id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
9,366 |
\frac{3}{36} + \frac{1}{36}*2 + \frac{1}{36} = \frac{6}{36}
|
353 |
2 = \frac17 \cdot (22 + 8 \cdot (-1))
|
3,680 |
8 + 3\left(-1\right) = 5 = 3*\frac{5}{3}
|
39,806 |
\binom{10}{3} = \frac{10!}{3! \cdot 7!}
|
25,680 |
x \times \left(x + \left(-1\right)\right) \times ... = x!
|
48,318 |
95=5\cdot19
|
32,868 |
\frac{1}{x + i} = \frac{1}{(1 + i) \cdot \left(\frac{x + (-1)}{1 + i} + 1\right)}
|
6,848 |
-t + t^2 = 2 + (t + 2 (-1)) (t + 1)
|
28,315 |
(1 + \cos(2 \cdot z))^2 = (1 + 2 \cdot \cos^2(z) + (-1))^2 = 4 \cdot \cos^4(z)
|
15,374 |
(1 + l)^{l + 1} = (l + 1) (1 + l)^l
|
-20,650 |
(70\cdot p + 10\cdot (-1))/30 = \tfrac{10}{10}\cdot \left(7\cdot p + (-1)\right)/3
|
-16,700 |
-3 = -3(-2x) - 21 = 6x - 21 = 6x + 21 (-1)
|
-20,610 |
-\tfrac{9}{4} \tfrac{7 - 5p}{-5p + 7} = \tfrac{45 p + 63 (-1)}{28 - 20 p}
|
6,565 |
1/(S_1\cdot S_2) = 1/\left(S_1\cdot S_2\right)
|
25,922 |
\left(1 + 1\right) \cdot \left(x + z\right) = (1 + 1) \cdot x + \left(1 + 1\right) \cdot z = x + x + z + z
|
33,397 |
(1 + y^4 + y^2 \cdot \sqrt{2}) \cdot (1 + y^4 - y \cdot y \cdot \sqrt{2}) = y^8 + 1
|
18,689 |
(3 + 6 + 3)\cdot (4\cdot 6 + 3 + 2\cdot 4 + 3\cdot 5) = 600
|
22,910 |
(-1) + z^3 - z^2 + z = (z^2 + 1)\cdot ((-1) + z)
|
-10,551 |
-\dfrac{5}{4\cdot \left(-1\right) + 4\cdot r}\cdot 5/5 = -\frac{25}{r\cdot 20 + 20\cdot (-1)}
|
11,351 |
(k + 1)/2 - \dfrac{1}{2} \times k = \frac12 = \frac{k}{2} - (k + (-1))/2
|
25,344 |
800 = {\left(-1\right) + 17 \choose 2} + {(-1) + 17 \choose 2} + {17 + (-1) \choose 3}
|
6,978 |
fg = (\left(g + f\right)^2 - \left(f - g\right)^2)/4
|
-20,543 |
\tfrac{p \cdot 15}{p \cdot (-9)} = -5/3 \cdot \frac{(-1) \cdot 3 \cdot p}{p \cdot \left(-3\right)}
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34,568 |
(Z + 2)^k + (Z + 2)^{2\cdot k + 3} + (Z + 2)^0 = (Z + 2)^{3\cdot k + 3} = \left(Z + 2\right)^{(k + 1)^3}
|
3,364 |
x = \frac{3}{x\cdot 3}\cdot x^2
|
45,376 |
-2\cdot 0.08 + 1 = 0.84
|
9,338 |
\frac{1}{n + 1} \cdot (n + 1)! = n!
|
10,139 |
π\cdot 5/12 = 75\cdot π/180
|
46,671 |
144 = 3!*4!
|
-21,216 |
\dfrac{1}{12}9 = \frac{3}{4}
|
-7,008 |
9/28 = \dfrac{6}{7} \cdot \dfrac{3}{8}
|
20,977 |
2^{2*\left(-1\right) + n}*2 = 2^{n + (-1)}
|
-10,711 |
-\frac{18}{18 + y \cdot 30} = 6/6 \cdot (-\dfrac{3}{y \cdot 5 + 3})
|
-20,640 |
\frac{6}{24 + 18 \cdot k} = \dfrac33 \cdot \frac{2}{k \cdot 6 + 8}
|
37,931 |
n\cdot {p \choose n} = {(-1) + p \choose n + (-1)}\cdot p
|
17,543 |
G_i \times G_x \times G_l = G_i \times G_x \times G_l
|
-4,155 |
\dfrac{1}{2 \cdot j^3} = \frac{1}{2 \cdot j^3}
|
17,010 |
z = 2 \cdot (z + 4 \cdot (-1)) + 4 - z + 4 \cdot \left(-1\right) = 2 \cdot (z + 4 \cdot (-1)) + 8 - z
|
2,247 |
4417 = 1 + 8^2\cdot 5 + 8^4
|
-15,530 |
\frac{1}{\dfrac{1}{r\times \frac{1}{m^3}}}\times (r^3)^3 = \tfrac{r^9}{m^3\times 1/r}
|
22,767 |
\sin\left((n + 1)^2 - n^2\right) = \sin\left(2 \cdot n + 1\right)
|
31,892 |
(\sqrt{x} - x)/(\sqrt{x}) + (-\sqrt{x} + 1)/1 = 2\cdot (1 - \sqrt{x})
|
-2,342 |
\tfrac{1}{20} = 4/20 - 3/20
|
31,351 |
\pi*2*(1 - 1/2) = \pi
|
4,866 |
n - j = j + n - j \cdot 2
|
24,901 |
\frac{1}{3}5 = \frac{5}{3}
|
12,936 |
(a + \sqrt{b}) (a - \sqrt{b}) = a a - \left(\sqrt{b}\right)^2 = a^2 - b
|
38,508 |
G^R \cdot G = G^R \cdot G
|
-15,791 |
-\frac{7}{10} + 1 = \frac{3}{10}
|
13,375 |
\left(p + 1\right)/2 = p - \frac12\cdot \left(p + (-1)\right)
|
-22,151 |
\frac{30}{27} = \dfrac{1}{9}\cdot 10
|
-499 |
(e^{i\pi/4})^{17} = e^{17 \frac{i\pi}{4}}
|
30,790 |
m = \left\{3, m, \dotsm, 2, 1\right\}
|
20,112 |
b \gt x rightarrow x * x \lt b^2 = \dfrac{1}{9}
|
20,996 |
\frac{1}{3} = 1/9/(\frac13)
|
-4,991 |
6.86*10 = \dfrac{6.86*10}{100} = \dfrac{6.86}{10}
|
8,153 |
\tan^2{-G\cdot z} = \tan^2{G\cdot z}
|
-2,092 |
23/12\cdot \pi + \pi/2 = \pi\cdot 29/12
|
-9,468 |
-5\cdot 2\cdot 2 - 5\cdot r = -5\cdot r + 20\cdot (-1)
|
-6,177 |
\frac{1}{(5(-1) + t)*2}2 = \frac{2}{t*2 + 10 \left(-1\right)}
|
17,160 |
\frac{1}{2}*\left(20 + 18*(-1)\right) + 18 = 19
|
-19,592 |
7/2*\frac159 = \frac{9*1/5}{2*\frac17}
|
-30,177 |
\frac{\mathrm{d}}{\mathrm{d}x} x^{12} = 12 \cdot x^{12 + (-1)} = 12 \cdot x^{11}
|
11,040 |
-c^p + x^p = \left(-c + x\right) \cdot (x^{p + \left(-1\right)} + x^{p + 2 \cdot (-1)} \cdot c + c \cdot c \cdot x^{p + 3 \cdot (-1)} + \dotsm + x \cdot c^{p + 2 \cdot (-1)} + c^{(-1) + p})
|
-26,552 |
2 \cdot y^2 - 40 \cdot y + 200 = 2 \cdot \left(y^2 - 20 \cdot y + 100\right) = 2 \cdot \left(y + 10 \cdot (-1)\right)^2
|
-3,736 |
p*\frac15*8 = 8*p/5
|
5,911 |
f^2 - 4 \cdot f + 5 \cdot (-1) = (f + 5 \cdot (-1)) \cdot (f + 1) = 0 \implies -1 = f, 5
|
20,710 |
{m \choose k} = \dfrac{m!}{k! \cdot (-k + m)!}
|
54,655 |
(0!)! = (1!)! = 1
|
6,273 |
\frac23 \cdot 2 = 4/3
|
3,002 |
-(\sqrt{5}*2 - \sqrt{11}) + 2\sqrt{5} + \sqrt{11} = \sqrt{11}*2
|
12,404 |
d\cdot \tau/d = d\cdot \tau/d
|
22,675 |
X \cap (A) = A \cap (A \cap X) = A \cap X
|
-23,230 |
\dfrac{1}{5} = 1 - 4/5
|
14,935 |
x*4 + w = w * w + x^2*2 \Rightarrow 0 = 2*x * x - 4*x + w^2 - w
|
21,824 |
4 (-1) + 2 (k\cdot 5 + 1) (5 k + 1)^2 + 7\cdot \left(1 + 5 k\right) = 250 k k k + k^2\cdot 150 + 65 k + 5
|
17,526 |
(ab)^{-1} = b^{-1} a^{-1} = ba
|
14,315 |
\sin(-x + \alpha) = \cos{x} \cdot \sin{\alpha} - \sin{x} \cdot \cos{\alpha}
|
4,275 |
y^4 + (-1) = (y^2 + \left(-1\right)) \times (y^2 + 1) = \left(y + (-1)\right) \times \left(y + 1\right) \times (y^2 + 1)
|
7,975 |
\frac{1}{k} = \frac{1}{(-1)^{1/2}} = (1/(-1))^{1/2} = (-1)^{1/2} = k
|
13,849 |
(-1)^{1 + k} = (-1)^k \cdot (-1)
|
2,783 |
(n + 1)*(n + 2)*...*2*n = (n*2)!/n!
|
21,281 |
t \cdot y \cdot q = t \cdot q \cdot y
|
-26,650 |
\left(5 + 8(-1)\right)^2 = 25 + 80 (-1) + 64
|
46,807 |
7 + 56 = 63
|
8,140 |
E = \left(E \cap Y\right) \cup (E \cap \overline{Y}) = Y \cup (E \cap \overline{Y})
|
-26,462 |
\left(-h + g\right)^2 = h^2 + g^2 - 2\cdot h\cdot g
|
20,923 |
2\sin\left(5x\right) \cos(4x) = \sin(5x + 4x) + \sin(5x - 4x) = \sin(9x) + \sin(x)
|
-2,298 |
\frac{3}{11} - 1/11 = 2/11
|
8,024 |
\left(\left(t + x = 0 \Rightarrow x = -t\right) \Rightarrow (-t)^2 = x * x\right) \Rightarrow x = t
|
22,446 |
a \cdot a \cdot c \cdot c = (c \cdot a)^2
|
-27,493 |
8\cdot f^2 = 2\cdot f\cdot f\cdot 2\cdot 2
|
-18,375 |
\frac{(q + 5) \cdot \left(q + 6\right)}{((-1) + q) \cdot (q + 5)} = \frac{1}{q^2 + 4 \cdot q + 5 \cdot (-1)} \cdot (q^2 + 11 \cdot q + 30)
|
30,919 |
x*\frac34 = \left(\frac12*x + x\right)/2
|
27,338 |
\{C_1, C_2\} \Rightarrow C_1 \cup C_2 \setminus C_1 = C_2
|
29,991 |
4 = \frac19(1 + 2 + 3 + 2 + 4 + 6 + 3 + 6 + 9)
|
-6,308 |
\frac{1}{q^2\cdot 3 + 243\cdot \left(-1\right)}\cdot (q + 9\cdot \left(-1\right) - 9\cdot q + 81\cdot \left(-1\right) + q\cdot 15) = \frac{90\cdot \left(-1\right) + 7\cdot q}{243\cdot (-1) + 3\cdot q^2}
|
5,276 |
\sin{\beta} = 2.71 \cdot \sin{46}/2.29 = 0.85 \Rightarrow 58.35 = \beta
|
9,812 |
b\cdot c = b\cdot e_x\cdot c = b\cdot e_x\cdot c
|
1,097 |
a y^2 + g y + f = 0 \Rightarrow y^2 + y g/a = -f/a
|
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