id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-26,620 |
(6 + x) \cdot (-x + 6) = 6^2 - x^2
|
32,272 |
5 \cdot 5 - \left\lceil{\frac56}\right\rceil + 5 \cdot (-1) = 19
|
3,747 |
3\cdot (2\cdot l^2 - 4\cdot l + 1) = l^2\cdot 6 - l\cdot 12 + 3
|
9,217 |
0 \lt -x \Rightarrow x \lt 0
|
-15,792 |
-\frac{1}{10} \cdot 2 \cdot 6 + 8 \cdot 8/10 = \frac{1}{10} \cdot 52
|
-3,971 |
\frac{1}{x^4}x = \dfrac{x}{xx x x} = \dfrac{1}{x^3}
|
17,005 |
(x + 1) (x + 5 (-1)) = x^2 - 4 x + 5 \left(-1\right)
|
-2,830 |
5\cdot \sqrt{6} + \sqrt{6} = \sqrt{6} + \sqrt{6}\cdot \sqrt{25}
|
7,747 |
|x_m - x_{m + 1}| = |x_{1 + m} - x_m|
|
12,748 |
0 = 25 + 9 + e\cdot 10 + f\cdot 6 + c \implies 10\cdot e + f\cdot 6 + c = -34\cdot \dots\cdot 2
|
-24,261 |
\dfrac{1}{9 + 5}126 = 126/14 = \frac{1}{14}126 = 9
|
-10,914 |
57 = \frac{1}{3}171
|
16,388 |
(x + y)\cdot \varphi = \left(x + y\right)\cdot (\varphi + 0) = x\cdot \varphi + y\cdot \varphi
|
-22,042 |
16/10 = \dfrac{8}{5}
|
10,129 |
rX = rY = l \Rightarrow l = rXY
|
19,125 |
(1 + 3) (1 + 2) = 12
|
41,812 |
268 = 2 \cdot 2\cdot 67
|
49,820 |
3 + 6 + 3 = 12
|
18,996 |
\dfrac13 = 4*\frac16/2
|
17,023 |
0 = (x^3 + (-1))*(x^6 + x^2 * x + 1) = x^9 + (-1)
|
3,624 |
v \cdot G_0 \cdot v = v \cdot G_0^{\tfrac12} \cdot G_0^{1/2} \cdot v = G_0^{1/2} \cdot v
|
27,765 |
x\cdot 8 = 90 \implies x = \frac{45}{4} = 11.25
|
5,309 |
x^3 + 2(-1) = \left(x \cdot x + x \cdot 2^{1/3} + 4^{\frac{1}{3}}\right) (x - 2^{\frac{1}{3}})
|
31,263 |
x_1 x_2 x_3 = x_3 x_2 x_1
|
-23,195 |
5 \cdot 3/2 = \frac{15}{2}
|
1,053 |
2 \cdot x \cdot y + x \cdot x + y^2 = (y + x)^2
|
521 |
\frac12 \cdot (2 + 6) = 4
|
-20,090 |
\frac{5\cdot \tfrac15}{x + \left(-1\right)} = \frac{5}{5\cdot x + 5\cdot (-1)}
|
-6,014 |
\frac{5\cdot s}{\left(s + 3\right)\cdot \left(2 + s\right)} = \frac{5\cdot s}{s^2 + 5\cdot s + 6}
|
-6,570 |
\frac{-12 a + a\cdot 6 + 54 (-1) + 4a + 36 (-1)}{a^2\cdot 3 - 54 a + 243} = \frac{-2a + 90 (-1)}{a^2\cdot 3 - a\cdot 54 + 243}
|
23,367 |
0^{2^{l + 1}} + l + 1 = 0^{2^l*2} + l + 1
|
1,283 |
4(\frac 14 \cdot \frac 6{13})=\frac 6{13}
|
37,062 |
O = E \cup x \backslash E \cap x = EO \cup xO
|
-11,532 |
-3 + 3 (-1) + 8 i = 8 i - 6
|
-20,108 |
\tfrac{7}{7} \cdot \tfrac{1}{x \cdot (-5)} \cdot (-x \cdot 2 + 10) = \dfrac{-x \cdot 14 + 70}{(-35) \cdot x}
|
2,633 |
0\cdot (x + 1) = x\cdot 0
|
295 |
(-1) + x^6 + x^4 + x^2\cdot 3 = (x^3 - x^2 + x + 1)\cdot (x^3 + x^2 + x + (-1))
|
11,194 |
(3 + y)^2 = y \cdot y + 6 \cdot y + 9
|
-20,624 |
\left(3(-1) + 5y\right)/(-6)*4/4 = (12 \left(-1\right) + 20 y)/(-24)
|
-20,982 |
\frac{4}{4}\cdot \tfrac{1}{-x + 9\cdot (-1)}\cdot (x\cdot (-3)) = \frac{x\cdot (-12)}{-x\cdot 4 + 36\cdot (-1)}
|
21,970 |
x + x^2*2 + 3*x * x * x + \ldots = \dfrac{1}{(-x + 1)^2}*x
|
8,946 |
2^{1 + x} + 2 \cdot (-1) = (2^x + (-1)) \cdot 2
|
7,744 |
660/6=110
|
20,883 |
Y = \tfrac{A}{A - \xi} = (Y - \xi) \cdot A
|
29,673 |
2 \cdot i + (2 \cdot i + 1)^3 + 1 = 8 \cdot i \cdot i \cdot i + 12 \cdot i^2 + 8 \cdot i + 1 = 4 \cdot (2 \cdot i^3 + 3 \cdot i^2 + 2 \cdot i + 1)
|
-15,682 |
\dfrac{1}{r^2\cdot \frac{1}{n^4}}\cdot n^4 = \frac{n^4}{\frac{1}{n^4\cdot \dfrac{1}{r^2}}}
|
6,134 |
x/48 + p/18 = \left(8 \times p + 3 \times x\right)/144
|
-15,747 |
\frac{p}{\dfrac{1}{\dfrac{1}{p^{25}}\cdot n^{15}}} = \frac{p}{\frac{1}{n^{15}}\cdot p^{25}}
|
-4,492 |
z^2 - z\cdot 4 + 3 = (z + 3\cdot (-1))\cdot \left((-1) + z\right)
|
-21,033 |
\dfrac{1}{-35\cdot g + 28\cdot (-1)}\cdot (-g\cdot 15 + 12\cdot (-1)) = \frac{-5\cdot g + 4\cdot \left(-1\right)}{4\cdot (-1) - g\cdot 5}\cdot 3/7
|
16,339 |
s \cdot (-s + \varphi + k) = s^2 + (-s + \varphi) \cdot s + (-s + k) \cdot s
|
20,534 |
\left(-1\right) + x^2 = (x + 1)*\left(x + (-1)\right)
|
-4,533 |
\frac{6 - 4 \cdot x}{x^2 - x \cdot 4 + 3} = -\frac{1}{x + (-1)} - \dfrac{3}{x + 3 \cdot (-1)}
|
10,121 |
\frac{1}{(-1) + u^2} = \left(\frac{1}{(-1) + u} - \frac{1}{u + 1}\right)/2
|
32,076 |
2 \cdot 17^2 = 578
|
19,740 |
0 = det\left(E\cdot G\right) = det\left(E\right)\cdot det\left(G\right)
|
4,041 |
\sqrt{-y^2 + 1} = \frac{(-1)\cdot y}{\sqrt{-y^2 + 1}}
|
34,243 |
R^1*...*R^k = R^\complement^k
|
32,637 |
0 = d^7 + 1 = (d + 1) \cdot (d^6 - d^5 + d^4 - d^3 + d \cdot d - d + 1)
|
-19,467 |
\tfrac18 3*3/2 = 3*\dfrac12/\left(1/3*8\right)
|
2,302 |
\left(i!\right)! = (i! + 2 \cdot (-1)) \cdot \left((-1) + i!\right) \cdot i! \cdot \ldots \cdot 2
|
35,695 |
z^6 + 1 = (z^2 + 1)\cdot \left(z^4 - z^2 + 1\right) = z^2 + 1
|
12,770 |
2^2 + 14^2 = 15^2 - 5 \cdot 5
|
-19,226 |
1/45 = \tfrac{A_p}{36 \cdot \pi} \cdot 36 \cdot \pi = A_p
|
-2,281 |
1/15 = -\frac{4}{15} + \frac{5}{15}
|
27,412 |
4^2 + 7^2 = 1^2 + 8^2
|
9,752 |
\binom{x}{k} = \frac{1}{k! \times (x - k)!} \times x!
|
-26,613 |
(7k - 9n)^2 = 81 n^2 + k^2\cdot 49 - 126 nk
|
-9,639 |
0.01\cdot (-24) = -24/100 = -0.24
|
-22,068 |
\tfrac{1}{4} \cdot 3 = 30/40
|
17,177 |
e^i \geq i \cdot 2 + 1 \Rightarrow e^{i + 1} > e^i + e^i > i \cdot i + 2 \cdot i + 1 = (i + 1)^2
|
29,419 |
1 = 2^2 - \sqrt{3} \times \sqrt{3}
|
1,527 |
n = k*2 \implies 6*k + (-1) = \left(-1\right) + n*3
|
-21,051 |
\frac{2}{3} \cdot 2/2 = \dfrac{1}{6} \cdot 4
|
-21,299 |
\frac{10^{-1}*10}{10} = \dfrac{10}{100}
|
12,224 |
(k \cdot x \cdot l)^2 = (x \cdot k \cdot l)^2
|
-20,889 |
\frac{1}{-2\cdot j + 20}\cdot (4 - 10\cdot j) = \dfrac{-5\cdot j + 2}{10 - j}\cdot 2/2
|
13,064 |
\frac{\partial}{\partial x} (h\cdot g) = h\cdot \frac{dg}{dx} + \frac{dh}{dx}\cdot g
|
25,555 |
z^2 + y\cdot 4\cdot z + 9\cdot y^2 = y^2\cdot 5 + (2\cdot y + z)^2
|
41,381 |
1*23 + 4\left(-1\right) + 5 + 6(-1) + 7(-1) = 11
|
4,344 |
z + y = 0 \implies z = -y
|
-20,385 |
7/4 \cdot (-\frac{3}{-3}) = -\frac{21}{-12}
|
-8,453 |
-7 = \frac{35}{-5}
|
22,550 |
((-1) + w)\cdot (1 + w \cdot w + w) = (-1) + w \cdot w \cdot w
|
15,646 |
\frac{1}{y^2 + 4 \left(-1\right)} (2 (-1) + y) = \tfrac{1}{y + 2}
|
-1,498 |
\frac{1}{8} \cdot 5 \cdot 9/7 = \frac{\frac{9}{7}}{8 \cdot 1/5} \cdot 1
|
25,333 |
\frac{1}{y} = \frac{1}{y} \cdot 0 = 0 = 0^y = (0 + 0)^y = (1 + 1)^y = 2^y
|
17,980 |
\cos{x} = \cos(-x + 2\times \pi)
|
29,414 |
5^g\cdot 5^h = 5^{g + h}
|
6,661 |
v*w*6 = w*3*2*v
|
27,654 |
\frac{1}{6} + 1/6 + \frac16 = \frac{1}{2}
|
-4,411 |
\dfrac{5 + y \cdot 3}{y^2 + y + 12 \cdot (-1)} = \frac{1}{3 \cdot \left(-1\right) + y} \cdot 2 + \frac{1}{y + 4}
|
23,441 |
1 + x + x \times x + \ldots + x^n = \frac{1}{-x + 1}\times \left(1 - x^{1 + n}\right)
|
31,153 |
-k^2*y^2 + x^2 = 1 \Rightarrow 1 = (x - k*y)*(y*k + x)
|
-25,807 |
2/42 = \frac{1\cdot 2}{6\cdot 7}
|
19,949 |
\left(s + 1/2\right) * \left(s + 1/2\right) + 3/4 = s^2 + s + 1
|
29,758 |
2 \cdot 5 + 3 \cdot \left(3 \cdot (-1) + k\right) = k \cdot 3 + 1
|
-6,695 |
50/100 + 3/100 = \frac{1}{10}\cdot 5 + 3/100
|
2,796 |
A + D_2 + D_1 = A + D_2 + D_1
|
-22,943 |
\frac{75}{120} = \frac{5 \cdot 15}{15 \cdot 8}
|
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