id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
16,637 |
A*a' = 1 rightarrow A = \frac{1}{a'}
|
35,573 |
[x_1,x_2] = \left[x_2, x_1\right]
|
15,394 |
\frac{7^{55}}{5^{72}} = (\frac{1}{5^4} \cdot 7 \cdot 7 \cdot 7)^{18} \cdot 7
|
4,522 |
9/29 = \tfrac{1}{29} \cdot 9
|
21,318 |
20 = 1/2 \cdot 5!/3
|
-1,771 |
\frac{1}{12} \cdot 13 \cdot \pi = 2 \cdot \pi - 11/12 \cdot \pi
|
13,749 |
\left(b + a\right)^4 = b^4 + a^4 + b*a^3*{4 \choose 1} + a^2*b^2*{4 \choose 2} + {4 \choose 3}*a*b^3
|
23,330 |
\binom{x}{k} = \frac{x!}{k!\cdot (x - k)!}
|
28,016 |
134 = \left\lfloor{\frac{1}{3*5}*2013}\right\rfloor
|
-24,883 |
\frac{11}{12} = \frac{1}{12 \cdot \pi} \cdot q \cdot 12 \cdot \pi = q
|
32,406 |
Z^{0 + m} = Z^m \cdot Z^0
|
-3,563 |
\frac{k}{k^2} = k/(k\cdot k) = \frac{1}{k}
|
6,724 |
25 + z \times z \times 4 + 20 \times z = (2 \times z + 5)^2
|
-22,257 |
42 + p^2 + p*13 = (p + 6)*(p + 7)
|
25,559 |
\left(dc\right)^2 = d * d c^2
|
-15,905 |
-\frac{4}{10}*5 + 6*6/10 = 16/10
|
-1,708 |
\frac{2}{3}\pi - \frac{2}{3}\pi = 0
|
13,404 |
(-1) + z^3 - 2\cdot z = (1 + z)\cdot ((-1) + z^2 - z)
|
-2,934 |
\sqrt{2} \sqrt{25} + \sqrt{2} \sqrt{16} - \sqrt{4} \sqrt{2} = 5\sqrt{2} + \sqrt{2}*4 - \sqrt{2}*2
|
37,847 |
y\cdot a = a\cdot y
|
11,847 |
|r| \lt 1 \Rightarrow 1 + r + r^2 + r^3 + \dots = \frac{1}{-r + 1}
|
32,902 |
\left(-1\right) + 3 + (-1) = 1
|
32,363 |
\dfrac{a^2 + d^2 + c^2}{d \cdot a + d \cdot c + a \cdot c} = 2 \cdot (-1) + \frac{(a + d + c)^2}{a \cdot d + c \cdot d + a \cdot c}
|
-12,140 |
4/9 = p/(6\cdot \pi)\cdot 6\cdot \pi = p
|
22,363 |
\left(1 + k + 1\right) (1 + k)! = (k + 1 + 1) (1 + k)!
|
-4,476 |
\tfrac{1}{10 + x^2 - 7 \cdot x} \cdot (33 - x \cdot 9) = -\frac{1}{5 \cdot (-1) + x} \cdot 4 - \frac{5}{x + 2 \cdot (-1)}
|
-1,129 |
8/1 \left(-\frac{1}{2}\right) = (\left(-1\right) \frac12)/(\frac18)
|
21,772 |
\frac{g\times a}{d_2\times d_1} = a\times \frac{1}{d_2}/(d_1\times 1/g)
|
2,858 |
1/h + 1/f + \frac1d = 0\Longrightarrow 0 = \frac{1}{f \cdot d \cdot h} \cdot \left(f \cdot h + d \cdot f + h \cdot d\right)
|
-6,708 |
\dfrac{4}{100} + \frac{1}{100} \cdot 80 = 8/10 + \dfrac{4}{100}
|
1,236 |
(d \cdot a + b \cdot a + b \cdot d) \cdot 2 + a^2 + b^2 + d^2 = (a + b + d)^2
|
40,310 |
x^r = x^{r + (-1)} x = 2^{(r + (-1))/2} x
|
1,827 |
(n + 1)^3 + 2 \cdot (n + 1) = n^3 + 3 \cdot n^2 + 5 \cdot n + 3 = n^3 + 2 \cdot n + 3 \cdot (n \cdot n + n + 1)
|
-2,656 |
\left(3 + 4(-1) + 2\right)\cdot 3^{\dfrac{1}{2}} = 3^{\dfrac{1}{2}}
|
18,138 |
1 + 2^{3^n}\cdot 2 = 2^{1 + 3^n} + 1
|
-30,263 |
49*\left(-1\right) + y^2 = (y + 7*\left(-1\right))*\left(7 + y\right)
|
-19,630 |
1/\left(2*\frac{2}{3}\right) = \frac{3*\tfrac{1}{2}}{2}
|
53,584 |
1 = \binom{4}{4}
|
1,753 |
1 + a = \frac{1 - a \cdot a}{-a + 1}
|
-11,762 |
(\frac{1}{16})^{1/4} = 16^{-\frac{1}{4}}
|
4,887 |
\cos(\tan^{-1}(x)) = \frac{1}{\sqrt{x^2+1}}
|
16,078 |
2 \cdot 2^{1 / 2} = 2^{1 / 2} + 3^{\frac{1}{2}} - 3^{1 / 2} - 2^{1 / 2}
|
-23,229 |
\frac{1/9}{2} \cdot 5 = \frac{5}{18}
|
-5,306 |
10^{-1 + 2}*24.0 = 10^1*24.0
|
-18,395 |
\dfrac{-n \times 8 + n \times n}{n^2 - 14 \times n + 48} = \dfrac{\left(n + 8 \times \left(-1\right)\right) \times n}{(n + 8 \times \left(-1\right)) \times (n + 6 \times (-1))}
|
5,370 |
(j_F L)^4 = \frac{(L j_F)^9}{(L j_F)^5}
|
11,988 |
(-1) + 2n = 2((-1) + n) + 1
|
25,374 |
\dfrac12 (2 x + 1 + (-1)) (2 + (-1)) = x
|
10,155 |
x^{\dfrac{1}{2}} \cdot x^{\frac{1}{2}} = x
|
17,211 |
\left(b + c = b\cdot c \Leftrightarrow 1 = c\cdot b - b - c + 1\right) \Rightarrow 1 = (c + (-1))\cdot (b + (-1))
|
30,835 |
(x + 2)^2 + 4*(-1) = x^2 + x*4
|
29,022 |
\left(-v + u\right)^2 + 2 \cdot v \cdot \left(-v + u\right) + (2 \cdot v)^2 = 3 \cdot v^2 + u^2
|
-13,086 |
2(-2) = \frac{2(-2)}{1} = -4/1
|
33,025 |
\sin^2{i} = -\cos^2{i} + 1
|
19,817 |
(-1)^{a \cdot d} = (-1)^{d \cdot a}
|
32,713 |
3 + x^2 + (-1) = 2 + x^2
|
-13,857 |
3 + \dfrac{3}{1} = 3 + 3 = 3 + 3 = 6
|
-23,065 |
--\frac43 \cdot 5 = 20/3
|
24,950 |
74 = 4\cdot 6 + 3^2 + 4^2 + 5^2
|
13,576 |
Y^{i + (-1)} = \frac{Y^i}{Y}
|
-29,383 |
-7/8 \cdot (-\dfrac{7}{5}) = \frac{(-7) \cdot (-7)}{8 \cdot 5} = 49/40
|
16,637 |
A\cdot a' = 1 \implies 1/a' = A
|
-17,530 |
30 - 7 = 23
|
4,359 |
\frac1n = \int\limits_{n + (-1)}^n 1/n\,dq \leq \int\limits_{n + \left(-1\right)}^n 1/q\,dq
|
50,122 |
e^{-y^n} = \sum_{i=0}^\infty (-y^n)^i/i! = \sum_{i=0}^\infty \frac{(-1)^i}{i!}\cdot y^{i\cdot n}
|
26,957 |
0 + 0 + C = (4 + 5(-1)) (14 + 2)/4 \Rightarrow C = -4
|
2,601 |
x \cdot i \cdot z = z \cdot i \cdot x
|
-17,029 |
-6 = -6x^2 - 16 x - 6*3x - 48 = -6x^2 - 16 x - 18 x + 48 (-1)
|
47,382 |
1768 = 40 \cdot 19 + 48 \cdot 21
|
-9,145 |
r\cdot 2\cdot 3\cdot 7 r = 42 r^2
|
26,988 |
\sqrt{n} \cdot \left(\sqrt{n} + 2 \cdot \left(-1\right)\right) = -\sqrt{n} \cdot 2 + n
|
25,914 |
9 = 4 \cdot 0 + 0 + 3 \cdot 3
|
21,274 |
\left(w_1 + w_2\right)/2 = (-1/2 + 1)\cdot w_2 + \frac{w_1}{2}
|
366 |
1 - \dfrac{5}{6} = 6/6 - 5/6 = (6 + 5\cdot (-1))/6 = 1/6
|
-4,622 |
(x + 1)\cdot (2\cdot (-1) + x) = 2\cdot (-1) + x^2 - x
|
28,765 |
\cos^2{t}*2 + \left(-1\right) = \cos{t*2}
|
31,623 |
1 + 2 + 3 + 4 \times \cdots = -\dfrac{1}{12}
|
26,517 |
\frac 12\left(7-(-1)\right) = 4
|
19,902 |
BE+EC+6=13 \implies BE=EC=\frac{13-6}{2}=3.5
|
-30,559 |
\frac16*1.5 = 6/24 = 24/96 = 1/4
|
9,501 |
\dfrac{1/2}{l + 1} + \frac{1/2}{1 + l} = \dfrac{1}{l + 1}
|
818 |
\left(-x B + B x\right)/x = B - \frac{B x}{x}
|
14,212 |
\lim_{x \to ∞} x = \lim_{x \to ∞} x*2
|
30,336 |
\rho = |\rho|\cdot e^{i\cdot \phi} = |\rho|\cdot (\cos{\phi} + i\cdot \sin{\phi})
|
-21,058 |
2/2 \cdot 2/4 = \frac48
|
15,459 |
\sin\left(x + π\right) = \sin{-x}
|
5,154 |
u + u + v + v = \left(u + v\right)\cdot (1 + 1) = u + v + u + v
|
39,079 |
3\left(-1\right) - 3*3 + 2*0 + 5(-1) = -17
|
29,074 |
2\cos{Z} \sin{Z} = \sin{2Z}
|
-9,453 |
84\cdot \left(-1\right) + x\cdot 36 = 2\cdot 2\cdot 3\cdot 3\cdot x - 2\cdot 2\cdot 3\cdot 7
|
-8,317 |
(-9)*\left(-2\right) = 18
|
5,072 |
70! = 64!*65*...*70
|
34,721 |
\arcsin{-\frac12} = (\pi\cdot (-1))/6
|
25,233 |
\frac{\mathrm{d}}{\mathrm{d}K} \left(K * K \sin{2K}\right) = 2\cos{K*2} K * K + K\sin{K*2}*2
|
-26,576 |
2 z^2 + 162 (-1) = 2 (z z + 81 (-1)) = 2 (z + 9) (z + 9 (-1))
|
13,420 |
a^{\frac13} = a^{1/3}
|
26,746 |
\left(2\sqrt{2} + (-1)\right) (1 + 2\sqrt{2}) = 7
|
51,331 |
77076 = 9 \cdot 8564
|
-12,071 |
\frac{19}{24} = \frac{Y}{4 \pi}*4 \pi = Y
|
15,819 |
10^k - 10^{k-1}=9\cdot10^{k-1}
|
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