id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
9,847 |
0 = e\cdot c + c\cdot d = c\cdot \left(e + d\right)
|
37,725 |
5! \cdot 4! \cdot 6 = 4! \cdot 6!
|
9,485 |
\frac{1}{n + 2}\cdot 2^{2\cdot n + 1} = 4^n\cdot \frac{1}{2 + n}\cdot 2
|
21,457 |
\left(z^{1/2} = j \implies (z^{1/2})^2 = j^2\right) \implies z = j^2
|
23,883 |
\left(120 = 4*d + 6*d \Rightarrow d = 12\right) \Rightarrow d^2 = 144
|
7,263 |
X \times Y = \tfrac{1}{4} \times (-(X - Y)^2 + (Y + X)^2)
|
29,907 |
y^4 - 5 \cdot y^3 + 5 \cdot y^2 + 5 \cdot y + 6 \cdot (-1) = (y^2 - 2 \cdot y + 3 \cdot (-1)) \cdot (y^2 - 3 \cdot y + 2) = (y + 1) \cdot (y + 3 \cdot \left(-1\right)) \cdot \left(y + (-1)\right) \cdot (y + 2 \cdot (-1))
|
-18,416 |
\frac{r}{((-1) + r) \cdot (2 + r)} \cdot ((-1) + r) = \frac{r^2 - r}{r^2 + r + 2 \cdot (-1)}
|
25,237 |
5/6*5/6 = (\frac{5}{6}) * (\frac{5}{6})
|
14,858 |
\left(\epsilon/x\right)^2 = \frac{\epsilon^2}{x^2}
|
34,656 |
\frac22 \cdot 3 = 3
|
32,119 |
140 * 140 = {50 \choose 3}
|
9,796 |
108 = 3^3 \cdot 2 2
|
25,998 |
5 + ((-1) + x)^4 + 3\times x^2 - x\times 6 = 2 + (\left(-1\right) + x)^4 + 3\times (x + (-1))^2
|
26,559 |
(8 + y \cdot 3) \cdot (y + 2) = y \cdot y \cdot 3 + 14 \cdot y + 16
|
18,349 |
z + 1 = (z + 1)^1
|
-6,385 |
\tfrac{3}{8*(-1) + s*2} = \frac{1}{2*(s + 4*(-1))}*3
|
-22,966 |
9\cdot 10/(9\cdot 7) = 90/63
|
-25,812 |
10^{-1}\times 3/6 = \frac{3}{60}
|
-4,946 |
0.95\cdot 10^{2\cdot (-1) + 9} = 10^7\cdot 0.95
|
5,343 |
\omega_0 = \omega_0 + \left(-1\right) + 1
|
14,228 |
x - h = \frac{-h^3 + x^3}{x^2 + h*x + h^2}
|
-725 |
\frac{\pi}{12} = \pi\cdot \frac{49}{12} - 4\cdot \pi
|
29,900 |
4 \cdot 15^2 = 4^2 + 10 \cdot 10 + 28^2
|
36,941 |
7 - 2*3 = 1
|
-3,510 |
\frac{12}{2 \cdot 50} \cdot 1 = 12/100
|
20,173 |
2*(1 + n) = n*2 + 2
|
12,158 |
\cos\left(b\right)\cdot \sin\left(g\right) + \sin(b)\cdot \cos\left(g\right) = \sin(g + b)
|
11,701 |
3^{z + (-1)} = 1 + 2 \implies z = 2
|
1,695 |
\sigma_k \sigma_l = \sigma_k \sigma_l
|
3,648 |
1 + x\cdot (a + 1) + x^2\cdot (1 + a + a^2) + \ldots = 1 + x + x\cdot a + x^2 + a\cdot x^2 + a^2\cdot x^2 + \ldots
|
2,914 |
2 \cdot e + 2 \cdot v - 3 \cdot v = e \cdot 2 - v
|
3,916 |
f^2 + \frac{3}{f^2 \cdot 4} = (2 \cdot f^2 + \dfrac{3}{f^2 \cdot 2})/2
|
907 |
4/36 \cdot \frac26 = 8/216
|
22,609 |
\cos(t) = \cos\left(2\pi + t\right)
|
6,177 |
4(-1) + (z + (-1))^2 = z^2 - z\cdot 2 + 3(-1)
|
13,615 |
\dfrac{1}{30}*(6 + 15 + 10 + \left(-1\right)) = 1
|
-21,603 |
\cos{-\dfrac{\pi}{2}} = 0
|
5,816 |
(A^2)^T = (A*A)^T = A^T*A^T = \left(A^T\right)^2
|
12,897 |
0 \geq a \implies |a| = -a
|
-8,038 |
\frac{5 + i \cdot 3}{-i + 1} = \dfrac{5 + 3 \cdot i}{-i + 1} \cdot \frac{1}{1 + i} \cdot (1 + i)
|
23,546 |
\int y\,\text{d}y = \frac{\frac{1}{2}}{y} \cdot y^2 = \frac{1}{2} \cdot y
|
-23,553 |
\frac{4}{15} = 2/3\cdot \frac{1}{5}\cdot 2
|
18,571 |
E^k B = E^k B
|
-16,914 |
5 = 5\times 3\times q + 5\times (-7) = 15\times q - 35 = 15\times q + 35\times (-1)
|
6,975 |
-(\left(-1\right) + n) + 2n + (-1) = n
|
-6,059 |
\frac{y}{(y + 6(-1)) (y + 9\left(-1\right))} = \frac{y}{y^2 - 15 y + 54}
|
24,710 |
2 \cdot (-1) + z^2 + z = (z + 2) \cdot \left(z + (-1)\right)
|
19,809 |
\frac1x + \frac{1}{x} - \dfrac{1}{x^2} = \frac{2}{x} - \frac{1}{x^2} \lt \frac1x\cdot 2
|
2,172 |
\cos(2) \lt 1 - 2 * 2/2! + \frac{1}{4!}*2^4 = -1/3 \lt 0
|
14,620 |
|\frac{d}{c} + y_0| = |y_0 - ((-1) d)/c|
|
20,243 |
16*\left(-1\right) + y^2 = (y + 4*(-1))*(y + 4)
|
31,327 |
b \cdot a \cdot z = a \cdot z \cdot b
|
859 |
2017^3 = (2017 \cdot 44)^2 + (2017 \cdot 9)^2
|
29,422 |
D \cup (A \cap B) = (A \cup D) \cap (B \cup D) = A \cap \left(B \cup D\right)
|
140 |
(\zeta + f) \cdot d = d \cdot \zeta + d \cdot f
|
5,014 |
1 + 2 \cdot s \cdot b = b^2 + 2 \cdot s \cdot b + s \cdot s = \left(b + s\right) \cdot \left(b + s\right)
|
27,828 |
y * y z + z = y + z^2 y\Longrightarrow z = y
|
-24,701 |
18\sqrt{144b^4}=18\sqrt{12^2\cdot \left(b^2\right)^2} =18\sqrt{12^2}\cdot\sqrt{\left(b^2\right)^2} =18\cdot 12\cdot b^2 =216b^2
|
6,281 |
720 = 3 3\cdot 2^4\cdot 5
|
44,385 |
375 = \frac14 \cdot 3 \cdot 500
|
29,510 |
2^{40} = 17 \cdot (2n + 1) + 1 = 34 n + 18
|
23,483 |
p^{p + 1} = p^p\cdot p
|
4,812 |
\sum_{n=1}^\infty (a_n + 2 \cdot n)^2 = \sum_{n=1}^\infty \left(a_n \cdot a_n + 4 \cdot a_n \cdot n + 4 \cdot n^2\right)
|
37 |
(x + c) \cdot (x + c) = c\cdot x\cdot 4 + (-x + c)^2
|
7,283 |
\cos\left((\pi\cdot (-1))/4\right) = \cos(\pi/4)
|
-2,535 |
\sqrt{10} \cdot 3 + 4 \cdot \sqrt{10} = \sqrt{10} \cdot \sqrt{16} + \sqrt{10} \cdot \sqrt{9}
|
-20,800 |
\frac{1}{7}\cdot 7\cdot \frac{10 - 2\cdot y}{3\cdot (-1) + y} = \frac{70 - y\cdot 14}{7\cdot y + 21\cdot (-1)}
|
-20,295 |
-\dfrac{9}{8} \cdot \frac{r + 6 \cdot \left(-1\right)}{r + 6 \cdot (-1)} = \frac{1}{48 \cdot \left(-1\right) + r \cdot 8} \cdot (-r \cdot 9 + 54)
|
-6,422 |
\frac{1}{5\cdot y + 50} = \frac{1}{5\cdot (10 + y)}
|
2,016 |
\frac{2*y}{\pi} + y'*x*2/\pi = (y^2 + 2*x*y'*y)*\sec^2{y^2*x}
|
19,842 |
8 + 1/3 - \frac{1}{z} = y \Rightarrow [3,8] = \left[z, y\right]
|
33,210 |
\frac{1}{s} = \frac1s
|
34,407 |
{9 + r \choose 9} = {(-1) + r + 10 \choose \left(-1\right) + 10}
|
27,117 |
B^2 = B*B
|
13,702 |
\cos(f - b) + \cos\left(f + b\right) = 2 \cdot \cos(b) \cdot \cos(f)
|
8,792 |
1.0000006^2 = (1 + \tfrac{6}{10^7})^2 = (1 + \frac{3}{5\cdot 10^6})^2
|
28,492 |
2 + c_x^2 + \dfrac{1}{c_x^2} = c_{1 + x}^2\Longrightarrow 2 + c_x^2 \lt c_{x + 1} * c_{x + 1}
|
31,462 |
\frac32 = -1/2 + 2
|
-20,012 |
\frac{1}{j \cdot 24 + 40} \cdot (25 + 15 \cdot j) = \dfrac{5 + j \cdot 3}{3 \cdot j + 5} \cdot 5/8
|
38,835 |
c = \frac{1}{\frac{1}{c}}
|
26,566 |
194689796301 = 21589*(3*7*11*13)^2
|
12,083 |
1 + g + g \cdot g + g^3 + \dotsm = \frac{1}{-g + 1}
|
22,533 |
\sin(\frac{\pi}{10}) = ((-1) + \sqrt{5})/4
|
7,218 |
y^7 + (-1) = (y + \left(-1\right)) (y^6 + y^5 + y^4 + y * y^2 + y^2 + y + 1)
|
-23,303 |
22\% = -78 \cdot 0.01 + 100\%
|
11,641 |
9 = 3*\left(-1\right) + 31 + 21*\left(-1\right) + 19*(-1) + 17 + 13 + 11*(-1) + 7 + 5*(-1)
|
-28,539 |
-z^2 + 12\cdot z + 32\cdot \left(-1\right) = -32 - z^2 - 12\cdot z = -32 + 36 - z^2 - 12\cdot z + 36 = 4 - (z + 6\cdot \left(-1\right))^2 = 2 \cdot 2 - (z\cdot (-6))^2
|
14,943 |
\left(1 + (\left(-1\right) + r)/2\right) \cdot 2 = r + 1
|
27,504 |
1/2 \cdot 2 \cdot 2 = 2 = 1/2 \cdot 0 = 0
|
773 |
16\cdot (-|E\cdot C| + |B\cdot D|) = 64 \Rightarrow 4\cdot (-1) + |B\cdot D| = |E\cdot C|
|
20,883 |
x = \frac{X}{X - V} = (x - V)\cdot X
|
-18,360 |
\tfrac{1}{(x + (-1)) \cdot x} \cdot (x + (-1)) \cdot (x + 9) = \frac{1}{x^2 - x} \cdot \left(9 \cdot (-1) + x \cdot x + 8 \cdot x\right)
|
9,182 |
(\sin(g + a) + \sin(a - g))/2 = \cos(g) \cdot \sin(a)
|
-2,010 |
\frac{1}{12}\cdot \pi - \pi\cdot \frac14\cdot 3 = -\pi\cdot 2/3
|
-20,386 |
\frac15\cdot 5\cdot \dfrac{1}{10\cdot y + 10}\cdot (-7\cdot y + 2) = \frac{1}{50 + 50\cdot y}\cdot (10 - y\cdot 35)
|
-10,732 |
8 = -4 \cdot x + 4 \cdot (-1) + 15 = -4 \cdot x + 11
|
-2,668 |
-\sqrt{6} + 3\times \sqrt{6} = \sqrt{6}\times \sqrt{9} - \sqrt{6}
|
-2,289 |
1/18 = -1/18 + 2/18
|
12,831 |
|z - u| = |-z + u|
|
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