id
int64 -30,985
55.9k
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|---|---|
-4,479 |
\frac{7\cdot i + 24}{i^2 + 7\cdot i + 12} = \frac{3}{i + 3} + \frac{1}{4 + i}\cdot 4
|
-12,002 |
2/9 = \frac{1}{18 \cdot \pi} \cdot i \cdot 18 \cdot \pi = i
|
12,730 |
f_1\cdot f_2\cdot c = f_1\cdot (-f_2 - c) = -f_1 - -f_2 - c = -f_1 + f_2 + c
|
1,001 |
(x^2 + 1)^3 = x^6 + 3x^4 + 3x \cdot x + 1 = (x + 1)^2 + 3(x^2 + x) + 3x^2 + 1 = 7x^2 + 5x + 2
|
4,637 |
\mathbb{E}(X)*\mathbb{E}(T^2) = \mathbb{E}(T^2*X)
|
14,554 |
t - (t + (-1))/2 = (t + 1)/2 = \frac12 (t + (-1)) + 1
|
26,451 |
c d a + (a + c) (d + c) (a + d) = (a d + d c + a c) (a + d + c)
|
27,088 |
3^2 + \left(-4\right)^2 = \left(-4 + 1\right)^2 + (1 + 3) \cdot (1 + 3)
|
16,825 |
x^4 - x^2 + 2(-1) = x^4 + 2x^2 + 1 = (x \cdot x + 1)^2
|
11,565 |
b*a = -a*\left(-b\right)
|
39,116 |
1/(x*y) = \frac{1}{x*y}
|
42,257 |
5\cdot 7 \cdot 7 + 3 = 3\cdot 9^2 + 5 = 248
|
22,542 |
a*0 + a*0 + a*0 = 0*a + a*0
|
-1,368 |
-3/8\cdot (-\frac87) = \frac{(-8)\cdot \frac17}{(-8)\cdot 1/3}
|
34,387 |
\frac{1}{2} = (1 - 1/3) \cdot (1 - 1/4)
|
-178 |
\binom{10}{6} = \dfrac{1}{6!*\left(6*(-1) + 10\right)!}*10!
|
22,211 |
\cos\left(\arctan(x)\right) = \tfrac{1}{\left(1 + x^2\right)^{1 / 2}}
|
-4,464 |
20 \cdot (-1) + y^2 - y = (4 + y) \cdot (5 \cdot (-1) + y)
|
-6,433 |
\dfrac{3}{32 + 4 \cdot t} = \frac{1}{4 \cdot \left(t + 8\right)} \cdot 3
|
36,791 |
\frac{W}{m \cdot m\cdot k} = \frac{W/(m\cdot k)}{m}
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23,429 |
(\left(-1\right) + x) (x x + x + 1) = x^3 + (-1)
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17,792 |
0.3*t*7/16 = t*21/160
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35,551 |
2^{3\cdot (-1) + 11}\cdot 155925 = 11!
|
11,580 |
5 = 200 (-1) + 120 + 85
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-27,655 |
1 - \frac13\cdot 2 + 9/2 = 1/3 + 9/2 = \dfrac{29}{6}
|
19,537 |
-(x - 2 \cdot y) \cdot (x - 2 \cdot y) = -(x \cdot x - 4 \cdot x \cdot y + 4 \cdot y^2) = -x^2 - 4 \cdot y^2 + 4 \cdot x \cdot y
|
-20,283 |
\dfrac{63}{r\cdot 9 + 36} = \frac{1}{4 + r}\cdot 7\cdot \frac{1}{9}\cdot 9
|
6,677 |
d\cdot 2 + 1 + 10\cdot (-1) = 9\cdot (-1) + 2\cdot d
|
38,991 |
2 + 1^{1/2} = 4^{1/2} + 1
|
20,547 |
1050 = 7^1*3^1*2^1*5^2
|
17,371 |
f \cdot f = f^1\cdot f^1
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-5,416 |
10^0\cdot 0.5 = 10^{4 + 4\cdot (-1)}\cdot 0.5
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19,857 |
x^2\cdot \zeta^2 = \zeta \cdot \zeta\cdot x^2
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12,751 |
\dfrac{1}{y^2} \cdot x \cdot x = 2/1\Longrightarrow 2 = x^2,1 = y^2
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31,042 |
\frac{125}{216} = (5/6)^3
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35,604 |
D \cap X^c = D - X = D - D \cap X
|
9,607 |
L\cdot M/K = |L\cdot M| = \max{|L|,|M|} = \max{\frac{L}{K},M/K} = \frac{1}{K}\cdot L\cdot \frac{M}{K}
|
37,857 |
2*(-1) + 0 = -2
|
5,576 |
2/15 = \dfrac{2}{3} \cdot 3/6 \cdot \frac{1}{10} \cdot 4
|
9,712 |
-z^2 + 1 = (1 - z) \cdot (1 + z)
|
15,661 |
t\cdot r\cdot M^{n + 1} \geq t\cdot r\cdot M^n\cdot t\cdot r\cdot M/2 = 19\cdot t\cdot r\cdot M^n > t\cdot r\cdot M^n
|
-27,421 |
338 = 10 (-1) + 348
|
10,356 |
\left(\frac{1}{G} = G \cdot 3 \Rightarrow x = 3 \cdot G^2\right) \Rightarrow x/3 = G \cdot G
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21,827 |
2018 = (6^2)^2 + 5^2 \cdot 5^2 + (3^2)^2 + 2 \cdot 2 \cdot 2 \cdot 2
|
5,356 |
z \Rightarrow (z^2 - 3z + 1)^2 - 3(z^2 - 3z + 1) + 1 = z^2 - 3z + 1 = z
|
16,617 |
2 \cdot \cos^2{x} = 2 - \sin^2{x} \cdot 2
|
18,857 |
\frac{2}{16} + \dfrac{1}{17} = 50/(17*16)
|
21,143 |
217 = (20 z + 3) t + \frac{1}{20}(20 z + 3 + 3(-1)) = (20 z + 3) (t + 1/20) - 3/20
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-3,989 |
\dfrac97 = \frac{9}{7}
|
-6,293 |
\frac{1}{45 + n\cdot 5} = \frac{1}{5\cdot (n + 9)}
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-7,760 |
(-36 + 4\cdot i - 45\cdot i + 5\cdot (-1))/41 = \frac{1}{41}\cdot (-41 - 41\cdot i) = -1 - i
|
14,575 |
0 = c + 4 + 36 + g \cdot 4 + 12 a \Rightarrow g \cdot 4 + 12 a + c = -40 \cdots \cdot 3
|
4,293 |
\tan{g_1\cdot g_2} = \tan(0.5\cdot g_1\cdot g_2 + 0.5\cdot g_1\cdot g_2) = \frac{2\cdot \tan{0.5\cdot g_1\cdot g_2}}{1 - \tan^2{0.5\cdot g_1\cdot g_2}}
|
13,127 |
\sin(2 \times \pi + x) = \sin(x)
|
-1,602 |
\pi*3/4 = -13/12*\pi + \pi*\frac16*11
|
41,794 |
1 = 0.999 \cdot \dotsm
|
-7,035 |
\frac18\cdot 2/7 = \frac{1}{28}
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-26,468 |
5x^2-20x+20=5(x^2-4x+4)
|
26,669 |
\dfrac{1}{2^{1/2}}\cdot |(t + \frac{1}{2}) \cdot (t + \frac{1}{2}) + \frac14\cdot 7| = \frac{1}{(1 \cdot 1 + 1^2)^{1/2}}\cdot |t^2 + 2 + t|
|
-18,250 |
\frac{x^2 - x\cdot 6 + 7\cdot \left(-1\right)}{x^2 - 7\cdot x} = \dfrac{(1 + x)\cdot \left(7\cdot (-1) + x\right)}{x\cdot (x + 7\cdot \left(-1\right))}
|
-26,579 |
-8^2 + y^2 = 64 (-1) + y * y
|
-11,608 |
-i\cdot 3 + 3 = 3 + 0\cdot \left(-1\right) - i\cdot 3
|
3,168 |
I = (I - E)\cdot \left(H + I\right) = H + I - E\cdot H - E
|
40,354 |
0.66 = 9 - 8.333*\ldots
|
-30,265 |
\frac{1}{z + 5}*\left(z^2 + 10*z + 25\right) = \frac{(z + 5)*(z + 5)}{z + 5} = z + 5
|
-16,589 |
\sqrt{112} \cdot 8 = 8 \sqrt{16 \cdot 7}
|
2,440 |
\|b\|_1 = 0 \Rightarrow b = 0
|
11,918 |
(x^{\frac12}*T^{\frac{1}{2}})^2 = x*T
|
12,089 |
0 = y * y - y + 380*(-1) = (y + 19)*(y + 20*(-1))
|
17,449 |
\left(1 \leq 0 \Rightarrow 0 = 1,0 \geq 2\right) \Rightarrow 0 = 2,\dots
|
-1,684 |
\frac{11}{6} \pi = \frac{1}{6}\pi + \dfrac{5}{3} \pi
|
8,639 |
(1 + l^5) \cdot \left((-1) + l^5\right) = l^{10} + (-1)
|
31,971 |
\frac{4}{52}\cdot \frac{3}{51} = 12/2652 = \frac{1}{221}
|
-1,207 |
\frac23 \times (-\dfrac37) = \frac{2 \times 1/3}{1/3 \times (-7)}
|
40,217 |
25^2 + 60 \cdot 60 = 65^2
|
28,526 |
2 = \frac{2*2}{2}
|
9,353 |
\frac{1}{-y + 1} \cdot (-y^{n \cdot 2 + 1} + 1) = (1 + y) \cdot (1 + y^2) \cdot (1 + y^4) \cdot \cdots \cdot (y^{2 \cdot n} + 1)
|
19,568 |
\left(z^2 = z + 3 \Leftrightarrow 3(-1) + z \cdot z - z = 0\right) \Rightarrow (1 \pm \sqrt{13})/2 = z
|
16,004 |
\binom{k}{x} = \frac{k!}{x! \left(k - x\right)!}
|
4,777 |
\dfrac{1}{\sqrt{z}} = \dfrac{\sqrt{z}}{z}
|
22,834 |
\left(d_2 + d_1\right)^2 = d_1^2 + d_1\times d_2\times 2 + d_2^2
|
-19,352 |
\phantom{\dfrac{2}{7} \times \dfrac{5}{2}} = \dfrac{2 \times 5}{7 \times 2} = \dfrac{10}{14}
|
-15,966 |
\frac{1}{10}\cdot 19 = \frac{7}{10}\cdot 7 - 3/10\cdot 10
|
11,871 |
t < 1 + u\wedge u \lt t + 1 \Rightarrow t = u
|
16,284 |
\binom{0 + 4 + (-1)}{0} \binom{4}{3} = 4
|
11,757 |
A \cdot A \cdot A = 0\cdot A^2 = 0\cdot A
|
17,075 |
n^2 \cdot 14 + 19 \cdot n + 6 = \left(1 + 2 \cdot n\right)^2 + 5 \cdot (1 + n \cdot 2) \cdot (n + 1)
|
-28,766 |
-\frac{9}{2 + x} + x^2 - x \cdot 2 + 4 = \frac{1}{x + 2} \cdot ((-1) + x^3)
|
24,629 |
(-1) + m + k = 2 + m + \left(-1\right) + k + 2\cdot (-1)
|
-14,602 |
5*86 + 2*100 = 630
|
-15,074 |
\frac{t^3*\frac{1}{x^2}}{t^{12}*\tfrac{1}{x^{20}}} = \frac{t^3}{t^{12}}*\frac{1}{x * x*\tfrac{1}{x^{20}}} = \frac{1}{t^9}*x^{-2 - -20} = \frac{1}{t^9}*x^{18}
|
26,080 |
E/F = E*F/F/F = \frac{E}{F}*1 = \frac{E}{F}
|
12,720 |
(a\cdot f)^1 = a^1\cdot f^1 = a\cdot f
|
-12,903 |
\frac{1}{28} \cdot 10 = 5/14
|
9,266 |
t\cdot z\cdot 6/5 = \frac{1}{5}\cdot z\cdot t\cdot 2 + 4\cdot t\cdot z/5
|
16,023 |
c \cdot 3 + 3 = c + 2 + c + c + 1
|
18,035 |
a + a*b + 2*\left(-1\right) - 2*b = (2*(-1) + a)*(1 + b)
|
-20,338 |
2/2\cdot \frac{3\cdot \left(-1\right) + x}{2\cdot (-1) + x} = \frac{6\cdot (-1) + x\cdot 2}{x\cdot 2 + 4\cdot (-1)}
|
7,766 |
\left(x = 3^{1 / 2} \cdot 2 + 1\Longrightarrow 12 = \left((-1) + x\right)^2\right)\Longrightarrow 0 = x^2 - x \cdot 2 + 11 \cdot \left(-1\right)
|
-30,847 |
2\cdot (-1) + x = \frac{1}{x^2 + 3\cdot x}\cdot (x^3 + x^2 - 6\cdot x)
|
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