id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
31,548 |
\dfrac{1}{23 - -7}\times 10 = \dfrac{1}{30}\times 10 = 1/3
|
3,388 |
Y_2 + Y_1 = Y_1 + x = 0, 1 = x + Y_2 \Rightarrow -Y_1 = x = Y_2 = \frac{1}{2}
|
29,600 |
\frac14\left(15 + 2 + 5 + 10\right) = 8
|
-27,438 |
c^2*(25 + c^2 - 10 c) = c^4 - c^3*10 + c^2*25
|
-7,535 |
(-35 - 95\times i - 28\times i + 76)/41 = \frac{1}{41}\times (41 - 123\times i) = 1 - 3\times i
|
44,085 |
6344 = 2^3 + 8^3 + 12^3 + 16 \cdot 16^2
|
9,310 |
2 = -(2 - 6^{1/2})\times \left(2 + 6^{1/2}\right)
|
10,847 |
\frac{1}{16} + 1/9 = 9/144 + \frac{1}{144} 16 = \frac{25}{144}
|
7,592 |
800\cdot \frac14\cdot 3 + \frac{1}{4}\cdot 3200 = 1400
|
20,021 |
j = (\frac{l_2}{l_1})^{j + (-1)} = l_1/(l_2) \left(\frac{1}{l_1}l_2\right)^j
|
6,193 |
\frac{\mathrm{d}}{\mathrm{d}k} \tfrac{1}{2 (-1) + k} = -\frac{1}{\left(k + 2 (-1)\right)^2}
|
-6,667 |
\frac{1}{3 \cdot \left(y + 4 \cdot (-1)\right)} \cdot 5 = \frac{1}{12 \cdot (-1) + 3 \cdot y} \cdot 5
|
-24,655 |
\frac{1}{24}\cdot 20 = \frac{4\cdot 5}{4\cdot 6}
|
28,808 |
(2\cdot x - z)\cdot 3 = x\cdot 6 - 3\cdot z
|
-19,192 |
7/24 = \frac{A_s}{64*\pi}*64*\pi = A_s
|
-4,403 |
\frac{n^2}{n^4} \cdot 70/120 = \frac{1}{n^4} \cdot n^2 \cdot \frac{7 \cdot 10}{10 \cdot 12}
|
19,339 |
1/6*2/2 = \frac{1}{6}
|
34,261 |
-\dfrac13 \pi = \operatorname{asin}\left(\sin{\frac{4}{3} \pi}\right)
|
-20,859 |
-\frac{6}{5} \frac{1}{(-1) + 5p}((-1) + 5p) = \dfrac{-p*30 + 6}{5(-1) + 25 p}
|
17,796 |
2^k = \left(k + 1\right)\cdot (2 + k)\cdot \ldots\cdot 2\cdot k
|
20,319 |
(\sqrt{2}*\left(i + 1\right)*\left(-1\right))/2 = \sin(π*5/4)*i + \cos(5*π/4)
|
21,768 |
5^{l\cdot 2}\cdot 5^2 = 5^{l\cdot 2 + 2}
|
-22,701 |
\frac{5\cdot 11}{11\cdot 9} = \frac{55}{99}
|
-22,775 |
\frac{8*5}{8*4} = 40/32
|
-10,216 |
0.01\cdot \left(-92\right) = -92/100 = -\frac{23}{25}
|
2,558 |
-1/2 = -\frac{1}{1*2}
|
29,582 |
\sin{y} = \int \cos{y}\,dy
|
33,263 |
\cos(a+b)=\cos a \cos b - \sin a \sin b
|
-20,865 |
\tfrac{1}{8 \cdot \left(-1\right) + 7 \cdot m} \cdot (7 \cdot m + 8 \cdot (-1))/5 = \dfrac{7 \cdot m + 8 \cdot \left(-1\right)}{35 \cdot m + 40 \cdot (-1)}
|
11,701 |
3^{y + (-1)} = 2 + 1 \Rightarrow y = 2
|
-20,606 |
\tfrac{1}{x + 4*\left(-1\right)}*\left(x + 3*(-1)\right)*9/9 = \frac{9*x + 27*(-1)}{x*9 + 36*(-1)}
|
17,893 |
y = \sin(x)*2 \Rightarrow x = \arcsin(\tfrac{y}{2})
|
31,210 |
3^i \cdot (1 + 2) + (-1) = 3^i + \left(-1\right) + 2 \cdot 3^i
|
1,956 |
(z + x) \cdot (x^2 - x \cdot z + z^2) = x^3 + z^3
|
15,244 |
\frac{a + 1}{\left(-1\right) + a} = 1 + \dfrac{1}{a + \left(-1\right)}*2
|
13,537 |
\left(-1\right) + 2 \cdot m + 1 + m \cdot 2 = 4 \cdot m
|
-4,648 |
\dfrac{5}{5 + z} - \frac{1}{3 \cdot (-1) + z} = \frac{20 \cdot \left(-1\right) + z \cdot 4}{15 \cdot (-1) + z^2 + z \cdot 2}
|
4,687 |
\mathbb{Var}\left[X\right] = \mathbb{Var}\left[X_1 + \dots + X_{10}\right] = \mathbb{Var}\left[X_1\right] + \dots + \mathbb{Var}\left[X_{10}\right]
|
29,283 |
8/3 = \frac{1}{3}(1 + 2 + 2) + 1
|
8,601 |
\dfrac{0}{0 \cdot (-1) + 1} + \frac{1000}{(-1) + 2} = 1000
|
-3,786 |
3/t = 3/t
|
35,669 |
y_0 \cdot c = c \cdot y_0
|
23,427 |
3 + 1 + 2 = \dfrac{4\cdot 3}{2}
|
11,285 |
( 2, 4, 8) = ( 2^1, 2 \cdot 2, 2 \cdot 2^2)
|
27,901 |
546 = 1109 + 563*\left(-1\right) = g - b - 4*g = 5*g - b
|
3,022 |
\left(0 = \mathbb{P}(Y) \implies 0 = (Y^Z + Y)/2\right) \implies -Y^Z = Y
|
37,854 |
\frac{1}{10} + \tfrac{1}{100} + 1/1000 + \dots = \frac19
|
15,649 |
3\cdot e = ((-1) + e)\cdot 2 + \lambda \Rightarrow \lambda = e + 2
|
-6,696 |
90/100 + \frac{1}{100} = \frac{1}{100} + \tfrac{9}{10}
|
4,248 |
g_2 \cdot g_1 \cdot h = g_1 \cdot g_2 \cdot h
|
27,048 |
\dfrac{12}{17} \cdot \frac132 = 8/17
|
1,910 |
(-f + b)*\frac12*(f + b) = \frac{1}{2}*(-f^2 + b^2)
|
13,893 |
\left(-1\right) + 5^x = \left(4 + 1\right)^x + (-1)
|
23,875 |
S_k = a_k + S_{(-1) + k} \Rightarrow -S_{(-1) + k} + S_k = a_k
|
19,724 |
\frac{1}{c * c} = \frac{1}{c^2}
|
5,875 |
j = e^{j\times \theta} = \cos{\theta} + j\times \sin{\theta}
|
693 |
e ^{ix}= 1 + \frac{ix}{1!} + \frac{{(ix)}^2}{2!} ...
|
17,354 |
x \cdot x \cdot 100 + 20 \cdot x = \left(x \cdot 5 + 1\right) \cdot 5 \cdot x \cdot 4
|
37,454 |
\frac16 + \dfrac{2}{3} = 5/6
|
36,125 |
1 - \dfrac12 + \frac{1}{3} - \frac14 + \ldots + \frac{1}{m\cdot 2 + (-1)} - 1/(2\cdot m) = \frac{1}{m + 1} + \ldots + 1/(2\cdot m)
|
-2,004 |
\pi = \pi\cdot 17/12 - \pi\cdot \frac{5}{12}
|
47,220 |
1 = i\cdot 0 + 1
|
-2,303 |
-\frac{1}{18}\cdot 2 + \dfrac{4}{18} = \frac{2}{18}
|
1,505 |
(-x_1 + x) \cdot (x - x_2) = x^2 - (x_1 + x_2) \cdot x + x_2 \cdot x_1
|
-4,703 |
\frac{-z\cdot 5 + 9}{z^2 - 3\cdot z + 2} = -\frac{4}{(-1) + z} - \frac{1}{2\cdot (-1) + z}
|
12,857 |
E\left(W\right) \cdot E\left(Q\right) = E\left(W \cdot Q\right)
|
-3,791 |
\frac{1}{x^3} \cdot x^5 \cdot \dfrac{45}{20} = \frac{45 \cdot x^5}{x^3 \cdot 20}
|
37,068 |
G_2\cdot G_2^{G_1} = G_2^{G_1}\cdot G_2
|
10,672 |
\cos(s) = 1 - 2*\sin^2(s/2)
|
-2,989 |
11^{1/2}*(4 + 3*(-1)) = 11^{1/2}
|
29,868 |
\dfrac{9*z^3 + 5}{2*z * z * z + (z^6)^{1/2}} = \dfrac{9*z^2 * z + 5}{3*z * z * z} = 3 + \dfrac{5}{3*z^3}
|
-5,016 |
0.84\cdot 10^2 \cdot 10 = 0.84\cdot 10^{2 - -1}
|
39,024 |
10*6 = 60
|
29,025 |
3 \cdot (l^2 - (l + (-1))^2) - 2 \cdot (l - l + (-1)) = 3 \cdot \left(2 \cdot l + (-1)\right) + 2 \cdot (-1) = 6 \cdot l + 5 \cdot (-1)
|
19,991 |
3*2/(2*2) = \frac32 = 1.5
|
10,359 |
(-1) + 2*(1 + l) = l*2 + 1
|
12,943 |
\frac{\partial}{\partial z} z^m = z^{m + (-1)} \cdot m
|
24,397 |
y^2 + 2*y - y^2 - 2*y = y^2 - y^2 + 2*y - y^2 + 2*y = 4*y
|
27,162 |
z^{100} = 1^{99} \cdot z^{100}
|
4,743 |
1 + 2 \cdot (-1) + 3 + 4 \cdot (-1) + 5 \cdot ... = \frac{1}{4}
|
-19,053 |
\tfrac{17}{24} = x_q/(36\cdot \pi)\cdot 36\cdot \pi = x_q
|
-10,628 |
-\frac{30}{r\cdot 60 + 100} = -\frac{3}{r\cdot 6 + 10}\cdot 10/10
|
31,859 |
{m + 1 \choose 2} = \sum_{i=0}^m {i \choose 1} = \sum_{i=0}^m i
|
-8,061 |
\frac{7i + 26}{-2 - i\cdot 5} \dfrac{1}{i\cdot 5 - 2}(5i - 2) = \dfrac{26 + 7i}{-2 - 5i}
|
1,522 |
-z^l + x^l = (x - z) \cdot (x^{(-1) + l} + x^{l + 2 \cdot (-1)} \cdot z + ... + x \cdot z^{2 \cdot (-1) + l} + z^{\left(-1\right) + l})
|
25,026 |
\frac19+\frac19=\frac29
|
14,911 |
-\int\limits_z^1 \frac1s\,\mathrm{d}s = \int\limits_1^z \frac1s\,\mathrm{d}s
|
3,897 |
1 = \frac{1}{1/2} \cdot 1/2
|
25,923 |
a^{h_2 \cdot h_1} = (a^{h_2})^{h_1} = (a^{h_1})^{h_2}
|
-1,289 |
\frac{1}{1/6}\cdot ((-1)\cdot 9\cdot 1/5) = 6/1\cdot (-9/5)
|
47,494 |
55*0.7 = 38.5
|
-3,191 |
(4 + 2 + 3\cdot (-1))\cdot \sqrt{3} = 3\cdot \sqrt{3}
|
16,085 |
V + b = V + b \Rightarrow [V,b]
|
-2,500 |
\sqrt{2} \cdot (4 + 5 + 2(-1)) = \sqrt{2} \cdot 7
|
37,050 |
2 = \frac{9}{16}*\left(-2/3\right) + \tfrac{19}{8}
|
35,359 |
z^2 + y\cdot z\cdot 5 + y^2\cdot 7 = (z + y\cdot 5/2)^2 + y^2\cdot 3/4
|
26,541 |
\dfrac{1.001}{64} = 1/64 + \frac{1}{512} = 0.017578125
|
12,667 |
ygg = gyg = ggy
|
23,815 |
\sqrt{6}\cdot 400 = 200\cdot 2 \sqrt{6}
|
23,711 |
69 = 1^2 + 7 \cdot 7 + 3^2 + 3^2 + 1^2
|
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