id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
10,346 |
1 - \sin^2{d} \cdot 2 = \cos{2 \cdot d}
|
29,981 |
0 = z_1 - z_2 + 3*\left(-1\right) \Rightarrow z_1 + 3*(-1) = z_2
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12,553 |
\mathbb{E}(N*X) = \mathbb{E}(N)*\mathbb{E}(X)
|
5,091 |
-\dfrac{1}{2} + \frac{3}{y} = \frac{6}{y\cdot 2} - y/(y\cdot 2)
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10,035 |
\binom{5}{2}\cdot 2! = \frac{\binom{5}{2}\cdot 3!}{3}
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1,057 |
A \cdot g' \cdot f \coloneqq f \cdot g' \cdot A
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16,248 |
a_3\cdot 3 = 1 rightarrow a_3 = 1/3
|
7,265 |
(l + k) \cdot (-k + l) = l^2 - k^2
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-4,183 |
\dfrac{2}{8} \cdot \dfrac{1}{z^4} \cdot z^4 = \frac{2 \cdot z^4}{z^4 \cdot 8}
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-4,410 |
(x + (-1)) \cdot (4 + x) = x^2 + 3 \cdot x + 4 \cdot (-1)
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16,170 |
2*h*((-1) + 2^{\frac{1}{2}}) = 2*h*2^{1 / 2} + h - 3*h
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-3,264 |
(2 + 5 + 3 (-1)) \sqrt{5} = 4 \sqrt{5}
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27,656 |
\lim_{h \to 0} (e^{x + h} - e^x)/h = \lim_{h \to 0} (e^x\cdot e^h - e^x)/h = \lim_{h \to 0} e^x\cdot \left(e^h + (-1)\right)/h = e^x\cdot \lim_{h \to 0} (e^h + (-1))/h
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17,484 |
1 + \left((-1) + m\right)^3 + 3(m + (-1)) \cdot (m + (-1)) + 3\left((-1) + m\right) = m \cdot m^2
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33,223 |
|1/z| = \tfrac{1}{|z|}
|
-530 |
(e^{\dfrac{\pi}{12} \cdot i})^{19} = e^{\frac{\pi}{12} \cdot i \cdot 19}
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3,776 |
\left(2^0 + 2^x = 2\Longrightarrow 2^x = 1\right)\Longrightarrow x = 0
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12,396 |
(\left(\left(-1\right) + m\right)/m)^1*2*\left(\frac1m\right)^2 = \frac{1}{m^3}*\left(m*2 + 2*(-1)\right)
|
-18,506 |
5*c + 10 = 6*(2*c + 2) = 12*c + 12
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8,148 |
1 + i + \left(-1\right) + d + (-1) = i + d + (-1)
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28,847 |
\tan^{-1}{-1} = -\pi/4
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22,508 |
(x^2 + x\cdot 0 + 1)\cdot (x + 0) = 0 + x^3 + x^2\cdot 0 + x
|
-7,195 |
\dfrac{2}{9} = \frac{1}{9}\cdot 4\cdot 5/10
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11,356 |
\frac{1}{n^2}*n^{\frac12} = \frac{1}{n^{3/2}}
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-4,618 |
\frac{5}{y + 4} + \dfrac{2}{1 + y} = \frac{y \cdot 7 + 13}{4 + y^2 + 5 \cdot y}
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28,317 |
3 = \frac{1}{1 - 2/3}
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10,770 |
k\cdot (1 - 0.6) = k\cdot 0.4
|
10,631 |
j = 14 (-1) + j \cdot 9 \Rightarrow \dfrac{1}{4} 7 = j
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1,470 |
(2^{7\%}*5) * (2^{7\%}*5) = \left(128\%*5\right)^2 = 3^2 = 9
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28,300 |
23 + w^2 + 6*w = 14 + (w + 3)^2
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10,812 |
\frac{x^2}{\left(-x + 1\right)^2} = (x + x^2 + \dots + x^{15})^2
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25,108 |
10^h \cdot 10^g = 10^{g + h}
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28,113 |
\left(44086^4 - 18748^4\right)\cdot 967 = 251477^4 - 146927^4
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2,393 |
\binom{3}{2} \binom{1}{1} \binom{5}{2} \binom{7}{2} = \frac{7!}{1!\cdot 2!\cdot 2!\cdot 2!}
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2,028 |
65/81 = 1 - (\frac{1}{3}\cdot 2)^4
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2,250 |
r^{n + 3 \cdot (-1)} \cdot \left(r + r^0\right) = r^{3 \cdot \left(-1\right) + n} \cdot \left(1 + r\right)
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15,689 |
b \times 3 = 9 + 3 \times \left(3 \times (-1) + b\right)
|
6,828 |
\pi\cdot k = \pi\cdot Q/3 \Rightarrow Q = 3\cdot k
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14,394 |
\dfrac{W^{12}}{W^{10}} = W^2
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31,995 |
\left(z_2 + z_1\right)^2 = (z_1 + z_2) \cdot (z_1 + z_2)
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14,442 |
\mathbb{E}[Z_1^t\cdot Z_2^x] = \mathbb{E}[Z_1^t]\cdot \mathbb{E}[Z_2^x]
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-2,980 |
8^{1 / 2} + 50^{\dfrac{1}{2}} = (25\cdot 2)^{1 / 2} + (4\cdot 2)^{\frac{1}{2}}
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49,414 |
\frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{5}{3}
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-7,646 |
\frac{-5 + 2i}{-5 + i*2} \dfrac{4 + 19 i}{-5 - i*2} = \frac{i*19 + 4}{-5 - 2i}
|
21,501 |
(-l + x)^2 = l^2 + x^2 - 2xl
|
34,098 |
\frac{z^2\cdot 3}{z^3} = 3/z
|
16,145 |
\dfrac42 = \frac63
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31,594 |
|z| \lt 1 \Rightarrow 1 - z + z^2 - z^3 + \cdots = \frac{1}{z + 1}
|
25,913 |
v_1^T\cdot v_2 = (H\cdot v_1)^T\cdot H\cdot v_2 = v_1^T\cdot H^T\cdot H\cdot v_2
|
10,727 |
n!^2/(2\cdot n) = \frac{n!^2}{2\cdot n\cdot 2}\cdot 2
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12,253 |
\tfrac{2}{3}\cdot 1/3\cdot \frac23 = \frac{1}{27}4
|
375 |
y + 144 = (9 + y)\times 11 \Rightarrow y + 144 = y\times 11 + 99
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36,755 |
\frac{1}{0\cdot (-1) + 6.04}\cdot (0 + 6\cdot (-1)) = -6/6.04
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31,527 |
r\cdot g\cdot s^2\cdot \left(-h_t + h_b\right) = g\cdot r\cdot s \cdot s\cdot (-h_t + h_b)
|
23,311 |
\left(2 + 1 rightarrow 1 = \cos(C)*l + \sin\left(C\right)*x\right) rightarrow (l*\cos(C))^2 = \left(1 - x*\sin(C)\right)^2
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-29,109 |
8\cdot 10^2\cdot 3/10 = 3/10\cdot 800
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-3,161 |
-3\cdot \sqrt{11} + \sqrt{11}\cdot 4 + \sqrt{11} = -\sqrt{11}\cdot \sqrt{9} + \sqrt{16}\cdot \sqrt{11} + \sqrt{11}
|
1,842 |
2/3 = \frac23*0 + 1/3 + \dfrac{1}{3}
|
28,741 |
(3a' - b')*4 = 6*(2a' - b')
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-5,637 |
\frac{(q + 8\cdot (-1))\cdot 25}{15\cdot (q + 4\cdot (-1))\cdot (q + 8\cdot (-1))} = \frac{5}{3\cdot \left(q + 4\cdot (-1)\right)}\cdot \frac{(q + 8\cdot (-1))\cdot 5}{5\cdot (q + 8\cdot (-1))}
|
-7,984 |
\frac{-13 + i}{i \cdot 2 - 1} = \dfrac{-i \cdot 2 - 1}{-1 - i \cdot 2} \cdot \frac{1}{2 \cdot i - 1} \cdot (-13 + i)
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31,750 |
13^2 \cdot 5 \cdot 5 \cdot 17 \cdot 29 \cdot 37 \cdot 41 = 3159797225
|
26,309 |
x^T Yx = x^T Y^T x = -x^T Y
|
-1,374 |
1/(7/4\cdot 7) = 4\cdot \frac{1}{7}/7
|
11,337 |
1 + ((-1) + p)/2 = \left(1 + p\right)/2
|
5,934 |
z = \frac{1}{R}\cdot H\cdot r\Longrightarrow z\cdot \tfrac{R}{H} = r
|
-20,381 |
-7/5 \cdot \dfrac{1}{-n + 5 \cdot (-1)} \cdot (-n + 5 \cdot (-1)) = \frac{n \cdot 7 + 35}{25 \cdot (-1) - 5 \cdot n}
|
4,857 |
\dfrac{40}{7} = 6 - 2/7
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-6,133 |
\dfrac{3}{(k + 9*\left(-1\right))*(k + 5*\left(-1\right))}*\dfrac{1}{4}*4 = \dfrac{12}{4*(5*\left(-1\right) + k)*(9*(-1) + k)}
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28,970 |
\dfrac{1}{x + g}\cdot (x + f) + (-1) = \frac{1}{x + g}\cdot (x + f - x + g) = \frac{1}{x + g}\cdot (f - g)
|
595 |
\dfrac{5}{5 + 3}\cdot ((-1)\cdot 0.4 + 1)\cdot 0.4\cdot \tfrac{4}{8 + 4} = \frac{1}{20}
|
22,413 |
\frac{1}{C\cdot B} = \frac{1}{C\cdot B}
|
26,815 |
50 = 5^2 \cdot 2 + 0^2
|
15,734 |
\left\{g\right\} = \cdots = \left\{g\right\}
|
-5,264 |
1.62*10 = 1.62*10*10^{11} = 1.62*10^{12}
|
10,871 |
5/6 = ((-1) + 3!)/3!
|
17,693 |
0 = z^2 - \dfrac{1}{6} \cdot 5 \cdot z + 1/6 = \left(z - \frac{1}{2}\right) \cdot \left(z - \frac{1}{3}\right)
|
-5,747 |
\frac{2}{2p + 18} = \dfrac{2}{2\left(p + 9\right)}
|
27,551 |
x_1 \overline{r_1} + \dotsm + \overline{r_n} x_n = r_1 x_1 + \dotsm + r_n x_n
|
17,636 |
-U^2 + U\cdot 2 + 5 = e^U \Rightarrow U^2 - 2\cdot U + e^U = 5
|
-6,688 |
\dfrac{9}{100} + \frac{6}{10} = \tfrac{60}{100} + \frac{1}{100}\cdot 9
|
-5,487 |
\frac{4}{5*(x + 2*(-1))} = \frac{1}{5*x + 10*(-1)}*4
|
9,659 |
6 + 4 = \frac{1}{35}(50 + 15 (-1)) (10 + 4(-1)) + 4
|
21,477 |
\dfrac{1}{5400}2362.5 = 0.4375 = 7/16
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35,753 |
\frac{1}{f_2^2} \cdot f_1 = \frac{1}{f_2^2} \cdot f_1
|
-5,261 |
1.6 \times 10 = \frac{10}{10^7} \times 1.6 = \dfrac{1}{10^6} \times 1.6
|
49,012 |
2 = -(1 + 0) + 3
|
14,094 |
0 = 15 \cdot (-1) + 3 \cdot w \cdot x \Rightarrow \dfrac{5}{w} = x
|
-21,030 |
\frac{5}{5} \cdot \frac{1}{z + 4} \cdot \left((-1) + 5 \cdot z\right) = \frac{5 \cdot (-1) + z \cdot 25}{5 \cdot z + 20}
|
18,567 |
x^2\cdot 4 = 2^2\cdot x^2
|
14,954 |
\frac{6000*n}{z} = \tan(\theta) \implies \cos(\theta)/\sin(\theta)*n*6000 = z
|
51,542 |
16 = 2\cdot 6 + 4
|
19,780 |
a_{l*2 + 2} = \left(a_{1 + 2 l}^2 + (-1)\right)/(a_{2 l}) \Rightarrow a_{l*2 + 1}^2 = a_{2 + l*2} a_{l*2} + 1
|
-7,828 |
\frac{1}{-(-2*i)^2 + 3^2}*(-3 + 15*i)*(2*i + 3) = \tfrac{(15*i - 3)*(3 + i*2)}{(3 + i*2)*(-i*2 + 3)}
|
5,498 |
t - \dfrac{t}{3} = t \cdot 2/3
|
4,363 |
1 + \cos(y) = 1 + 2*\cos^2(\frac{y}{2}) + (-1) = 2*\cos^2\left(\tfrac{y}{2}\right)
|
26,341 |
(g^2 + a^2 - a\cdot g)\cdot (a + g) = g^3 + a^3
|
9,633 |
\left(\left(-1\right) + 5^l\right)*5 + 4 = \left(-1\right) + 5^{l + 1}
|
16,006 |
\dfrac{a*f}{x*t} = a/x*\frac{f}{t}
|
6,937 |
2(-1) + x \cdot x + y \cdot y - x \cdot 2 - 2y = 14 + x^2 + y \cdot y - 6x - 6x\Longrightarrow 4 = x + y
|
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