id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
7,149 |
x_j = x_j\cdot 0\cdot 0
|
32,665 |
{2 + x \choose 2} = {3 + x \choose 3} - {x + 2 \choose 3}
|
-4,027 |
\frac{t^3}{t^2} = \frac{t*t*t}{t*t} = t
|
19,618 |
12 = 6\cdot 4 + 12\cdot (-1)
|
-10,696 |
\dfrac{1}{30 \cdot x + 18} \cdot (18 \cdot (-1) + 4 \cdot x) = \frac{1}{x \cdot 15 + 9} \cdot (x \cdot 2 + 9 \cdot (-1)) \cdot \frac{2}{2}
|
20,866 |
-7 = 8/5\cdot f\Longrightarrow -35/8 = f
|
19,793 |
-z_1^2 + z_2^2 = \left(z_1 + z_2\right)\cdot (-z_1 + z_2)
|
32,171 |
\|b*c\|_1 = \|b*c\|_1
|
7,175 |
\frac{5^2}{5^2}\cdot \frac{1}{40}\cdot 17 = \frac{1}{1000}\cdot 425
|
1,437 |
\frac69 = \tfrac23
|
34,985 |
\dfrac12(3 + 25) = 14
|
27,644 |
ba = 1 \implies ab = 1
|
-2,581 |
\sqrt{6} = \left(2 + (-1)\right)\cdot \sqrt{6}
|
8,345 |
a^4 - 6\times a^2 + 1 = (a^2 + (-1))^2 - 4\times a^2 = (a^2 - 2\times a + (-1))\times (a^2 + 2\times a + (-1))
|
-19,460 |
7/5\cdot 9/8 = 7\cdot 1/5/\left(8\cdot 1/9\right)
|
5,926 |
\tfrac{n!}{(-r + n)! \cdot r!} = \binom{n}{r}
|
5,567 |
1 + 2\cdot \cos\left(2\cdot z\right) = 1 + 2\cdot (1 - 2\cdot \sin^2(z)) = \tfrac{1}{\sin(z)}\cdot \sin\left(3\cdot z\right)
|
-30,540 |
\frac{dz}{dx} = xe^{-z} + 10 e^{-z} = \frac{1}{e^z}\left(x + 10\right)
|
-17,418 |
66 = 70 + 4\cdot \left(-1\right)
|
-1,835 |
-π \times \frac{3}{4} = -π \times \dfrac{1}{12} \times 11 + \tfrac16 \times π
|
3,924 |
\sqrt{5} + 2 = (17 \cdot \sqrt{5} + 38)^{1/3}
|
-18,319 |
\frac{1}{(7\cdot \left(-1\right) + x)\cdot x}\cdot (x + 6\cdot (-1))\cdot (x + 7\cdot (-1)) = \frac{1}{-x\cdot 7 + x^2}\cdot (42 + x^2 - 13\cdot x)
|
9,945 |
3 = \frac{1}{24}\cdot 72
|
6,625 |
\frac{2}{(n + 3)!}\cdot n! = \frac{1}{(n + 1)\cdot (n + 2)\cdot (n + 3)}\cdot 2 \leq \frac{2}{n^2}
|
-2,041 |
\pi/12 - 5/6*\pi = -\frac{3}{4}*\pi
|
8,335 |
2\cos(z) \sin(z) = \sin\left(2z\right) rightarrow \sin^{22}\left(z\right) = \sin^2(z) \cos^2(z)\cdot 4
|
-2,874 |
(4 + 3 + 1) \cdot 13^{1/2} = 8 \cdot 13^{1/2}
|
-19,673 |
\dfrac19 \cdot 18 = \frac19 \cdot 18
|
23,519 |
3*\sec(\theta) = z \Rightarrow \sec(\theta) = \frac{z}{3}
|
-4,600 |
-\dfrac{2}{z + 4\cdot (-1)} + \dfrac{4}{5 + z} = \dfrac{2\cdot z + 26\cdot (-1)}{20\cdot (-1) + z^2 + z}
|
-25,789 |
4/40 = \frac{1}{5 \cdot 8}4
|
5,736 |
\sqrt{\frac14} = \frac12 \gt \tfrac14
|
-5,234 |
10^{(-5)\cdot \left(-1\right) - 1}\cdot 0.98 = 0.98\cdot 10^4
|
-2,397 |
6 * 6 = 6*6 = 36
|
194 |
4 \cdot y \cdot x = -(-y + x)^2 + (x + y)^2
|
6,385 |
720 = 2\times 3\times 4\times 5\times 6
|
-24,650 |
11/20 = -\frac{3}{10} + \dfrac14 + \frac35
|
-29,935 |
d/dy (-y^3) = -d/dy y \cdot y \cdot y = -3 \cdot y^2 = -3 \cdot y^2
|
-6,383 |
\frac{1}{3\cdot (z + 5)\cdot (z + 8\cdot (-1))}\cdot 6 = \frac{2}{(z + 8\cdot (-1))\cdot (5 + z)}\cdot \tfrac33
|
-5,648 |
\dfrac{1}{2*(9*\left(-1\right) + t)}*3 = \frac{3}{2*t + 18*(-1)}
|
21,565 |
( 11, 60, 61) = ( 6^2 - 5^2, 60, 6^2 + 5^2)
|
13,433 |
d_{1 + x} + d_x = h_{1 + x} \Rightarrow d_x = h_{x + 1} - d_{1 + x}
|
28,796 |
x^{\frac{1}{2}\cdot 2} = x^1
|
13,154 |
A \pm 2 \cdot (A + (-1))^{1/2}^{1/2} = \left((A + (-1))^{1/2} \pm 1^2\right)^{1/2} = |(A + (-1))^{1/2} \pm 1|
|
18,282 |
\mathbb{E}[2\cdot \mathbb{E}[s]\cdot s] = \mathbb{E}[s]\cdot \mathbb{E}[s]\cdot 2
|
-2,592 |
\left(2 + (-1) + 4\right) \cdot \sqrt{13} = 5 \cdot \sqrt{13}
|
33,851 |
\frac17(2^7 + 2(-1)) = 18
|
770 |
a + n^2*4 + 2*b*n = a + (2*n + b)*n*2
|
5,356 |
z\Longrightarrow (z^2 - 3*z + 1)^2 - 3*(z^2 - 3*z + 1) + 1 = z^2 - 3*z + 1 = z
|
-26,631 |
108 - 3\cdot x^2 = (-x \cdot x + 36)\cdot 3
|
-8,395 |
21 = \left(-7\right) (-3)
|
-23,160 |
\frac{32}{27} \cdot 2/3 = 64/81
|
1,656 |
\left(x^2 + (-1)\right)/x = -1/x + x
|
34,366 |
(6 + \left(-1\right))*\left(2*(-1) + 6\right)/2 = 10
|
6,789 |
y_s \cdot y_n = y_s \cdot y_n
|
23,832 |
50x+20y = 1020 \implies 5x+2y = 102
|
3,553 |
1 + x^3 + 3x^2 + x\cdot 3 = \left(x + 1\right)^3
|
22,985 |
2^{k + 1} - k^2 + 3 (-1) = 3 (-1) + (1 + 1)^{k + 1} - k^2
|
11,680 |
\mathbb{E}(Q_2) \cdot \mathbb{E}(1/(Q_1)) = \mathbb{E}(Q_2/(Q_1))
|
2,223 |
-(1 + 2 + 3 + 4) = 16 \left(-1\right) + 1 + 4\left(-1\right) + 9
|
2,314 |
\cos(y) = \frac{1}{2} \times (e^{i \times y} + e^{-i \times y}) = \frac{1}{2 \times e^{i \times y}} \times (e^{2 \times i \times y} + 1)
|
-1,295 |
\frac{1}{15}\cdot 30 = \frac{30\cdot \dfrac{1}{15}}{15\cdot 1/15} = 2
|
31,259 |
\left(I = B\cdot A\Longrightarrow B = B\cdot B\cdot A\right)\Longrightarrow B\cdot A = I
|
-3,408 |
-\sqrt{3} + \sqrt{3} \times \sqrt{9} = -\sqrt{3} + 3 \times \sqrt{3}
|
9,778 |
\frac{1}{40}\left(3000 + 2x\right) = \frac{1}{40}3000 + 2x/40 = 75 + x/20
|
30,121 |
\tfrac{1}{x^2} \cdot \left(x \cdot x + x\right) = 1 + \frac1x
|
7,786 |
2*3^4*7*19*73*87211*262657 = 2*(-1) + 2^{55}
|
22,976 |
p^p - p^p = p\cdot 2 rightarrow 0 = p\cdot 2
|
-7,178 |
\frac{3}{9}\cdot 2/8 = \frac{1}{12}
|
14,964 |
x \cdot \tfrac{y}{100} = x/100 \cdot y
|
32,092 |
0.03 + 0.1 y = 0.08 (1 + y) = 0.08 + 0.08 y
|
9,338 |
m! = \frac{1}{1 + m}*(m + 1)!
|
-22,844 |
5*10/(2*10) = \tfrac{1}{20}*50
|
28,864 |
{6 \choose 1} \cdot {7 \choose 0} = 6
|
-11,511 |
13\cdot i - 1 = 13\cdot i - 6 + 5
|
20,484 |
Var[T] (1 - p) + \frac{1}{p}\left(1 - p\right) + p*0 = (1 - p) \left(Var[T] + 1/p\right)
|
23,516 |
a*a^p*a*a^p*a^p*a = a*a^p*a*a^p*a^p*a
|
13,335 |
10 = 5*2 = 5*(3 + \left(-1\right)) = 5*((3^4)^{1/4} + \left(-1\right))
|
-8,037 |
\frac{18 - i}{3*i - 4} = \frac{1}{i*3 - 4}*(-i + 18)*\frac{-3*i - 4}{-4 - i*3}
|
3,621 |
1/(G*z) = \frac{1}{G*z}
|
13,382 |
\int\limits_a^b 1\,\mathrm{d}x = -\int\limits_b^a 1\,\mathrm{d}x
|
-12,907 |
8/18 = 4/9
|
15,779 |
\frac{\partial}{\partial x} x^m = m x^{m + (-1)} \frac{\mathrm{d}x}{\mathrm{d}x} = m x^m
|
19,759 |
\frac{1}{1/\left(\sqrt{k}\right)}\cdot x_k = x_k\cdot \sqrt{k}
|
29,094 |
(2 (-1) + x x + x) \left(x + \left(-1\right)\right) + 3 x + 3 (-1) = x^3 + (-1)
|
8,344 |
x\frac1y/z = \frac{x\frac1z}{y} = x/(yz)
|
24,219 |
h_2 \cdot h_1 \cdot 2 = h_2 \cdot h_1 \cdot 2
|
5,471 |
\dfrac{1}{2}\cdot (1 - 5^{1/2}) = 1/2 - \dfrac12\cdot 5^{1/2}
|
14,554 |
t - (t + (-1))/2 = \frac{1}{2} \cdot \left(t + 1\right) = \frac12 \cdot (t + (-1)) + 1
|
3,564 |
x \cdot x + (-1) = (x + (-1))\cdot (2\cdot (x + 1) + \frac{1}{x + \left(-1\right)}) = 2\cdot (x + (-1))\cdot (x + 1) + 1
|
40,749 |
147 + 245 \cdot (-1) + 343/3 = -98 + 114 + 1/3 = 16 + \frac13 = 49/3
|
12,342 |
F \cdot z \cdot 2 + 2 \cdot x = ((-1) + x \cdot 4 + 4 \cdot F \cdot z) \cdot \left(2 \cdot x^2 + 2 \cdot z^2 - x\right) \cdot 2
|
7,067 |
1 = 1^{\frac{1}{2}} = ((-1)^2)^{\frac{1}{2}} = (-1)^{2\times \frac{1}{2}} = (-1)^1 = -1
|
20,732 |
(d^{\tfrac{1}{3}} x)^3 = dx^3
|
24,321 |
\frac{1}{12}\cdot \pi = -\pi/6 + \frac{\pi}{4}
|
-9,428 |
11 + 99 \cdot r = 11 + 3 \cdot 3 \cdot 11 \cdot r
|
38,094 |
66^2 + 467 \cdot 467 = 222445
|
19,256 |
(a + (-1))^2 = a^2 - 2\cdot a + 1 < a^2 + 1
|
15,956 |
\sin(y*2) = \frac{2*\tan(y)}{1 + \tan^2(y)}
|
2,535 |
r' = r^2 \Rightarrow r = r'^{1/2}
|
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