id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
30,415 |
\sin(x + y) = \sin{y}\cdot \cos{x} + \sin{x}\cdot \cos{y}
|
21,576 |
a*b = \frac12*(a*b + b*a) = b*a
|
30,119 |
\left(z + x\right) (x - z) = -z^2 + x * x
|
29,679 |
\frac12 + \frac{\sqrt{7} j}{2} 1 = (\sqrt{-7} + 1)/2
|
21,600 |
(a + x)^\psi = (a + x)\cdot (a + x)^{\psi + (-1)}
|
-20,198 |
-\frac{50}{70} = 10/10\cdot (-\dfrac17\cdot 5)
|
7,428 |
\frac{1}{1^4\cdot 4!}4! = 1
|
19,046 |
\frac{1}{3 + 2}*3*\frac{1}{3 + 2}*3 = 9/25 = 0.36
|
883 |
3 \cdot 2^{(-1) + k} - 2^{k + (-1)} + 3 + 2 (-1) = 1 + 2 \cdot 2^{k + (-1)}
|
11,187 |
8(-1) + 210 + (-1) + 2(-1) + 3(-1) + 4\left(-1\right) = 192
|
11,175 |
w = \frac{y + 3(-1)}{4(-1) + y}\Longrightarrow y = \frac{1}{w + \left(-1\right)}(3(-1) + w \cdot 4)
|
-20,773 |
\dfrac{1}{r\cdot 3 + 15}\cdot \left(40\cdot (-1) - 8\cdot r\right) = -8/3\cdot \dfrac{r + 5}{r + 5}
|
2,482 |
(y + 2*(-1))^2 = (2*(-1) + y)*(y + 2*(-1))
|
34,033 |
g \cdot g \cdot d = d = g \cdot g \cdot d
|
-10,595 |
\frac22 \cdot \frac{4}{4x + 2(-1)} = \dfrac{8}{x \cdot 8 + 4(-1)}
|
1,163 |
\frac{1}{l^l} \cdot 2^l \cdot l! = \frac{1}{l^l} \cdot 96 \cdot l \cdot \dots
|
-3,048 |
6 \cdot 11^{1 / 2} = (5 + 1) \cdot 11^{1 / 2}
|
8,493 |
(i\cdot \delta + l\cdot e)\cdot g = g\cdot \delta\cdot i + l\cdot e\cdot g
|
15,188 |
z^3 \cdot 4 - z \cdot 3 = -\dfrac12 \implies 1 + z^3 \cdot 8 - 6 \cdot z = 0
|
16,202 |
\sin{5 \cdot y} = \sin\left(4 \cdot y + y\right) = \sin{4 \cdot y} \cdot \cos{y} + \cos{4 \cdot y} \cdot \sin{y}
|
-20,070 |
-\frac13*\frac{1}{y*(-8)}*(y*(-8)) = 8*y/((-24)*y)
|
4,275 |
z^4 + \left(-1\right) = (z^2 + (-1))\cdot \left(z \cdot z + 1\right) = (z + (-1))\cdot (z + 1)\cdot (z^2 + 1)
|
1,638 |
(x^9 \cdot x^3)^2 = x^{24}
|
-24,896 |
5*4*3 = \frac{5!}{(5 + 3\left(-1\right))!} = 60
|
18,228 |
\sin(\tan^{-1}{x}) = \dfrac{x}{\sqrt{1 + x^2}}
|
52,274 |
43 = 7 + 9\cdot 4
|
12,224 |
(m \cdot k \cdot x)^2 = \left(m \cdot k \cdot x\right)^2
|
-6,344 |
\dfrac{2}{(8 + r) \times (r + 6)} \times \frac22 = \frac{1}{2 \times (6 + r) \times (8 + r)} \times 4
|
22,930 |
0 = \cos\left(x\right) + \sin(x)*\tan(x)\Longrightarrow (\sin^2(x) + \cos^2(x))/\cos(x) = 0
|
-18,954 |
3/4 = \frac{H_q}{4 \cdot \pi} \cdot 4 \cdot \pi = H_q
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-22,235 |
(k + 9) (6 + k) = k^2 + k*15 + 54
|
21,760 |
1/\tan(z) = \tan\left(-z + \pi/2\right)
|
7,057 |
z^{f + c} = z^f z^c
|
-24,699 |
2\cdot (8\cdot b \cdot b \cdot b)^{1 / 2}\cdot 9\cdot (18\cdot b)^{\dfrac{1}{2}} = 2\cdot 9\cdot \left(8\cdot b^3\right)^{1 / 2}\cdot \left(18\cdot b\right)^{\frac{1}{2}} = 18\cdot \left(144\cdot b^4\right)^{\dfrac{1}{2}}
|
13,073 |
x_k = YZ \Rightarrow YZ = x_k
|
16,666 |
-y = x^2 - 2\cdot x + 7\cdot (-1) = (x + (-1))^2 + 8\cdot (-1) rightarrow (x + (-1))^2 = -(y + 8\cdot (-1))
|
26,332 |
(1 + 1) (1 + 2) = 6
|
9,011 |
d/dx \operatorname{asin}(x) = 1/\cos(\operatorname{asin}\left(x\right))
|
17,319 |
2 = 2 \cdot \cos{0}
|
-1,714 |
-\pi\cdot 5/12 + 5/4 \pi = \pi\cdot 5/6
|
23,877 |
\sin\left(y\right) = \sin(\dfrac{y}{2} + \frac{y}{2}) = 2 \cdot \sin\left(\frac{y}{2}\right) \cdot \cos\left(\dfrac{y}{2}\right)
|
7,040 |
\dfrac{1}{18} = 17/18 \cdot \frac{\dfrac{16}{17}}{16} \cdot 1
|
10,656 |
(1 + 2 \cdot k)^2 = 2 \cdot (2 \cdot k + 2 \cdot k \cdot k) + 1
|
34,443 |
-4\cdot c^2 + h^2 = (h + c\cdot 2)\cdot (h - 2\cdot c)
|
-20,429 |
\frac{1}{9\cdot (-1) + q}\cdot (36 - 4\cdot q) = -\frac41\cdot \frac{1}{9\cdot (-1) + q}\cdot (q + 9\cdot (-1))
|
4,296 |
(n + 1)^2 = n^2 + 1 + 2 n > n + 1 + 1 + 2 n = 3 n + 2 > n + 2
|
46,287 |
(-1)^2 = 1 * 1
|
12,856 |
\left(\beta + \gamma\right) \cdot \alpha = \alpha \cdot \beta + \gamma \cdot \alpha
|
22,762 |
(6^{1/2} + 2^{1/2})^2 = 8 + 3^{1/2}\cdot 4
|
-27,436 |
14= {2}\times{7}
|
29,879 |
26/52\cdot 4/25 = 104/1300
|
38,815 |
\left(x \cdot x\right)^2 = x^4
|
-9,289 |
10\cdot z + 14 = 2\cdot 5\cdot z + 2\cdot 7
|
33,686 |
60 * 60^2 = 3^2*2*5*5 * 5*2*2^4*3
|
35,144 |
\arcsin\left(x\right) = \arcsin\left(x\right)
|
1,073 |
\int (z + (-1)) \times \left(3 \times z + 1\right)\,dz = \int \left(3 \times z^2 - 2 \times z + 1\right)\,dz = z^3 - z^2 + z
|
42,759 |
360 = 5*\binom{4}{2}*4*3
|
28,286 |
n^{1/n} \lt (1 + n^{-1/2})^2 = 1 + \tfrac{1}{n^{1/2}}\cdot 2 + \frac{1}{n} \lt 1 + \frac{3}{n^{1/2}}
|
6,441 |
3\tan^2(x) = 3\sec^2(x) - 3
|
7,703 |
1 + kz + z = 1 + \left(k + 1\right) z \leq (1 + z)^k + z
|
35,562 |
-((-1) + 3) + 5 = 3
|
3,298 |
\left(((\left(7^2\right)^2*7)^2 * (\left(7^2\right)^2*7)^2*7)^2 * ((\left(7^2\right)^2*7)^2 * (\left(7^2\right)^2*7)^2*7)^2*7\right)^2 * \left(((\left(7^2\right)^2*7)^2 * (\left(7^2\right)^2*7)^2*7)^2 * ((\left(7^2\right)^2*7)^2 * (\left(7^2\right)^2*7)^2*7)^2*7\right)^2 = 7^{340}
|
23,091 |
\left(k^3 - k \cdot k + k \cdot k - k + 1\right) \cdot \left(k^2 + k + 1\right) = (1 + k^2 + k) \cdot (k^2 \cdot k - k + 1)
|
18,285 |
1 - \cos\left(u\right) = 2*\sin^2\left(u/2\right) \leq u^2/2
|
38,435 |
124^{1/2} = (2^2\cdot 31)^{1/2} = (2^2)^{1/2}\cdot 31^{1/2} = 2\cdot 31^{1/2}
|
19,362 |
\dfrac13 11! = 11!\cdot 2/6
|
19,236 |
\frac{1 - x^2}{1 + x^2} = \frac{1}{1 + x^2} \cdot (2 - 1 + x \cdot x) = \frac{1}{1 + x^2} \cdot 2 + \left(-1\right)
|
-4,294 |
1/\left(9*y\right) = \frac{1}{9*y}
|
950 |
11 - 4 \cdot k = 3 rightarrow 2 = k
|
4,591 |
15\cdot x = 5\cdot x\cdot 3
|
10,115 |
4 \cdot \left(16 + (-1)\right) = 60
|
-2,752 |
7 \cdot \sqrt{7} = \sqrt{7} \cdot \left(4 + 5 + 2 \cdot (-1)\right)
|
1,231 |
8/45 = \frac{8}{3} \cdot \frac{1}{15}
|
-15,517 |
\dfrac{{r^{-5}a^{-5}}}{{r^{25}a^{5}}} = \dfrac{{r^{-5}}}{{r^{25}}} \cdot \dfrac{{a^{-5}}}{{a^{5}}} = r^{{-5} - {25}} \cdot a^{{-5} - {5}} = r^{-30}a^{-10}
|
-6,706 |
\frac{1}{100} + \frac{8}{10} = 80/100 + 1/100
|
-2,141 |
2/3 \pi + \frac{\pi}{3} = \pi
|
15,004 |
((-1) + 1 + f)^3 = f^3
|
12,374 |
\cos(g + a) = \cos(a)\times \cos(g) - \sin\left(a\right)\times \sin(g)
|
506 |
\frac{1}{a \cdot A} = \frac{1}{a \cdot A} \Rightarrow A \cdot a = A \cdot a
|
10,193 |
a^3 = a\times a^2 = a = a
|
8,595 |
(Y_2 + Y_1)^2 = Y_2^2 + Y_2*Y_1 + Y_1*Y_2 + Y_1^2 = Y_2*Y_1 + Y_1*Y_2 = 2*Y_2*Y_1
|
24,670 |
\dfrac{1}{r^7 - r} = \frac{7\cdot r^6}{r^7 - r}\cdot 1 - \tfrac{\left(-1\right) + r^6\cdot 7}{r^7 - r}
|
-1,170 |
-8/3*(-\dfrac{1}{9}*8) = ((-1)*8*\frac{1}{3})/(1/8*(-9))
|
3,852 |
1 + 5\cdot k^4 + k^3\cdot 10 + 10\cdot k^2 + 5\cdot k = (1 + k)^5 - k^5
|
43,953 |
1 + 2436*5 = 937*13
|
687 |
3^2 + 2 \cdot 2 + 2\cdot 2\cdot 3 = \left(2 + 3\right)^2
|
-20,495 |
\dfrac{-9}{10n + 4} \times \dfrac{7}{7} = \dfrac{-63}{70n + 28}
|
11,689 |
2^{l + 1} \cdot ... = 2 \cdot 2^l
|
-20,060 |
\frac{1}{-x \cdot 18 + 6 \cdot (-1)} \cdot \left(x \cdot 30 + 10\right) = -\frac{5}{3} \cdot \frac{-6 \cdot x + 2 \cdot (-1)}{-x \cdot 6 + 2 \cdot \left(-1\right)}
|
9,109 |
\delta^2 - z^2 = (\delta - z)\cdot (\delta^{1 + 0\cdot \left(-1\right)}\cdot z^0 + \delta^{1 + (-1)}\cdot z^1) = \left(\delta - z\right)\cdot \left(\delta + z\right)
|
13,117 |
48 = (2 + 1)\cdot (1 + 7)\cdot (1 + 1)
|
-6,012 |
\frac{3}{(5*(-1) + a)*3} = \dfrac{1}{3*a + 15*(-1)}*3
|
5,418 |
d/dx (x*\ln(x)) = \ln(x) + 1
|
7,961 |
\left( 1, 0\right) - ( 1, 1) + ( 0, 1) = \left( 1 + (-1), -1 + 1\right) = \left\{0\right\}
|
5,694 |
3 + \sqrt{3 + \sqrt{3 + \ldots}} = X \Rightarrow X = (3\cdot (-1) + X)^2
|
14,221 |
\dfrac{1}{2*\sqrt{2} + 3} = 3 - \sqrt{2}*2
|
16,073 |
\left(17*x = 16 + x^2 \Rightarrow (x + (-1))*(x + 16*(-1)) = 0\right) \Rightarrow x = 16
|
6,782 |
10^{-k - p} = 10^{-(p + k)}
|
-29,575 |
3*y = \frac{y^2*3}{y}
|
21,513 |
2*27 = 90 + 36*(-1)
|
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