id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
4,392 |
(-b^2 + a^2) u = u\cdot (a - b) (a + b)
|
6,129 |
\dfrac{1}{2} - \dfrac{1}{4 \cdot 3} = \frac{1}{3 \cdot 4} + \frac13
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-10,323 |
\frac{1}{y*20}*(8*\left(-1\right) + 2*y) = 2/2*\tfrac{1}{10*y}*(4*(-1) + y)
|
15,810 |
\frac{36!}{(36 + 2*(-1))!} = 1260
|
10,698 |
1 + n\cdot 2 = 5 + x\Longrightarrow x = 2n + 1 + 5(-1) = 2n + 4(-1)
|
-1,758 |
\pi\times 13/12 = 23/12\times \pi - \frac{5}{6}\times \pi
|
281 |
n \geq k + 28 \implies k \leq n + 28*(-1)
|
35,425 |
1/(2*2) + 1/(2*2) = 1/4 + \frac{1}{4} = 1/2
|
7,969 |
\tfrac{1}{2} \cdot (f + d) = d + \left(-d + f\right)/2
|
-2,332 |
9/16 - \frac{1}{16} 4 = \frac{1}{16} 5
|
-1,808 |
\pi/4 = \pi \frac{1}{12}19 - \frac{1}{3}4 \pi
|
31,642 |
\cos\left(E + Rx\right) R = \frac{\partial}{\partial x} \sin(E + Rx)
|
-7,849 |
(-6 - 18\cdot i + 3\cdot i + 9\cdot \left(-1\right))/5 = \dfrac15\cdot (-15 - 15\cdot i) = -3 - 3\cdot i
|
30,468 |
1/x = \dfrac{1}{x} = \tfrac{x}{x^2}
|
24,073 |
0.5/4 + 2 \cdot 0.5/16 = \dfrac{1}{16} \cdot 5 \lt 1
|
19,404 |
\frac{\tan(G)}{1 + \tan^2(G)} \cdot 2 = \sin(G \cdot 2)
|
-3,761 |
\frac{k^4\cdot 35}{k^4\cdot 15} = 35/15\cdot \dfrac{1}{k^4}\cdot k^4
|
26,899 |
\cos\left(2\cdot x\right) = 1 - \sin^2(x)\cdot 2\Longrightarrow \sqrt{(1 - \cos(x\cdot 2))/2} = \sin(x)
|
38,079 |
12288 = 4096\times 3
|
-15,860 |
7 \cdot 5/10 - 8 \cdot \frac{1}{10} \cdot 5 = -5/10
|
31,975 |
EB = BE
|
8,505 |
25 = \left(y_2 + y + y_1\right)^2 = y_2^2 + y^2 + y_1^2 + 2*\left(y_2*y + y_2*y_1 + y*y_1\right) = y_2^2 + y * y + y_1^2 + 16
|
-26,509 |
10^2 + (9 \cdot x)^2 + x \cdot 9 \cdot 10 \cdot 2 = (10 + 9 \cdot x)^2
|
3,940 |
\sum_{l=3}^n l * l = \sum_{l=1}^n l^2 - 1^2 + 2^2 = \sum_{l=1}^n l^2 + 5\left(-1\right)
|
18,952 |
-((2 \cdot x + 1)^6)^{\frac{1}{2}} = -|(2 \cdot x + 1)^3| = -|2 \cdot x + 1|^3
|
-19,007 |
5/6 = X_x/\left(4\pi\right)*4\pi = X_x
|
-19,012 |
17/18 = \frac{A_s}{9\cdot \pi}\cdot 9\cdot \pi = A_s
|
38,327 |
X^TX = XX^T
|
14,882 |
{(-1) + 7 + 0(-1) \choose 3 + (-1)} {3 \choose 0} = 15
|
45,111 |
\sqrt{-x}=\sqrt{-x}
|
2,119 |
\cos\left(\frac{\pi*2014}{12}\right) = \cos(-83*\pi*2 + \frac{1}{12}2014 \pi)
|
-21,589 |
\sin{3*π} = 0
|
40,489 |
|\overline{y} + 2(-1)| = |\overline{y + 2(-1)}| = |y + 2(-1)|
|
20,856 |
A^T\times A\times A\times A^T\times A\times A^T = A\times A^T\times A\times A^T\times A\times A^T
|
309 |
9\cdot x \cdot x + (-1) = (3\cdot x)^2 - 1^2 = (3\cdot x + (-1))\cdot (3\cdot x + 1)
|
27,526 |
\sin(f)*\cos\left(c\right) + \cos(f)*\sin\left(c\right) = \sin(c + f)
|
-3,351 |
2^{1 / 2}*(1 + 4) = 2^{1 / 2}*5
|
21,365 |
f^x = f^x \cdot \frac{x!}{x! \cdot 0!}
|
-3,410 |
(3 + (-1))*\sqrt{3} = \sqrt{3}*2
|
6,551 |
734 = 34 + 500 + 334 + 200 + 167\cdot \left(-1\right) + 100\cdot (-1) + 67\cdot \left(-1\right)
|
12,290 |
149 \cdot 103 = 15347
|
-26,151 |
9\cdot 1^{\frac13\cdot 4} - 9\cdot \left(-1\right)^{\frac13\cdot 4} = 9 + 9\cdot (-1) = 0
|
-9,426 |
f*2*2*2*3*f = f^2*24
|
20,939 |
\left(5\cdot x + 1\right)\cdot (2\cdot (-1) + t) = (2\cdot (-1) + x)\cdot (5\cdot t + 1) \Rightarrow 2\cdot (-1) + t\cdot x\cdot 5 - 10\cdot x + t = 2\cdot (-1) + t\cdot x\cdot 5 - 10\cdot t + x
|
-22,042 |
\frac{1}{10}*16 = \frac85
|
-1,340 |
\dfrac{5}{4} \cdot (-\frac18 \cdot 9) = \frac{5}{1/9 \cdot \left(-8\right)} \cdot 1/4
|
20,505 |
\left(693 + 5\cdot (-1)\right)/2 = 344
|
48,718 |
4^2 = 3^2 + 4 + 3 = 9 + 4 + 3 = 16
|
24,544 |
-2 + 2\times (-1) + 2\times (-1) = (-3)\times 2
|
20,983 |
-32 + 32\times i = (i + (-1))\times 2^5
|
7,490 |
5^2*2*7 * 7 = 2450
|
8,770 |
a^2 + b^2 \geq a^2 = a^{\alpha} \times a^{2 - \alpha} \geq a^{\alpha} \times b^{2 - \alpha}
|
-22,937 |
\frac{9 \cdot 9}{5 \cdot 9} = \frac{81}{45}
|
18,362 |
-(-d + 3) = 3 \cdot (-1) + d
|
36,661 |
3^{10^x} = 9^{10^x/2} = \left(10 + (-1)\right)^{10^x/2}
|
-13,244 |
\frac{6}{4 + 2 (-1)} = 6/2 = 6/2 = 3
|
37,649 |
G_1 + Y_1 = G_1 + Y_1
|
16,012 |
\sqrt{\frac{2}{1 + 5/13}} = \sqrt{13}/3
|
20,699 |
11 \cdot e = e + e \cdot 10
|
-6,723 |
20/100 + \frac{5}{100} = 2/10 + \dfrac{5}{100}
|
2,769 |
x \cdot \nu + \nu \cdot \beta = \nu \cdot (\beta + x)
|
12,651 |
\mathbb{E}(B + T) = \mathbb{E}(T) + \mathbb{E}(B)
|
-3,923 |
\dfrac{1}{q^3\cdot 96}\cdot q^3\cdot 80 = \frac{q^3}{q^3}\cdot \tfrac{80}{96}
|
-16,377 |
\sqrt{44}*10 = \sqrt{4*11}*10
|
23,266 |
4^{m + 1} + 15 \times (m + 1) + \left(-1\right) = 4 \times 4^m + 15 \times m + 15 + (-1) = 4^m + 15 \times m + \left(-1\right) + 3 \times (4^m + 5)
|
28,184 |
3/1024 = (1/4)^4*3/4
|
-23,242 |
5/18 = \frac58\cdot \frac{4}{9}
|
28,440 |
\dfrac{(-1) + l}{4\cdot l^2} + \dfrac{1}{l^2\cdot 4} + \frac{(-1) + l}{l \cdot l\cdot 4} = \tfrac{1}{4\cdot l^2}\cdot ((-1) + 2\cdot l)
|
26,043 |
2*B*C = B*C + B*C
|
-1,127 |
\tfrac{1/2\times (-7)}{\frac18\times (-9)} = -\frac89\times \left(-\frac{1}{2}\times 7\right)
|
-642 |
(e^{\pi i/3})^8 = e^{\pi i/3 \cdot 8}
|
-7,174 |
2/7*4/7 = \frac{8}{49}
|
29,975 |
\frac{10!}{3!\cdot 3!\cdot 4!} = 4200
|
26,596 |
z^2 - 3*z + 2 = (z + \left(-1\right))*\left(z + 2*(-1)\right)
|
8,223 |
\cos^{\sin\left(y\right)}(y) = (\cos^2\left(y\right))^{\frac{\sin(y)}{2}} = (1 - \sin^2(y))^{\sin(y/2)}
|
-11,740 |
81/16 = (\frac94) (\frac94)
|
23,701 |
(1 + d)^2 - d^2 = d*2 + 1
|
13,803 |
\frac13\cdot \left(-1/3 + 1\right) = \frac19\cdot 2
|
808 |
\cos{y} = (e^{iy} + e^{-iy})/2 = \overline{\cos{y}} = \dfrac{1}{2}\left(e^{-iy} + e^{iy}\right)
|
39,323 |
0 = 3 + 1 + 4(-1)
|
-24,655 |
\dfrac{4 \cdot 5}{4 \cdot 6} = \dfrac{20}{24}
|
32,587 |
675 = 3^3 \times 5^2
|
42,458 |
\dfrac{1}{19} \cdot 36 = 1 + \frac{17}{19} = 1 + \frac{1}{19 \cdot \frac{1}{17}} = 1 + \frac{1}{1 + 2/17} = 1 + \frac{1}{1 + \dfrac{1}{17 \cdot 1/2}} = 1 + \tfrac{1}{1 + \frac{1}{8 + \frac12}}
|
21,961 |
\Z_{28} = \left\{5, 1, \ldots, 4, 0, 27, 3, 2\right\}
|
2,595 |
2*(-1) + n = (n + 3*(-1)) + 1
|
-18,273 |
\frac{1}{(9 + z) (z + 5)} (9 + z) z = \frac{9 z + z^2}{45 + z^2 + z \cdot 14}
|
48,454 |
1 = 632\times 2452 - 313\times 4951
|
34,033 |
I*I*f = f = I*I*f
|
5,018 |
\frac{(3 \cdot (-1) + n) \cdot (n + 4 \cdot (-1))}{((-1) + n) \cdot (n + 2 \cdot (-1))} = \frac{1}{\binom{n + (-1)}{2}} \cdot \binom{n + 3 \cdot (-1)}{2}
|
-15,892 |
(5\cdot\dfrac{3}{10}) + (-10\cdot\dfrac{7}{10}) = -\dfrac{55}{10} = -
|
14,964 |
\frac{1}{100}\cdot y\cdot z = y\cdot \frac{z}{100}
|
18,103 |
7/2 \cdot 2 = 7
|
10,628 |
-(y^2 + (-1)) + y^2 + y = y + 1
|
-12,332 |
\sqrt{24} = 2\sqrt{6}
|
-10,788 |
-\dfrac{30}{z^2 z\cdot 80} = \dfrac15 5 (-\frac{6}{z^3\cdot 16})
|
-1,719 |
-\pi\cdot 7/6 + 0 = -\pi\cdot 7/6
|
6,302 |
0 = x \cdot 3 + (-1) \Rightarrow \frac13 = x
|
10,154 |
v' + D = v + 1 \implies v' = v - D + 1
|
17,109 |
\sin{B} \cos{B}\cdot 2 = \sin{2B}
|
-20,336 |
\frac{2}{-x\cdot 7 + 5\cdot (-1)}\cdot 2/2 = \dfrac{4}{10\cdot (-1) - x\cdot 14}
|
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