id
int64 -30,985
55.9k
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stringlengths 5
437k
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17,525 |
22 - 4\cdot (16 + 21\cdot (k + (-1)) + (-1)) = 42 - 84\cdot k = 21\cdot (2 - 4\cdot k)
|
21,040 |
\lim_{t \to \infty} \frac1t \cdot (t + 2 \cdot (-1)) = \lim_{t \to \infty} |t + 2 \cdot (-1)|/t
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18,556 |
\mathbb{P}(F) \mathbb{P}(A) + 1 - \mathbb{P}(A) - \mathbb{P}(F) = (1 - \mathbb{P}\left(F\right)) (-\mathbb{P}(A) + 1)
|
21,496 |
x \cdot x + 2 \cdot x + 1 = \left(x + 1\right)^2
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-7,732 |
\left(40 + 16 i + 100 i + 40 (-1)\right)/29 = \frac{1}{29} (0 + 116 i) = 4 i
|
2,964 |
\sin(x + z) = \cos(z) \cdot \sin\left(x\right) + \sin\left(z\right) \cdot \cos(x)
|
28,143 |
3 + x^2 - 3*x = \left(\left(-1\right) + x\right)*(x + (-1)) - x + 2*(-1)
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39,548 |
18.75 = \frac{1}{4} \cdot 75
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54,605 |
1^{\frac{1}{5}} = 1
|
3,306 |
9^x\cdot 8 = 9^{1 + x} - 9^x
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17,953 |
\left(q = h\cdot 120 - 205 q \Rightarrow h\cdot 120 = q\cdot 206\right) \Rightarrow h = q\cdot 103/60
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-16,346 |
\sqrt{4 \cdot 7} \cdot 10 = 10 \sqrt{28}
|
46,173 |
\frac{1}{30}\cdot 96 = 3.2
|
21,576 |
c\cdot g = \dfrac{1}{2}\cdot (c\cdot g + g\cdot c) = g\cdot c
|
-3,097 |
\sqrt{6} \cdot 9 = (5 + 4) \sqrt{6}
|
3,060 |
r \cdot r \cdot (-\frac{1}{8 \cdot r \cdot r} + 1) + \frac14 = r^2 + 1/8
|
3,591 |
\sin\left(J \cdot 2\right) = \sin\left(J\right) \cdot \cos(J) \cdot 2
|
10,859 |
\cos{v \cdot x} = \cos{-x \cdot v}
|
-12,841 |
\frac{3}{4} = \tfrac{1}{24} \cdot 18
|
-20,867 |
\frac{80 \cdot k}{80 + 8 \cdot k} = \frac{10}{k + 10} \cdot k \cdot \frac18 \cdot 8
|
-23,704 |
\frac23\dfrac13 = 2/9
|
-27,731 |
d/dy (14\cdot \sin{y}) = \cos{y}\cdot 14
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32,427 |
\frac11*0 = \frac02
|
5,878 |
|F*u| = |F|*|u|
|
1,598 |
\binom{m}{m - k} = \frac{m!}{(m - k)!\cdot (m - m - k)!} = \frac{1}{(m - k)!\cdot k!}\cdot m! = \binom{m}{k}
|
-4,171 |
\frac{8}{7 \cdot t^4} = \frac{8}{t^4} \cdot 1/7
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37,857 |
-2 = 2 \cdot (-1) + 0
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17,837 |
\frac{1}{x^3 + (-1)} = \left(-\dfrac{x + 2}{x^2 + x + 1} + \frac{1}{(-1) + x}\right)/3
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22,622 |
y \geq z \implies y = z
|
-19,688 |
\frac{24}{8} = 8*3/(8)
|
-563 |
(e^{i\cdot \pi/2})^{10} = e^{\dfrac{\pi\cdot i}{2}\cdot 10}
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3,211 |
\left(7 = (-1) + 8 \implies 8\cdot M + \left(-1\right) = 7^{1 + n\cdot 2}\right) \implies 1 + 7^{1 + 2\cdot n} = M\cdot 8
|
-6,710 |
2/100 + \frac{60}{100} = \dfrac{1}{10}6 + 2/100
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8,072 |
\left(1 + |z_2|\right) |z_1| = (1 + |z_1|) |z_2|\Longrightarrow |z_2| = |z_1|
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11,212 |
{-1 \choose r} = (\left(-1\right)*\left(-2*\dotsm*(-1 - r + 1)\right))/r! = (-1)^r
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26,037 |
\sqrt{2} \pi/2 = \frac{1}{\sqrt{2}}\pi
|
20,481 |
(a\times f)^n = a^n\times f^n = 1 \Rightarrow f^{-n} = a^n
|
245 |
\frac{1}{2 + z} = y \implies (1 - 2\cdot y)/y = z
|
16,133 |
2860 = {4 \choose 1} \cdot {3 \choose 3} \cdot {13 \choose 4}
|
23,523 |
\frac{7}{161} = 1/23
|
23,592 |
\frac{1}{21}5*6/22 = \frac{1}{77}5
|
15,629 |
\left\lceil{\frac{10}{5 + (-1)}}\right\rceil = \left\lceil{\dfrac{10}{4}}\right\rceil = \left\lceil{2.5}\right\rceil = 3
|
27,597 |
\frac{1}{2^{\frac{1}{n}}} = \tfrac{h}{x}\Longrightarrow \frac{x}{h} = 2^{1/n}
|
-30,652 |
5 \cdot (-1) - 5 \cdot \lambda^2 = -5 \cdot (1 + \lambda^2)
|
19,836 |
1 + y + y^2 + y^3\times \dotsm = \dfrac{1}{-y + 1}
|
-7,593 |
(22 + 32 \cdot i + 55 \cdot i + 80 \cdot \left(-1\right))/29 = (-58 + 87 \cdot i)/29 = -2 + 3 \cdot i
|
29,551 |
a^4 \cdot z = z = a^3 \cdot z
|
37,365 |
\operatorname{atan}\left(-4\right) = x \Rightarrow \tan(x) = -4
|
7,577 |
\frac{1}{y^2 + 1}(2y^2 + y) = 1 + \frac{y^2 + y + (-1)}{y^2 + 1} = 1 + \frac{2y^2 + 2y + 2(-1)}{2\left(y * y + 1\right)}
|
8,855 |
\frac{1}{13}*\left(3^{x + 1} + 3^x + 3^{(-1) + x}\right) = 3^{(-1) + x}
|
32,686 |
6y'^2 v + 3v^2 y'' + 6x = 0 \Rightarrow vy' * y'*2 + v^2 y'' + x*2 = 0
|
22,571 |
\lim_{l \to \infty} \sin\left(y_l\right) = 0 \neq 1 = \lim_{l \to \infty} \sin\left(y_l\right)
|
35,278 |
(-X)^m = X^m = -X^m
|
-5,012 |
3.6\times 10^{2 + 0} = 10 \times 10\times 3.6
|
18,469 |
\tfrac{1}{(1 - x)^2}\cdot (1 + x^2 + x) = \frac{\left(1 - x\right)^2 + 3\cdot x}{(1 - x)^2} = 1 + \dfrac{3}{(1 - x)^2}\cdot x
|
1,520 |
\sqrt{625/2 + \dfrac{1}{2}\cdot 625} = \sqrt{625} = 25
|
-10,719 |
\dfrac{3}{3}\cdot \left(-\dfrac{1}{16\cdot \left(-1\right) + s\cdot 4}\cdot 6\right) = -\frac{18}{s\cdot 12 + 48\cdot (-1)}
|
15,050 |
128^{1/2} = (11^2 + 7)^{1/2} \approx 11 + \dfrac{7}{22}
|
26,402 |
\frac{3}{2} \cdot \frac{1}{2}/2 = 3/8
|
10,185 |
a^{b \times b} = a^{b^2}
|
15,877 |
(x \cdot x - x \cdot z + z^2) \cdot (x + z) = z \cdot z \cdot z + x^3
|
9,896 |
\dfrac{1}{-\dfrac{1}{f} + \frac{1}{f - 1/b}} = -f + b*f*f
|
8,815 |
x \lt y \implies \frac{x}{2} \lt \frac{y}{2}
|
54,750 |
799 = 17\cdot 47
|
-30,547 |
15/30 = 30/60 = \dfrac{60}{120} = \frac{1}{2}
|
12,951 |
1 + x^4 = (x^3 - x^2 + x + (-1))*(1 + x) + 2
|
-8,363 |
-\frac{1}{-4}*24 = 6
|
17,756 |
2^{\frac{1}{2}} = 1.414213562373 \times \dots
|
-5,573 |
\frac{2\cdot z}{z^2 - z + 2\cdot (-1)}\cdot 1 = \tfrac{2\cdot z}{(1 + z)\cdot \left(z + 2\cdot (-1)\right)}
|
874 |
\frac{\partial}{\partial Z_2} Z_1 = \frac{1}{Z_2 + Z_1}\cdot (3\cdot Z_2 - Z_1) = \dfrac{1}{1 + Z_1/(Z_2)}\cdot (3 - \dfrac{1}{Z_2}\cdot Z_1)
|
-4,681 |
(1 + z) (z + 5) = z^2 + 6z + 5
|
15,010 |
m + {m \choose 2} \cdot 2 = m \cdot m
|
21,014 |
z^3 + z*3 + 2 (-1) = 6 (-1) + \left(z + 1\right) (z^2 - z + 4)
|
29,919 |
\frac{r_3}{(x + (-1))^2} + \frac{1}{(-1) + x} \cdot r_2 = \frac{r_3 + r_2 \cdot (\left(-1\right) + x)}{((-1) + x) \cdot ((-1) + x)}
|
2,336 |
\frac{10}{24} = (6 + 4)/24
|
-2,888 |
\sqrt{3} \cdot (1 + 4) = \sqrt{3} \cdot 5
|
2,324 |
y^V*A*y = (y^V*A*y)^V = y^V*A^V*y = -y^V*A*y \Rightarrow y*A*y^V = 0
|
-26,544 |
100 - 9\cdot z \cdot z = 10^2 - (z\cdot 3) \cdot (z\cdot 3)
|
-5,785 |
\frac{1}{20 + 4 \cdot y} \cdot 2 = \tfrac{2}{4 \cdot \left(y + 5\right)}
|
44,865 |
\overline{0} = \overline{0} \overline{4}
|
25,876 |
-\dfrac{1}{x_n \cdot 2} \cdot \left(2 \cdot \left(-1\right) + x_n^2\right) + x_n = (x_n + \frac{2}{x_n})/2
|
11,891 |
\frac{Z}{b} \cdot a^{1/2} = \frac{Z \cdot x}{( x^2 - a, b)} \cdot 1 = \frac{Z}{x^2 - a} \cdot \frac{1}{b \cdot x}
|
38,771 |
7 = -\frac{10}{2} + 12
|
-9,123 |
2 \cdot 2 \cdot 3 \cdot 3 \cdot p - 2 \cdot 2 \cdot 3 = 36 \cdot p + 12 \cdot (-1)
|
10,440 |
\binom{n + 3 + (-1)}{3 + (-1)} = \binom{n + 2}{2} = \tfrac12 \cdot \left(n + 1\right) \cdot \left(n + 2\right)
|
5,965 |
\sum_{n=1}^\infty c \cdot (2 \cdot (-1) - 1)^n \cdot n = \sum_{n=1}^\infty c \cdot n \cdot (-3)^n
|
-1,822 |
\pi\cdot \dfrac{1}{3}\cdot 4 = \pi\cdot 13/12 + \dfrac{\pi}{4}
|
10,775 |
\frac{1}{x + (-1)} \cdot (x^2 \cdot x + (-1)) = x^2 + x + 1
|
-16,492 |
8 \cdot 275^{1/2} = 8 \cdot (25 \cdot 11)^{1/2}
|
6,311 |
\sin(x + u) = \sin{u} \cos{x} + \sin{x} \cos{u}
|
41,105 |
1000\cdot \left(-1\right) + 1 = -999
|
9,844 |
( x + w, x + w) = \left\{w\right\} \implies 0 = [x,w]
|
4,685 |
6/y \leq -8 \implies y \geq -\frac{6}{8} = -\frac143
|
6,783 |
z + 2\times (-1) = 4\times (z + 2) = 4\times z + 8
|
37,731 |
E^2 = E^2
|
-23,150 |
-4 = 3 (-4/3)
|
-3,605 |
\tfrac{40\cdot n^2}{32\cdot n} = 40/32\cdot \dfrac{n^2}{n}
|
16,780 |
\frac{e^{-9} 9^9}{9!} = \frac{e^{-9} 9^8 * 9}{8! * 9}
|
40,547 |
\cos{4*x} = \cos^2{2*x} - \sin^2{2*x} = 2*\cos^2{2*x} + (-1)
|
874 |
\frac{\mathrm{d}x}{\mathrm{d}U} = \frac{3\cdot U - x}{U + x} = \tfrac{1}{1 + \dfrac{x}{U}}\cdot \left(3 - \frac1U\cdot x\right)
|
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