id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
20,290 |
1.6^{(-1) + x} = 1.6 \cdot 1.6^{2 \cdot (-1) + x}
|
35,224 |
\sin{r \cdot 2} = \cos{r} \cdot \sin{r} \cdot 2
|
25,085 |
(a + b + c)^3 = a^3 + b^3 + c^3 + \left(c + a + b\right) \cdot (b \cdot a + b \cdot c + c \cdot a) rightarrow a^3 + b^3 + c^3 = 0
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34,796 |
13570 = 430*\left(-1\right) + 14000
|
-6,442 |
\frac{5\cdot g}{g^2 - g\cdot 13 + 36} = \dfrac{5\cdot g}{(g + 4\cdot (-1))\cdot (g + 9\cdot \left(-1\right))}
|
-20,109 |
\frac{1}{6 \cdot (-1) + c} \cdot \left(6 \cdot \left(-1\right) + c\right) \cdot \frac37 = \frac{18 \cdot \left(-1\right) + c \cdot 3}{7 \cdot c + 42 \cdot (-1)}
|
-19,959 |
-\frac14*5 = -1.25
|
19,604 |
\left(x + i\right) \cdot w = i \cdot w + w \cdot x
|
22,032 |
-(\binom{s}{2} + s) + s^2 = (-s + s^2)/2
|
10,945 |
k\cdot b = k = b\cdot k
|
-23,019 |
\frac{3 \cdot 5}{10 \cdot 5} = \dfrac{15}{50}
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23,671 |
1^2 \cdot 2 + 4^2 = 18
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51,893 |
S = \sum_{k=1}^{10} \dfrac{1}{2^k}*k = 2*\sum_{k=1}^{10} \frac{1}{2^{k + 1}}*k = 2*\sum_{k=2}^{11} \frac{1}{2^k}*(k + (-1)) = 2*\sum_{k=1}^{10} \frac{1}{2^k}*(k + (-1)) + \tfrac{10}{2^{10}} = 2*S - \sum_{k=1}^{10} \dfrac{1}{2^{k + (-1)}} + \tfrac{10}{2^{10}}
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33,563 |
|w| = |y| rightarrow w = y
|
39,097 |
(a - c)^2 = -(d - b)^2 rightarrow 0 = \left(a - c\right)^2 + \left(-b + d\right)^2
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-19,016 |
11/12 = Y_p/(36\cdot \pi)\cdot 36\cdot \pi = Y_p
|
16,784 |
(Ix + I')^2 = Ix + I'
|
793 |
(z + 100 (-1))^2 + \left(y + 42 (-1)\right) * \left(y + 42 (-1)\right) = (z + 33 (-1))^2 + (y + 74 \left(-1\right))^2 = (z + 26)^2 + (y + 6(-1))^2
|
968 |
0.1944 = 6*0.3 * 0.3*0.6^2
|
-29,346 |
(3 \cdot y + 7) \cdot (3 \cdot y + 7 \cdot (-1)) = \left(3 \cdot y\right)^2 - 7^2 = 9 \cdot y^2 + 49 \cdot (-1)
|
-20,745 |
\dfrac19\cdot 9\cdot \frac{1}{-8}\cdot (-10\cdot x + 5) = \frac{1}{-72}\cdot (-x\cdot 90 + 45)
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27,612 |
1 = -i\Longrightarrow 1^2 = (-i)^2 = -1
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24,207 |
x_{2l + 1} = \dfrac{1}{1 + l*2} \implies 0 = \lim_{l \to \infty} x_{2l + 1}
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43,214 |
1 + 1 + 1 + (-1) = 2
|
-20,964 |
\frac11\times 9\times \frac{1}{7 + k}\times (k + 7) = \frac{63 + 9\times k}{7 + k}
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-4,612 |
\frac{1}{5(-1) + y \cdot y - y\cdot 4}(5y + 19 (-1)) = \dfrac{1}{5(-1) + y} + \frac{1}{1 + y}4
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17,446 |
i^n = e^{i\cdot π\cdot n/2} = (-1)^{n/2}
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37,577 |
{6 \choose 6} + {6 \choose 5} + {6 \choose 4} + {6 \choose 3} + 8\times (-1) = 34
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35,513 |
3 = 2 + \cos{\pi*2*4}
|
8,243 |
33 = 35 + 2 \left(-1\right)
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-15,801 |
-\frac{6}{10} + 1 = \frac{1}{10}\cdot 4
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12,307 |
2^2*2 + 3^2*(-1) = 8 + 9*(-1) = -1
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55,004 |
\lim_{n \to \infty} 2^n+1 = \lim_{n \to \infty} 2^n(1+\frac{1}{2^n})=\lim_{n \to \infty} 2^n\cdot \lim_{n\to \infty}(1+\frac{1}{2^n})=\lim_{n \to \infty} 2^n \cdot 1= \lim_{n \to \infty}2^n
|
-1,688 |
\dfrac{5}{12}\cdot \pi - \pi\cdot \frac{1}{4}\cdot 5 = -\tfrac{5}{6}\cdot \pi
|
6,862 |
\left(g + c\right) (g - c) = g^2 - c^2
|
-15,855 |
-\frac{2}{10}*9 + 8/10*8 = 46/10
|
10,525 |
-\frac{1}{6}\pi + 2\pi = \frac{11}{6}\pi
|
-22,215 |
(n + 8)*((-1) + n) = n^2 + 7*n + 8*(-1)
|
13,053 |
x^{r + 1} = x^r\cdot x \gt x^r
|
22,676 |
\cos(y^3) + (-1) = 1 + \left(-1\right) - y^6/2 + \cdots = \frac{1}{2} \cdot ((-1) \cdot y^6) + \cdots
|
21,783 |
(1 + z^2 - z) (z^2 + z + 1) \left(z + 1\right) (1 - z) = -z^6 + 1
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-18,336 |
\dfrac{k \cdot k - k \cdot 4 + 5 \cdot \left(-1\right)}{4 + k \cdot k + k \cdot 5} = \frac{1}{\left(k + 1\right) \cdot (k + 4)} \cdot (1 + k) \cdot (k + 5 \cdot (-1))
|
33,336 |
\frac{420 + t*41}{20 (-1) + t^2 - t} = \frac{625}{9 (t + 5 (-1))} - \frac{256}{9 (t + 4)}
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36,471 |
x\times x + x\times y + y\times x + y\times y = x \times x + x\times y + y\times x + y^2 = x + x\times y + y\times x + y
|
14,848 |
16^2 + 2^2 = 8^2 + 14^2
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-2,011 |
5/12 \times \pi - 23/12 \times \pi = -\pi \times 3/2
|
1,516 |
(z + 2)^{\frac{1}{2}} = \left(4 + z + 2\cdot (-1)\right)^{1/2} = 2\cdot (1 + (z + 2\cdot (-1))/4)^{1/2}
|
-20,611 |
\frac{-45 \cdot x + 27}{12 \cdot (-1) + x \cdot 20} = \frac{3 \cdot (-1) + 5 \cdot x}{3 \cdot (-1) + 5 \cdot x} \cdot (-\frac{1}{4} \cdot 9)
|
2,065 |
-\dfrac{1}{\left(1 - \frac1x\right)^2\cdot x^2} = -\frac{1}{x \cdot x\cdot \left(1 - \frac1x\right)^2} = -\frac{1}{(x + (-1)) \cdot (x + (-1))} = -\frac{1}{(x + (-1))^2}
|
16,761 |
\frac{\partial}{\partial z} (-r + z) = -r + \frac{dz}{dz}
|
6,397 |
\dfrac{1}{x_j} \cdot (I + J) = \frac{I}{x_j} + \frac{J}{x_j}
|
21,779 |
(1+\omega^2)^4=1+(\omega^4)^2=1+(\omega+1)^2=(1+\omega^2)+1
|
15,067 |
\sqrt{163} = \dfrac{12767}{\left(1 - \frac{1}{163 \cdot 10^6}3711\right)^{1/2}}\frac{1}{1000}
|
5,530 |
1 + x = \frac{1}{x + \left(-1\right)} \cdot ((-1) + x) \cdot (1 + x)
|
13,026 |
U*L = L*U
|
-10,415 |
2/2*\left(-7/x\right) = -14/(2*x)
|
-11,696 |
1/5 * 1/5 = 1/25
|
-22,036 |
\dfrac{4}{8}=\dfrac{1}{2}
|
9,084 |
E(U_i \cdot U_k) = \mathbb{Cov}(U_i,U_k) + E(U_i) \cdot E(U_k) = \mathbb{Cov}(U_i,U_k)
|
24,201 |
2 \times 2^n = 2^{n + 1}
|
7,766 |
\left(1 + 2\sqrt{3} = z \Rightarrow 12 = (z + \left(-1\right)) \cdot (z + \left(-1\right))\right) \Rightarrow z^2 - z \cdot 2 + 11 \left(-1\right) = 0
|
4,661 |
(1 + 2 + 3 + 4)/4 = \dfrac{1}{4} \cdot 10 = 5/2
|
14,686 |
( |a|, |d|) = 1 \implies 1 = \left(a, d\right)
|
-1,863 |
\frac{1}{12}\cdot 11\cdot \pi - \pi\cdot 0 = \pi\cdot 11/12
|
-20,119 |
\dfrac13\cdot 10\cdot \dfrac{1}{m + 2}\cdot (2 + m) = \frac{20 + m\cdot 10}{3\cdot m + 6}
|
4,830 |
b^2 \cdot k + \left(k + a\right) \cdot b + a = \left(b \cdot k + a\right) \cdot (b + 1)
|
7,075 |
3*17/(4*17) = 51/68
|
3,603 |
\sin\left(x\right) = \cos(-x + \frac{1}{2} \cdot π)
|
6,308 |
14 + 3 \cdot z^2 - 13 \cdot z = 0 \Rightarrow 0 = \left(7 \cdot (-1) + 3 \cdot z\right) \cdot (2 \cdot (-1) + z)
|
-9,358 |
-3\cdot 3 - 2\cdot 3\cdot 5\cdot t = 9\cdot (-1) - 30\cdot t
|
-20,466 |
-\frac149 \frac{10 + t}{t + 10} = \dfrac{1}{40 + 4t}(90 (-1) - t*9)
|
17,266 |
d \cdot b/f = b \cdot d/f
|
10,785 |
(n + 62)^2 - (34 + n) \cdot 113 = 2 + n^2 + n \cdot 11
|
9,460 |
\arccos(\cos(\pi - \arccos{t})) = \arccos{-t} \implies \pi - \arccos{t} = \arccos{-t}
|
9,658 |
(y + (-1)) (1 + y^6 + y^5 + y^4 + y^3 + y^2 + y) = y^7 + (-1)
|
20,220 |
x^2 - z z = (z + x) (x - z)
|
4,061 |
573 = 3\cdot 191
|
-28,971 |
14 + 12\cdot (-1) = 2
|
8,026 |
-\frac54 + (1/2 + q)^2 = q^2 + q + (-1)
|
20,062 |
\frac2x*1/2 = \frac{1}{x}
|
-4,183 |
\dfrac{x^4}{x^4} \cdot \tfrac{1}{8} \cdot 2 = \frac{2 \cdot x^4}{8 \cdot x^4} \cdot 1
|
7,578 |
13 + 2 \cdot 2 = 17
|
912 |
(\left(i\cdot 2 + 1\right)\cdot (-6))/(-2) = 3\cdot (2\cdot i + 1)
|
12,834 |
z^2 + (-1) = (z + (-1)) \cdot \left(1 + z\right)
|
-2,051 |
5/12*\pi + \dfrac{5}{6}*\pi = 5/4*\pi
|
28,534 |
p^n\cdot e^{x\cdot p} = \frac{1}{e^{-p\cdot x}}\cdot p^n
|
35,931 |
180 = 2^2*3^2*5
|
8,949 |
1 + \sqrt{-2} \cdot 2 = (-\sqrt{-2} + 1) \cdot \left(\sqrt{-2} - 1\right)
|
-20,019 |
8/8 \cdot \frac{1}{9 + 7 \cdot p} \cdot (10 \cdot \left(-1\right) + p) = \frac{1}{p \cdot 56 + 72} \cdot \left(p \cdot 8 + 80 \cdot (-1)\right)
|
24,628 |
(a + \nu) \cdot (\nu - a) = \nu \cdot \nu - a^2
|
-10,950 |
\frac{195}{13} = 15
|
2,357 |
640320^3 = \left(2^6 \cdot 3 \cdot 5 \cdot 23 \cdot 29\right)^3
|
17,618 |
(x + 1)^{2 \cdot n} = (1 + x)^n \cdot \left(x + 1\right)^n
|
-7,605 |
\left(-14 + 5 i - 56 i + 20 \left(-1\right)\right)/17 = \frac{1}{17} \left(-34 - 51 i\right) = -2 - 3 i
|
-26,673 |
(x\cdot 2 + 5\cdot (-1))\cdot (1 + x\cdot 4) = x^2\cdot 8 - 18\cdot x + 5\cdot (-1)
|
-7,684 |
\frac{1}{25}*(-60 + 30*i - 80*i + 40*(-1)) = \frac{1}{25}*(-100 - 50*i) = -4 - 2*i
|
-20,558 |
\frac13 \cdot 3 \cdot \frac{1}{2 \cdot (-1) + j} \cdot \left(-3 \cdot j + 3 \cdot \left(-1\right)\right) = \frac{1}{6 \cdot (-1) + 3 \cdot j} \cdot (-j \cdot 9 + 9 \cdot \left(-1\right))
|
17,023 |
0 = (y^3 + (-1))*(y^6 + y^3 + 1) = y^9 + (-1)
|
2,440 |
\|e\|_1 = 0 \implies 0 = e
|
13,429 |
0 = x*2^{1/2} + q*5^{1/2} + r*10^{1/2} + t = t + x*2^{1/2} + (q + r*2^{1/2})*5^{1/2}
|
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