id
int64 -30,985
55.9k
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stringlengths 5
437k
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-1,074 |
\frac{(-1) \frac{1}{8}}{1/4 (-3)} = -\frac{1}{8} (-\frac43)
|
-9,747 |
0.01 (-84) = -\dfrac{84}{100} = -\frac{21}{25}
|
13,662 |
\frac1q \cdot X \cdot x \cdot l = x \cdot X/q \cdot l
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9,080 |
\tfrac{1000}{102} = 9.9 - 0.099 + 0.00099 - 9.9*10^{-6} = 9.801 + 0.0009801 = 9.801
|
-26,577 |
-8^2 + y^2 = (8(-1) + y) (y + 8)
|
-27,369 |
519\cdot (-1) + 725 = 206
|
2,172 |
\cos{2} < 1 - \frac{2^2}{2!} + \frac{2^4}{4!} = -\dfrac{1}{3} < 0
|
-188 |
\frac{1}{3! \cdot (3 \cdot \left(-1\right) + 8)!} \cdot 8! = \binom{8}{3}
|
4,812 |
\sum_{m=1}^\infty (m^2*4 + x_m^2 + 4*x_m*m) = \sum_{m=1}^\infty (x_m + 2*m)^2
|
17,909 |
\sin(-a \cdot \omega) = -\sin(\omega \cdot a)
|
30,345 |
m + x + 1 = 1 + m + x
|
-11,880 |
\dfrac{2.478}{1000} = 2.478\cdot 0.001
|
42,891 |
\binom{3+2-1}{2} = 6
|
13,188 |
3\cdot i\cdot i\cdot 3 + z\cdot z - z\cdot i\cdot 3 - z\cdot 3\cdot i = (z - 3\cdot i)\cdot \left(-i\cdot 3 + z\right)
|
-5,585 |
\dfrac{1}{30 + k^2 + 13\cdot k}\cdot k = \dfrac{1}{\left(3 + k\right)\cdot (10 + k)}\cdot k
|
21,505 |
\dfrac123 = 1/2 - \tfrac22 + 4/2
|
15,786 |
h^{s + \mu} = h^\mu \cdot h^s
|
1,128 |
u_x + cu_y = 1 = ( 1, c) ( u_x, u_y)
|
-2,435 |
(2 + 3*(-1) + 4)*7^{1/2} = 7^{1/2}*3
|
9,464 |
({202 \choose 2} - 3\cdot 101)/3! = \frac16\cdot (20301 + 303\cdot \left(-1\right)) = 3333
|
1,147 |
\tan{y} + (-1) = \sin{y}/\cos{y} + (-1) = (\sin{y} - \cos{y})/\cos{y}
|
11,391 |
3\cdot (3334\cdot \left(-1\right) + 33333)/3 + 1 = \frac13\cdot (10002\cdot (-1) + 99999) + 1
|
-24,141 |
5\cdot 6 + 8\cdot \tfrac{8}{1} = 5\cdot 6 + 8\cdot 8 = 30 + 8\cdot 8 = 30 + 64 = 94
|
-5,620 |
\frac{3}{(x + 6)\cdot (x + 8\cdot (-1))} = \dfrac{1}{x^2 - x\cdot 2 + 48\cdot (-1)}\cdot 3
|
1,372 |
29 = 42 + 6\cdot (-1) + 7\cdot \left(-1\right)
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-25,866 |
6^4/6 = \dfrac{1}{6^1}6^4 = 6^{4 + (-1)} = 6^3
|
22,677 |
x_i \cdot (\alpha + 1) = x_i + x_i \cdot \alpha
|
22,903 |
1/12 + \frac{1}{2} + 1/4 + \frac{1}{6} = 1
|
18,861 |
\frac{1}{\cos(z)} \cdot \sin\left(z\right) = \tan(z)
|
17,070 |
\cos{x} = t \Rightarrow \arccos{t} = x
|
3,129 |
c^2 - J^2 = (c - J) (J + c)
|
9,119 |
\sqrt{d^6} = \sqrt{(d^3)^2} = d^3
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-15,753 |
\frac{1}{d^{20}*\dfrac{1}{d^2 * d*r^{15}}} = \frac{\frac{1}{d^{20}}*d * d * d}{\frac{1}{r^{15}}}*1 = \frac{1}{d^{17}}*r^{15} = \frac{r^{15}}{d^{17}}
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-20,391 |
-4/\left(-4\right) = \frac{1}{1}\cdot (1/(-4)\cdot (-4))
|
1,563 |
\binom{4}{2}*\binom{6}{2}*\binom{2}{2} = 90
|
20,776 |
(z^2 + z + 1)\cdot ((-1) + z) = (-1) + z^3
|
604 |
r\cdot e_x = r = e_x\cdot r
|
15,720 |
\max{a, e, c} = \max{a, \max{e,c}} = \max{\max{a,e},c}
|
7,706 |
D_2^2 D_1^2 = \left(D_1 D_2\right)^2
|
7,380 |
1000 = 6999 + 6000 (-1) + 1
|
-5,537 |
\frac{4}{35 (-1) + n \cdot n + n\cdot 2} = \frac{4}{\left(7 + n\right) (n + 5(-1))}
|
8,307 |
\mathbb{P}(y) = \int (4 \cdot y^4 + 1)\,\mathrm{d}y = 4 \cdot \int y^4\,\mathrm{d}y + \int 1\,\mathrm{d}y
|
59 |
\tfrac{1}{(1 + m - j) * (1 + m - j)}*\left((-1) + j\right) = \frac{-(m - j + 1) + m}{(m - j + 1)^2}
|
5,711 |
a + id = di + a
|
17,457 |
\frac{3\cdot 3/4}{4}/4 = \tfrac{1}{64}\cdot 9
|
13,684 |
1 + 2\cdot 2k = 1 + k\cdot 4
|
-21,595 |
\sin{\dfrac{1}{2}\cdot 3\cdot \pi} = -1
|
12,235 |
\dfrac{b^7\cdot f^2}{f^3\cdot b}\cdot 1 = b^6/f
|
-30,324 |
6(-1) + 10 = 4
|
12,841 |
1^3 = 1 = \left(\frac{2}{2} \cdot 1\right) \cdot \left(\frac{2}{2} \cdot 1\right)
|
-22,772 |
54/90 = \frac{3}{18*5}18
|
66 |
\left(a\cdot x + b + I\right)^2 = a^2\cdot x^2 + 2\cdot a\cdot b\cdot x + b^2 + I = 2\cdot a\cdot b\cdot x + b \cdot b + 2\cdot a^2 + I
|
22,947 |
\frac{d}{dt}e^{-tB} = -Be^{-tB} = -e^{-tB}B
|
-30,269 |
\frac{1}{x + (-1)}\cdot (x^2 + 2\cdot x + 3\cdot (-1)) = \frac{1}{x + \left(-1\right)}\cdot (x + 3)\cdot (x + (-1)) = x + 3
|
8,154 |
-i = i*\sin{3*\pi/2} + \cos{\pi*3/2}
|
-22,153 |
30/50 = \frac35
|
5,634 |
\dfrac{1}{l_1^2}\cdot (l_2 + (-1)) = (\left(-1\right) + l_2)\cdot \frac{1}{l_1}/(l_1)
|
33,844 |
\frac{1}{2}2^{2/3} = 2^{-\frac13}
|
28,098 |
z^9 \cdot I^9 = (z \cdot I)^9
|
17,441 |
y + \frac{1}{y}*(3 - i) = 3 \Rightarrow 3 - i + y^2 - 3*y = 0
|
30,624 |
\tfrac{6!}{2! (6 + 2(-1))!} + \frac{1}{3! (4 + 3(-1))!}4! = 19
|
-13,506 |
2 - 5\cdot 6 + 45/9 = 2 - 5\cdot 6 + 5 = 2 + 30 (-1) + 5 = -28 + 5 = -23
|
32,872 |
(1/n + x)*(x + \frac{1}{n}) = x^2 + \frac{x*2}{n} + \frac{1}{n^2}
|
-7,908 |
\tfrac{1}{20}\cdot (-32 - 56\cdot i + 16\cdot i + 28\cdot (-1)) = (-60 - 40\cdot i)/20 = -3 - 2\cdot i
|
25,106 |
(z - y)\cdot \left(z^{m + \left(-1\right)} + y\cdot z^{m + 2\cdot (-1)} + z^{3\cdot (-1) + m}\cdot y^2 + \dots + y^{m + 2\cdot (-1)}\cdot z + y^{m + \left(-1\right)}\right) = z^m - y^m
|
44,325 |
y y = y^2 = y^2
|
-26,468 |
20 + 5*x^2 - x*20 = 5*(x^2 - 4*x + 4)
|
-6,597 |
\tfrac{1}{2r + 6} = \frac{1}{2(3 + r)}
|
473 |
\frac{1}{7\cdot \left(-1\right) + m}\cdot (m + 13) = \frac{1}{7\cdot (-1) + m}\cdot 20 + 1
|
8,708 |
\sqrt{3 \cdot 3 + 1^2} = \sqrt{10}
|
1,968 |
\frac{1}{\frac{1}{1/3 + 2} + 2} = \frac{7}{17}
|
-30,579 |
70*(-1) + 40*x = (4*x + 7*(-1))*10
|
21,231 |
\cos(\frac{1}{2}\pi + h) = -\sin\left(h\right)
|
19,613 |
\left(5 + 5 + h\right)*(5*\left(-1\right) + 5 + h) = h^2 + h*10
|
14,309 |
\vartheta G = \vartheta G
|
15,518 |
\frac{(-1) + n^2 c_n}{c_n^2 + n \cdot n} = -\frac{1 + c_n^3}{n \cdot n + c_n^2} + c_n
|
-28,771 |
-\frac12 - \frac{1}{-z\cdot 2 + 2}\cdot 4 = -1/2 + \frac{1}{(-1) + z}\cdot 2
|
25,773 |
-x\cdot 2 + 1 = 1 - x^2 - -x^2 + 2x
|
29,061 |
3*n + n = 4*n
|
11,615 |
0 = 8 \sin{\pi \cdot 2}
|
21,378 |
1/27 = \dfrac{1}{6^3}\cdot 2^3
|
12,263 |
h_2^{h_1} \cdot h_2^b = h_2^{b + h_1}
|
18,664 |
Y^5 + (-1) = (Y + (-1)) (1 + Y^4 + Y \cdot Y \cdot Y + Y^2 + Y)
|
-18,529 |
z + 3\cdot (-1) = 4\cdot \left(5\cdot z + 8\cdot (-1)\right) = 20\cdot z + 32\cdot (-1)
|
9,229 |
\frac{(1 + z + z^2)*\left(-z + 1\right)}{(1 - z)^2 * \left(1 - z\right)} = \dfrac{1 + z + z^2}{(-z + 1)^2}
|
12,399 |
y^4 + 5*y + 1 = \left(y^2 + 1\right)*(y^2 + (-1)) + 5*y + 5*(-1) = (y + \left(-1\right))*\left(y^3 + y * y + y + 6\right)
|
19,999 |
\sin\left(9 \cdot y\right) + \sin(y) = 2 \cdot \sin((9 \cdot y + y)/2) \cdot \cos\left((9 \cdot y - y)/2\right) = 2 \cdot \sin(5 \cdot y) \cdot \cos(4 \cdot y)
|
4,916 |
(m + 3 \cdot \left(-1\right))^{1 / 2} = (-(3 - m))^{\frac{1}{2}} = i \cdot \left(3 - m\right)^{\frac{1}{2}}
|
2,769 |
\beta \cdot x + \gamma \cdot x = (\beta + \gamma) \cdot x
|
-24,370 |
\frac{1}{6 + 8}*70 = 70/14 = \tfrac{1}{14}*70 = 5
|
-10,264 |
-\frac{1}{z + 5} \cdot \frac{3}{3} = -\dfrac{3}{3 \cdot z + 15}
|
-14,026 |
\dfrac{1}{4 + 6} \cdot 40 = \frac{1}{10} \cdot 40 = \frac{40}{10} = 4
|
3,569 |
(5 \cdot 5^{\frac12})^3 = 5^{\frac{1}{2} \cdot 3} \cdot 5^{\frac{1}{2} \cdot 3} \cdot 5^{\frac{1}{2} \cdot 3} = 5^{\tfrac92} = 5^4 \cdot \sqrt{5}
|
25,791 |
(2^4)^i = 2^{4\cdot i}
|
16,859 |
1 + m \times (3 + 2 \times m) = m^2 \times 2 + 3 \times m + 1
|
8,448 |
\frac{1}{4}\cdot \left(1 + 2\cdot x\right)^2 = (\frac{1}{2} + x)^2
|
-6,636 |
\frac{1}{3 \times y + 3} \times 2 = \frac{2}{(y + 1) \times 3}
|
8,809 |
\frac{3y + 2(-1)}{y + 1} = \frac{1}{y + 1}\left(3\left(y + 1\right) + 5(-1)\right) = 3 - \frac{5}{y + 1}
|
-6,566 |
\frac{1}{k*4 + 36} = \frac{1}{4*\left(9 + k\right)}
|
1,760 |
( x + 2\cdot (b - h), y) = ( 2\cdot b - -x + 2\cdot h, y)
|
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