g_1\right) + f_2/\left(g_2\right) = \frac{1}{g_2 \cdot g_1} \cdot (g_1 \cdot f_2 + g_2 \cdot f_1)
|
3,711 |
\frac12\cdot (2\cdot x + 6\cdot (-1)) = x + 3\cdot \left(-1\right)
|
-5,317 |
10^7*0.74 = 0.74*10^{(-1)*\left(-1\right) + 6}
|
15,380 |
15 = 5 \cdot v \implies 3 = v
|
-6,631 |
\dfrac{5}{(x + 8) \cdot (5 \cdot (-1) + x)} = \frac{5}{x^2 + 3 \cdot x + 40 \cdot \left(-1\right)}
|
-19,194 |
\frac{1}{30} \cdot 11 = \dfrac{1}{4 \cdot \pi} \cdot Z_q \cdot 4 \cdot \pi = Z_q
|
10,081 |
(2Hy)^2 = 2^2 H^2 y^2 = 4H * H y^2
|
34,033 |
bb f = f = bbf
|
22,013 |
2 = 1*2 = (4 + 2) \left(4 + 2 \left(-1\right)\right) = 4^2 - 2^2
|
23,949 |
2^{66} + (-1) = 2^{33} * 2^{33} + (-1) = \left(2^{33} + 1\right) (2^{33} + \left(-1\right))
|
-7,674 |
\dfrac{-9\cdot i + 2}{2 + i} = \frac{2 - i}{2 - i}\cdot \frac{1}{2 + i}\cdot (2 - i\cdot 9)
|
5,415 |
\sqrt{2} = x rightarrow -\sqrt{2} + x = 0
|
9,986 |
5^F \cdot 6 + 6\left(-1\right) - 5^F + 5 = (-1) + 5^F \cdot (6 + \left(-1\right))
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-20,997 |
(-4\cdot x + 12\cdot (-1))/(x\cdot 8) = 4/4\cdot \dfrac{1}{x\cdot 2}\cdot (3\cdot (-1) - x)
|
13,897 |
d = \frac{1}{1 - 3\cdot d \cdot d}\cdot (3\cdot d - d^3) + 2 \Rightarrow (d + 2\cdot \left(-1\right))\cdot (-3\cdot d^2 + 1) = -d^3 + d\cdot 3
|
14,542 |
-2d_2 d_1 + (d_2 + d_1)^2 = d_2 * d_2 + d_1^2
|
4,200 |
0 + 0 + 0 = 1 + (-1) + (1 + (-1))\cdot ...
|
52,541 |
\arctan(x) = \int_0^x \frac{1}{1 + t^2}\,dt = \int\limits_0^x (1 - t^2 + \frac{1}{1 + t * t}*t^4)\,dt = x - 1/3*x^3 + \int\limits_0^x \frac{t^4}{1 + t^4}\,dt
|
-12,026 |
1/18 = \frac{x}{6\cdot \pi}\cdot 6\cdot \pi = x
|
3,019 |
\frac{1}{\left(l + 1\right)^2} \cdot \left(l^2 + 2 \cdot l\right) = \frac{l}{\left(l + 1\right)^2} \cdot (l + 2)
|
18,022 |
\left(A \cdot x = c\Longrightarrow x \cdot A/A = \dfrac{1}{A} \cdot c\right)\Longrightarrow x = \dfrac{c}{A}
|
13,501 |
\pi\cdot \tfrac13\cdot 85 = \pi\cdot \frac{5}{6}\cdot 34
|
21,392 |
\tan{u} = \frac{2*\tan{\frac{u}{2}}}{1 - \tan^2{u/2}} \gt 2*\tan{\frac{u}{2}}
|
-10,413 |
-2 = 60 + 20r - 50 = 20r + 10
|
29,871 |
\|Y \cdot y\|_2 = \|Y\|_2 = \|Y\|_2 \cdot \|y\|_2
|
8,046 |
(1 + 10^{1 + n} \cdot 8)/9 = 1 + 8 \cdot \frac{1}{9} \cdot ((-1) + 10^{n + 1})
|
-1,628 |
-π \cdot \frac14 \cdot 3 + 2 \cdot π = 5/4 \cdot π
|
28,039 |
\frac{0}{2} + \frac12\cdot 1000 = 500
|
-3,349 |
(5 + 3*(-1) + 4)*\sqrt{13} = 6*\sqrt{13}
|
-5,258 |
0.66 \times 10^{2\,-\,5} = 0.66 \times 10^{-3}
|
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