id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-11,524 |
-9 + 10 + 21 i = 1 + i*21
|
-13,536 |
7 + 7*3 = 7 + 21 = 7 + 21 = 28
|
35,250 |
\sin^2\left(x\right) = \sin^2\left(x\right)
|
-13,652 |
5 + \tfrac{1}{8}32 = 5 + 4 = 9
|
7,032 |
-\frac{1}{13^{1/2}}*5*k + 13^{1/2}*k = \frac{8*k}{13^{1/2}}
|
-5,689 |
\dfrac{y*2}{(1 + y)*(6*\left(-1\right) + y)} = \frac{2*y}{6*(-1) + y * y - y*5}
|
-2,911 |
-(4 \cdot 13)^{1/2} + (16 \cdot 13)^{1/2} = -52^{1/2} + 208^{1/2}
|
32,506 |
\left(B^t\right)^t = B = \frac{1}{B^t}
|
-21,908 |
-\frac95 + \frac{9}{3} = -\dfrac{27}{5 \cdot 3} \cdot 1 + \frac{9 \cdot 5}{3 \cdot 5} = -\frac{27}{15} + 45/15 = -\frac{1}{15} \cdot \left(27 + 45\right) = \frac{18}{15}
|
3,653 |
n + 6\cdot n^2 = n\cdot (1 + n\cdot 6)
|
33,861 |
x^{\left(k + (-1)\right) \cdot 2} = x^{2 \cdot k + 2 \cdot \left(-1\right)}
|
6,044 |
\frac{y}{y + 2} = \frac{1}{y + 2}\cdot (y + 2 + 2\cdot (-1)) = 1 - \frac{2}{y + 2}
|
2,378 |
4 \cdot l_2 \cdot l_2 = l_1^2 \cdot 4 + 100 \cdot l_1 + 76\Longrightarrow (2 \cdot l_2) \cdot (2 \cdot l_2) = (2 \cdot l_1)^2 + 2 \cdot l_1 \cdot 2 \cdot 25 + 625 + 76 + 625 \cdot (-1)
|
22,931 |
2\cdot z \cdot z + z\cdot 6 + 3 = (\frac{5}{2} + z)\cdot (2\cdot z + 1) + \dfrac12
|
-19,472 |
\frac{1}{5\cdot \frac12}\cdot \dfrac{7}{4} = \dfrac74\cdot \tfrac15\cdot 2
|
33,285 |
\dfrac25 = \dfrac25
|
-19,305 |
\frac{5 / 4}{1/5 \cdot 3} \cdot 1 = \dfrac{5}{3} \cdot \frac14 \cdot 5
|
4,041 |
\sqrt{-x^2 + 1} = \dfrac{(-1) \cdot x}{\sqrt{1 - x^2}}
|
23,902 |
\frac{1}{5} + \frac13 + 1/4 = \frac{1}{60}47
|
-20,160 |
\frac{24}{-12\cdot y + 36\cdot (-1)} = \frac{6}{-3\cdot y + 9\cdot \left(-1\right)}\cdot \frac44
|
17,457 |
\frac{9}{64} = \frac{1}{4} \cdot \frac{9}{4}/4
|
23,834 |
100\cdot x^2 = 16\cdot (16 + x^2) \Rightarrow 84\cdot x^2 = 256
|
15,657 |
z z - z*2 + 1 = 1 + z z - z - z
|
10,985 |
\cos{\pi*2}*3 = 3
|
29,045 |
\frac{1}{z^6} = (\tfrac{1}{z})^6
|
4,792 |
\frac{m}{m + u} + (-1) = \dfrac{u*(-1)}{u + m}
|
21,443 |
k = \left\{2, 1, k, \ldots\right\}
|
12,401 |
\frac{1}{n \cdot n + n} = 1/n - \frac{1}{n + 1}
|
-6,480 |
\dfrac{3*x}{x * x + x*13 + 40} = \dfrac{x*3}{\left(5 + x\right)*(x + 8)}
|
10,968 |
f^K\cdot f^x = f^{x + K}
|
3,638 |
9\cdot \sqrt{10 + (-1)} = 27
|
918 |
\frac{\frac{1}{2^l} \cdot l}{-\dfrac{1}{2^l} + 1} = \frac{l}{2^l + (-1)}
|
27,057 |
\frac{2}{e^{\left(-1\right) (\left(-2\right)*1.0*10^{-10})*1000}} = 2*0.999999 = 1.99999
|
13,945 |
b^x = \left(\dfrac{1}{b}\right)^{-x} = \left(\tfrac1b\right)^{-x}
|
27,994 |
\mathbb{E}(X^4) = \mathbb{E}(X^3)*\mathbb{E}(X)
|
38,939 |
x^{A + 1} = x*x^A
|
26,832 |
(2^5 + \left(-1\right)) \cdot \frac{(-1) + 2^{15}}{(2^5 + \left(-1\right)) \cdot (2^3 + (-1))} \cdot ((-1) + 2^2 \cdot 2) = \left(-1\right) + 2^{15}
|
28,476 |
\binom{6+3-1}{3-1}=\binom{8}{2}=\frac{8\cdot7}{2\cdot 1}=28
|
50,022 |
60 = 17*3 + 9
|
35,625 |
6 (-1) + x^3 - x = 0 \implies x = 2
|
12,611 |
{k \choose x}^2 = {k \choose x} {k \choose -x + k}
|
-6,348 |
\frac{3}{12 \cdot (-1) + 2 \cdot t} = \frac{1}{2 \cdot \left(t + 6 \cdot (-1)\right)} \cdot 3
|
17,374 |
\frac{1}{\arctan{x}}\cdot x = (1 - x^2/3 + \frac{x^4}{5} - x^6/7 + \dotsm)^{-1}
|
-5,530 |
\frac{3}{3*x + 30*(-1)} = \frac{1}{3*(x + 10*\left(-1\right))}*3
|
-7,839 |
\frac{-1 + i \times 32}{-5 \times i + 4} = \frac{-1 + 32 \times i}{4 - i \times 5} \times \frac{4 + 5 \times i}{i \times 5 + 4}
|
7,896 |
61 = 7^2 + 3 * 3 + 1^2 + 1^2 + 1^2 = 5^2 + 5 * 5 + 3^2 + 1^2 + 1^2
|
20,103 |
2^m = 2^{\left(-1\right) + m}*x^m \Rightarrow 2 = x^m
|
-10,395 |
\tfrac{20}{20} \cdot \frac{5}{2 \cdot (-1) + q \cdot 3} = \dfrac{100}{q \cdot 60 + 40 \cdot (-1)}
|
1,120 |
(E_2 \cdot E_1 - E_1 \cdot E_2) \cdot E_1 = -E_2 \cdot E_1^2 + E_1 \cdot E_2 \cdot E_1
|
50,692 |
u_1 = -u_1
|
33,914 |
-1 = 239 239 - 2*13^4
|
-10,340 |
\frac{180}{180*x + 120} = \frac{20}{20}*\frac{9}{9*x + 6}
|
20,092 |
(x + (-1))^2 = (x + \left(-1\right))*(x + (-1)) = x*(x + (-1)) - x \pm 1
|
27,612 |
-i = 1 \Rightarrow 1 \times 1 = (-i)^2 = -1
|
3,574 |
det\left(I + A\cdot B\right) = det\left(I + A\cdot B\right)
|
11,603 |
2\cdot (-z\cdot 2 - 2\cdot y) = 3\cdot y - z\cdot 7 + z\cdot 3 - 7\cdot y
|
-1,453 |
-\dfrac{14}{20} = (\left(-14\right)*1/2)/(20*1/2) = -\dfrac{1}{10}*7
|
-20,216 |
\dfrac{1}{-y \cdot 45 + 72 \cdot (-1)} \cdot (56 + y \cdot 35) = -\frac19 \cdot 7 \cdot \dfrac{8 \cdot (-1) - 5 \cdot y}{8 \cdot (-1) - 5 \cdot y}
|
12,370 |
\left(z + 2\cdot \tau\right)^2 = 4\cdot (z\cdot \tau)^2 - 24\cdot z\cdot \tau + 49 = 4\cdot z\cdot \tau\cdot (z\cdot \tau + 6\cdot \left(-1\right)) + 49
|
4,979 |
\sin(\pi/2 + x) = \sin(\frac{\pi}{2} - -x) = \cos(-x) = \cos(x)
|
37,295 |
2^{\tfrac12} = 2^{\frac{1}{2}}
|
33,084 |
\sin^2{\frac{4*\pi}{7}} - \sin^2{\frac{2*\pi}{7}} = 2*\sin{\pi/7}*\cos{\frac{3*\pi}{7}} \gt 0
|
-12,111 |
8/15 = \dfrac{x}{12 \cdot \pi} \cdot 12 \cdot \pi = x
|
26,929 |
1 + z = \frac{(-1) + z^2}{(-1) + z}
|
28,782 |
(1 + y * y - y)*(1 + y) = 1 + y^3
|
22,039 |
\left(h^2 + h\cdot f + f^2\right)\cdot (-f + h) = -f^3 + h^3
|
29,289 |
F^1 = \dfrac1F
|
-20,878 |
\frac{-70 \cdot x + 21 \cdot \left(-1\right)}{7 \cdot \left(-1\right) + 7 \cdot x} = \frac{1}{x + (-1)} \cdot (-10 \cdot x + 3 \cdot \left(-1\right)) \cdot \frac77
|
9,409 |
\left(a_2 \cdot a_1\right)^6 = a_1^2 \cdot a_1^2 \cdot a_1^2 \cdot (a_2^3)^2
|
-26,648 |
100 \cdot (-1) + Z^8 \cdot 81 = \left(9 \cdot Z^4\right)^2 - 10^2
|
2,684 |
3/28 = \frac174 \cdot 0 + 3 \cdot 1/7/4
|
30,928 |
e^{\ln\left(D\right)} = D
|
8,533 |
\left(x + 1\right) \cdot \left(x + 2\right) = x \cdot x + 3 \cdot x + 2 \gt 2 \cdot x
|
17,926 |
x = -k \cdot k \cdot k + \dfrac{r}{3 \cdot k} \Rightarrow 0 = k^6 + k \cdot k^2 \cdot x - \dfrac{r^3}{27}
|
-24,658 |
2/18 = \dfrac{2}{2 \times 9}
|
26,253 |
-\frac{1}{7} \cdot 2 = -2/7
|
32,226 |
|49\cdot (-1) + x \cdot x| = |x + 7\cdot (-1)|\cdot |x + 7|
|
-27,759 |
\frac{\text{d}}{\text{d}y} (2 \tan(y)) = 2 \frac{\text{d}}{\text{d}y} \tan(y) = 2 \sec^2\left(y\right)
|
13,619 |
-\sin(x) \sin\left(z\right) + \cos(x) \cos(z) = \cos(x + z)
|
-7,936 |
(100 - 105 \cdot i - 40 \cdot i + 42 \cdot \left(-1\right))/29 = \frac{1}{29} \cdot \left(58 - 145 \cdot i\right) = 2 - 5 \cdot i
|
-504 |
(e^{\frac{13}{12}\cdot \pi\cdot i})^{16} = e^{16\cdot i\cdot \pi\cdot 13/12}
|
-13,782 |
2 + 5 \times 6 = 2 + 30 = 32
|
-17,403 |
1.173 = 117.3/100
|
21,235 |
100! = 97 \cdot 95! \cdot 96 \cdot 98 \cdot 99 \cdot 100
|
22,870 |
((\tfrac54)^n + (-1)) \cdot 4^n = 5^n - 4^n
|
30,013 |
(z + 1)\cdot (z + 3\cdot (-1)) = z^2 - 2\cdot z + 3\cdot \left(-1\right)
|
19,238 |
(-b + h) \cdot (h + b) = h^2 - b^2
|
7,212 |
e^{|-z + x| + 1} = e^1 e^{|x - z|}
|
22,043 |
\frac{1}{4} 3 = \frac14 3
|
28,727 |
2\cdot (2\cdot (-1) + 2^{n + 1}) = 2^{2 + n} + 4\cdot (-1)
|
2,115 |
z/\vartheta = \frac{z}{\vartheta}
|
3,189 |
\left(k + 1\right)! = (k + 1) \cdot k! > (k + 1) \cdot 2^k
|
13,278 |
0 = y'' + 2 + 4\cdot (-1)\Longrightarrow y'' = 2
|
4,649 |
x*g_i = g_i*x
|
13,744 |
\frac{\frac{1}{(1 - x)^2}}{1 - x}\cdot 1 = \frac{1}{(1 - x)^3}
|
4,886 |
-x^2 + (x + k)^2 = k \cdot (k + x \cdot 2)
|
1,556 |
{x \choose r} = \frac{x!}{r! \cdot (x - r)!}
|
-7,710 |
(8 - 4 i - 16 i + 8 (-1))/20 = (0 - 20 i)/20 = -i
|
6,649 |
y^2 \cdot 9 + x^2 - 6 \cdot x \cdot y = 16\Longrightarrow 16 = (-3 \cdot y + x)^2
|
34,868 |
2 = \frac{1}{4} \cdot 4 + 7/7
|
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