id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
29,703 |
x = z rightarrow z = x
|
5,675 |
\frac{|x|}{|c|} = |x/c|
|
-6,188 |
\dfrac{2}{2\cdot (2 + t)} = \frac{2}{4 + 2\cdot t}
|
-743 |
e^{\dfrac{\pi}{6} \cdot i \cdot 16} = (e^{\frac{\pi}{6} \cdot i})^{16}
|
-4,052 |
100/40 \cdot m/m = \dfrac{100}{40 \cdot m} \cdot m
|
-7,601 |
\frac{-7 + i \cdot 22}{3 - i \cdot 2} \cdot \frac{3 + 2 \cdot i}{3 + i \cdot 2} = \frac{1}{3 - 2 \cdot i} \cdot \left(i \cdot 22 - 7\right)
|
14,128 |
0 = p^4 + 3 \cdot p^2 - 2 \cdot p + 3 = (p^2 + 1) \cdot (p^2 + 1) + (p + (-1))^2 + 1
|
16,487 |
x^4 + 2x \cdot x \cdot x - x\cdot 2 + (-1) = (x + (-1)) (x + 1)^3
|
-595 |
(e^{\dfrac{i}{12}*\pi})^{13} = e^{\dfrac{\pi*i}{12}*13}
|
37,733 |
\frac{\sin{z \cdot i}}{i \cdot z} \cdot i \cdot i = i \cdot \sin{z \cdot i}/z
|
5,513 |
f^c\cdot f^h = f^{h + c}
|
9,934 |
c \cdot x + c \cdot y = c \cdot \left(x + y\right)
|
2,536 |
E_1 \cup E_2^c = E_1^c \cup E_2^c = E_1 \cup E_2
|
1,045 |
\frac19 \cdot (2^{3^x} \cdot 2^{3^x} \cdot 2^{3^x} + 1) = \frac{1}{9} \cdot (1 + 2^{3^{x + 1}})
|
35,620 |
\left(a = a\cdot 2 \implies a = a + a\right) \implies a = 0
|
-16,967 |
-6 = -6 \times (-2 \times q) - -24 = 12 \times q + 24 = 12 \times q + 24
|
21,428 |
3^n\cdot \sin{\tfrac{a}{3^n}} = \frac{\sin{\frac{1}{3^n}\cdot a}}{\frac{1}{3^n}}
|
32,235 |
f \cdot h \cdot 2 + h \cdot h + f^2 = \left(h + f\right)^2
|
-5,640 |
-\dfrac{1}{2*\left(5 + x\right)*(x + 6*(-1))}*4 + \frac{5}{2*(x + 6*\left(-1\right))*(x + 5)}*(x + 6*(-1)) - \dfrac{(5 + x)*2}{(5 + x)*\left(x + 6*(-1)\right)*2} = \frac{1}{(x + 6*(-1))*(x + 5)*2}*(4*\left(-1\right) + (6*(-1) + x)*5 - (5 + x)*2)
|
4,477 |
\left(x \cdot c/c\right) \cdot \left(x \cdot c/c\right) = \frac{x}{c} \cdot c \cdot \frac{c}{c} \cdot x = x^2 \cdot c/c
|
25,663 |
-b/s = (b*\left(-1\right))/s
|
28,750 |
\operatorname{E}[b]\cdot \operatorname{E}[h] = \operatorname{E}[b\cdot h] = 0\Longrightarrow b\cdot h = 0
|
-20,580 |
\dfrac{1}{x \times 10 + 10 \times (-1)} \times \left(15 \times (-1) + x \times 5\right) = \frac{1}{2 \times (-1) + 2 \times x} \times (x + 3 \times (-1)) \times \frac55
|
36,153 |
144 = \left(a + d\right)^2 = a^2 + d^2 + 2\cdot a\cdot d = 100 + 2\cdot a\cdot d
|
7,839 |
\frac{1 + 0}{1 + 0(-1)} = 1
|
9,610 |
(x + b*i)*(x - b*i) = x^2 - b^2*i^2 = x^2 + b * b
|
11,087 |
b + 2 = 3 \Rightarrow 1 = b
|
19,878 |
\cos(t*2) = \cos^2(t) - \sin^2(t)
|
16,259 |
(4/6)^5 = (\frac{1}{3}\cdot 2)^5
|
29,705 |
\frac{11\cdot 10\cdot 9}{4\cdot 3\cdot 2}8 = 330
|
22,272 |
v_1 \cdot v_2 \cdot \cdots \cdot v_N = v_1 \cdot v_2 \cdot \cdots \cdot v_N
|
3,833 |
x^6 + \left(-1\right) = (x^3 + (-1))\cdot (x^3 + 1) = (x + (-1))\cdot (x + 1)\cdot (x^2 + x + 1)\cdot \left(x^2 - x + 1\right)
|
6,356 |
-s + 1/2 = \frac{1}{(-1/2 + s)^4} \Rightarrow -1 = (s - 1/2)^5
|
25,811 |
-\sin{\frac12\cdot k\cdot \pi} = \sin{\pi\cdot (k + 2)/2}
|
31,704 |
\frac{120}{5} + \left\lfloor{\frac{1}{25}120}\right\rfloor = 24 + 4 = 28 < 30
|
1,333 |
2^8 + (-1) - 2\cdot ((-1) + 2^4) = 1 + 2^8 - 2^5
|
28,702 |
l^2 - \frac{3l}{2} - \dfrac{3l}{2} + 9/4 = l^2 - 6l/2 + 9/4 = l^2 - 3l + \frac94
|
18,693 |
( z, y) + \left( x'' + x', y'' + y'\right) = ( x', y') + ( x'', y'') + ( z, y)
|
33,892 |
\cos(i\cdot x) = \frac12\cdot (e^{-x} + e^x) = \cosh\left(x\right)
|
18,719 |
\sec^2(\dfrac{1}{2} \times y) = \frac{1}{(1 + \cos(y)) \times 1/2} = \frac{1}{1 + \cos(y)} \times 2
|
26,377 |
((z + 1)^2 - z*3)*(z + 1) = 1 + z^3
|
6,338 |
\frac{1}{2\cdot 2} + 1/2 = \frac34
|
4,040 |
((-1) + p)\cdot \left(q + (-1)\right) + (-1) = p\cdot q - p - q
|
11,774 |
(a \times 0)^2 = a \times 0
|
-24,834 |
\frac{2094}{6} = 349
|
-21,642 |
\frac{1}{4}\cdot 3 = \frac34
|
12,592 |
(g_1 + g_2)\cdot F = g_2\cdot F + F\cdot g_1
|
7,368 |
P(y) = (y - a - g \cdot \sqrt{c}) \cdot (y - a + g \cdot \sqrt{c}) = y \cdot y - 2 \cdot a \cdot y + a^2 - g^2 \cdot c
|
14,644 |
\frac{l^2}{l + 1} > \tfrac{l^2 + \left(-1\right)}{l + 1} = \frac{1}{l + 1}\cdot (l + 1)\cdot (l + \left(-1\right)) = l + (-1)
|
1,587 |
1 = 2 - (-\frac{1}{2} + 1)^3 \cdot 2 - (1 - 1/2)^2 \cdot 3
|
17,873 |
\cos{B}*\sin{A} = (\sin(A - B) + \sin(B + A))/2
|
-5,616 |
\frac{1}{\left(y + 5\right) \left(y + 6 \left(-1\right)\right)*2} 4 = 2/2*\dfrac{2}{(6 (-1) + y) (5 + y)}
|
890 |
X/m + \left(-1\right) + (X - \frac{X}{m})\cdot m/X = X/m + m + 2\cdot \left(-1\right)
|
-26,365 |
-\dfrac34\cdot\left(-\dfrac34\right)=\dfrac{9}{16}
|
5,265 |
1 + x + x^2 + x^3 + \ldots + x^n = \dfrac{1 - x^{1 + n}}{-x + 1}
|
-4,493 |
\dfrac{21 \left(-1\right) + 9x}{x^2 - 5x + 4} = \dfrac{4}{x + (-1)} + \frac{5}{x + 4\left(-1\right)}
|
50,093 |
7^{12}=7^6\times7^6
|
32,592 |
\cot\left(z*2\right) = 1 \Rightarrow \tan(z*2) = 1
|
26,424 |
2 + 8 + 24 + 64 + \dotsm + 2^n n = \left(1 + (n + \left(-1\right))*2^n\right)*2
|
-1,650 |
\tfrac{9}{4}\cdot \pi = 11/12\cdot \pi + \pi\cdot 4/3
|
-20,346 |
-\frac{1}{3}*5*\frac{t*4 + 10*(-1)}{10*(-1) + t*4} = \frac{-t*20 + 50}{t*12 + 30*(-1)}
|
30,665 |
2/18 = \dfrac{1}{3*6} + \frac{1}{3*6}
|
4,710 |
\frac{1}{16^{\frac34}\cdot 27^{\frac{2}{3}}} = \frac{1}{(16^3)^{1/4}\cdot (27^2)^{1/3}}
|
23,530 |
h * h - b^2 = (-b + h)*(b + h)
|
2,120 |
y^2 + x^2 = 25 \implies y = \sqrt{-x^2 + 25}
|
-1,596 |
3\times \pi - 2\times \pi = \pi
|
9,596 |
\frac{1}{2 \cdot 2} \cdot 1/2/2 = \frac{1}{16}
|
23,047 |
\frac{1}{221} + \frac{16}{221} = 17/221 = \frac{1}{52}*4
|
26,208 |
\frac{1}{\left(2 \cdot m\right)!} \cdot m = \frac{m}{2 \cdot m \cdot (2 \cdot m + \left(-1\right))!} = \dfrac{1}{2 \cdot (2 \cdot m + (-1))!}
|
9,369 |
\left(2\cdot 10^n + 1\right)/3 = (10^n + (-1))/9\cdot 6 + 1
|
12,596 |
(0 + 1 + 4)*(1 + 1 + 1)*(1 + 0 + 0) = 15
|
-5,138 |
0.82*10^{0 - -2} = 0.82*10^2
|
8,250 |
\tanh\left(T\right) = \tanh\left(z\right) \Rightarrow z = T
|
19,756 |
0 = 0\left( 1, 4, 0\right) + 0( 2, 2, 2)
|
568 |
c_2 \cdot c_1 = ((c_2 + c_1)^2 - c_2^2 - c_1^2)/2
|
33,893 |
C_2 \times C_1 = C_1 \times C_2
|
-19,052 |
7/24 = \frac{1}{81 \times \pi} \times A_s \times 81 \times \pi = A_s
|
29,232 |
\frac{1}{36}\times 6 = \dfrac{1}{6}
|
9,108 |
-y \cdot z + x \cdot z = (x - y) \cdot z
|
6,876 |
(-a + x) * (-a + x) + b^2 = x^2 - 2ax + a^2 + b^2
|
40,575 |
1 = -7\cdot 8 + 3\cdot 19
|
16,600 |
5^x \cdot 6 - 5^x = ((-1) + 6) \cdot 5^x
|
35,387 |
(a + x)^2 = a^2 + x*a + a*x + x * x = a^2 + 2*a*x + x^2
|
-10,553 |
5/5\cdot \frac{1}{a\cdot 3}\cdot 10 = 50/(15\cdot a)
|
31,426 |
(\sqrt{2} + \sqrt{3})^2 = 5 + 2\times \sqrt{6}
|
15,895 |
\phi C = gC \Rightarrow \frac{C}{g} = C/\phi
|
-16,468 |
5\sqrt{4\cdot 5} = 5\sqrt{20}
|
53,338 |
6 = 20 \cdot 0.3
|
23,832 |
1020 = 20\cdot z + x\cdot 50 \Rightarrow x\cdot 5 + 2\cdot z = 102
|
10,289 |
\cos(\frac12 \cdot \pi) + i \cdot \sin(\pi/2) = i
|
21,155 |
\frac{-z * z + 1}{1 - z} = z^1 + z^0
|
11,569 |
g \cdot d = \dfrac{1}{1/g \cdot 1/d} = \frac{1}{\frac{1}{d} \cdot \frac1g} = d \cdot g
|
20,692 |
100\cdot \dfrac{1}{100}/2 = 1/2 = 1/2
|
10,425 |
x \cdot z = \left(-z \cdot z + (x + z)^2 - x^2\right)/2
|
6,836 |
1/(x\cdot \beta) = \frac{1}{\beta\cdot x}
|
3,455 |
z \cdot 0 = 0z + 0
|
7,552 |
\frac{x}{d} \implies x/d
|
14,487 |
\dfrac{1}{(t + (-1))^2} = -\frac{\mathrm{d}}{\mathrm{d}t} \frac{1}{t + (-1)}
|
37,354 |
(-y + x) (x + y) = -y^2 + x^2
|
-10,286 |
20/20\cdot (-\frac{4}{i + 2\cdot \left(-1\right)}) = -\frac{1}{40\cdot (-1) + 20\cdot i}\cdot 80
|
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