id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-3,179 |
(4\cdot 6)^{1/2} + (25\cdot 6)^{1/2} = 150^{1/2} + 24^{1/2}
|
3,771 |
1/(\chi\cdot x) = \frac{1}{\chi\cdot x}\Longrightarrow \chi^2\cdot x \cdot x = (\chi\cdot x)^2
|
2,714 |
-\frac{2}{y^3} = \frac{\mathrm{d}}{\mathrm{d}y} \frac{1}{y \cdot y}
|
25,710 |
6^k \cdot 6 + (-1) = 6^{k + 1} + (-1)
|
15,765 |
(-\dfrac{9}{2} + 4)^2 = (5 - 9/2) \cdot (5 - 9/2)
|
34,486 |
9*(-16) = (-24)*6 = -144
|
3,160 |
\frac1267 = 8 + 2 + 7 + 25/2 + 4
|
19,997 |
1^2 + 3 * 3 - 3 = 7
|
20,032 |
14 = 5 \cdot (5^{98} + 3) - (1 + 5^{99})
|
16,498 |
b \cdot b + f^2 + fb \cdot 2 = (f + b) \cdot (f + b)
|
12,430 |
\frac{2\times \pi}{3} = 4\times \pi/6
|
32,692 |
\sin\left(q\right) = \tan\left(q\right)/\sec(q)
|
8,602 |
(\dfrac{1}{6612}*45539)^2 = \frac{2073800521}{43718544}
|
14,125 |
0 = -y_4 + y_1 - y_3 \implies y_1 = y_3 + y_4
|
14,951 |
(-101) \cdot (-101) + (-99)^2 + (-100)^2 = 99^2 + 100^2 + 101^2
|
14,526 |
(10 \cdot 10 \cdot 10) \cdot (10 \cdot 10 \cdot 10) = 10^2 \cdot 10^2 \cdot 10^2 = 10^6
|
13,665 |
\left(b \cdot a/a\right)^{n + 1} = (\frac{a}{a} \cdot b)^n \cdot b \cdot a/a = \frac{b^n}{a} \cdot a \cdot b \cdot a/a
|
22,340 |
\frac1x = \tfrac{1}{x^{1/2} \cdot x^{1/2}}
|
25,287 |
3/7 + 5/42 = \dfrac{1}{42} 18 + \frac{5}{42} = \frac{1}{42} 23
|
-6,088 |
\frac{1}{3 \cdot x + 3 \cdot \left(-1\right)} \cdot 5 = \dfrac{5}{3 \cdot ((-1) + x)}
|
-744 |
(e^{\frac{1}{12}\cdot 7\cdot i\cdot \pi})^{13} = e^{\frac{7}{12}\cdot i\cdot \pi\cdot 13}
|
22,110 |
8! = 7!2!2!2!
|
-2,576 |
5^{1/2}\cdot 4^{1/2} + 5^{1/2} = 5^{1/2}\cdot 2 + 5^{1/2}
|
24,946 |
0*\left(-1\right) + \frac{2*\pi}{3} = \frac{\pi*2}{3}*1
|
12,981 |
\frac{16}{25} + 4/25 = 4/5
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-19,670 |
\frac{10\cdot 8}{9} = \frac19\cdot 80
|
15,940 |
0.111111 \cdot \ldots = 1
|
19,668 |
\dfrac{1}{5^{\frac{1}{3}}}\cdot \int 1\,\text{d}x = \int \dfrac{1}{5^{1/3}}\,\text{d}x
|
5,988 |
x^2 = |x|^2 > 4 \Rightarrow |x| \gt 4^{\dfrac{1}{2}} = 2
|
21,147 |
\left(x + 1\right)^{1 + x} = (1 + x) \left(x + 1\right)^x
|
10,515 |
((-1) + X) (1 + X^2 + X) = X^3 + (-1)
|
15,686 |
\operatorname{E}\left[U + x\right] = \operatorname{E}\left[x\right] + \operatorname{E}\left[U\right]
|
23,994 |
\max{\mathbb{E}\left(V_1\right),...,\mathbb{E}\left(V_n\right)} = \mathbb{E}\left(\max{V_1, ..., V_n}\right)
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-20,132 |
-\frac{2}{9} \frac{10 (-1) + z}{10 \left(-1\right) + z} = \frac{-z \cdot 2 + 20}{z \cdot 9 + 90 (-1)}
|
-9,374 |
r\cdot 2\cdot 3\cdot 7 + 2\cdot 3\cdot 7 = 42 + 42\cdot r
|
2,547 |
\dfrac{1}{3}*(1 - 6*n) = \frac13 - \dfrac{6*n}{3} = 1/3 - 2*n
|
7,958 |
z = \sqrt{k + \sqrt{k + \dotsm}} = \sqrt{k + z} \Rightarrow -k + z^2 - z = 0
|
26,940 |
x^3 - y^3 = (x - y) \cdot (y^2 + x^2 + y \cdot x)
|
-20,068 |
\frac{9}{4}\cdot \frac{(-5)\cdot p}{p\cdot (-5)} = \frac{(-1)\cdot 45\cdot p}{(-1)\cdot 20\cdot p}
|
17,030 |
y - e \lt \delta\Longrightarrow y \lt \delta + e
|
-19,618 |
\frac{6\cdot \frac17}{6\cdot 1/5} = \frac{5}{6}\cdot 6/7
|
-1,600 |
\dfrac{1}{12}\cdot 19\cdot \pi = -5/12\cdot \pi + \pi\cdot 2
|
34,545 |
\frac{1}{k^2 - k}\cdot (p^2 - p) = \frac{1}{k + (-1)}\cdot ((-1) + p)\cdot \frac{1}{k}\cdot p
|
21,871 |
16 = \left(-16\right)*(-1)
|
12,129 |
2 \tfrac{1}{2} (\sqrt{5} + 3 (-1)) + 3 = \sqrt{5}
|
15,891 |
\dfrac{y^6 + (-1)}{1 + y + y^2 + y \cdot y^2 + y^4 + y^5} = y + (-1)
|
19,441 |
a\frac{w_2}{w_4} = \dfrac{aw_2}{w_4}1
|
46,471 |
\int \frac{(1 + t)^2}{\left(1 - t^2\right)^2}\,\mathrm{d}t = \int \tfrac{1}{(1 - t)^2\cdot (1 + t)^2}\cdot (1 + t)^2\,\mathrm{d}t = \int \frac{1}{(1 - t)^2}\,\mathrm{d}t
|
39,015 |
2\cdot \tan(\theta/2 + \pi/4) = 2\cdot \dfrac{1}{1 - \sin{\theta/2}/\cos{\theta/2}}\cdot (\sin{\theta/2}/\cos{\frac{\theta}{2}} + 1) = 2\cdot \frac{\sin{\theta/2} + \cos{\frac{\theta}{2}}}{\cos{\theta/2} - \sin{\frac{\theta}{2}}}
|
26,570 |
-(17 + 3 \cdot \sqrt{34}) \cdot (17 - \sqrt{34} \cdot 3) = 17
|
923 |
\frac{z}{7.5} + x/10 + y/6 = 1\Longrightarrow 4z + x \cdot 3 + 5y = 30
|
38,375 |
0 = det\left(H\right) \Rightarrow H
|
30,730 |
\sum_{k=1}^n k\cdot \sum_{m=1}^n m^2 = \sum_{k=1}^n k\cdot \sum_{m=1}^n m^2
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-19,683 |
\frac{5*4}{9} = \frac{20}{9}
|
19,285 |
-4 * 4*3 + 60 = 12
|
-260 |
{8 \choose 6} = \frac{8!}{(8 + 6(-1))!*6!}
|
-659 |
(e^{i\cdot \pi\cdot 4/3})^{10} = e^{10\cdot \pi\cdot i\cdot 4/3}
|
-22,224 |
x^2 + x\cdot 9 + 20 = (5 + x) (x + 4)
|
34,467 |
30 \cdot 44 = 1320
|
-12,414 |
4 = \dfrac{30}{7.5}
|
903 |
h^{d + c} = h^c*h^d
|
-23,092 |
-\frac12 4 = -2
|
9,403 |
-\frac{1}{27}*12 + 1 = \frac{5}{9}
|
37,731 |
H^2 = H^2
|
40,219 |
\frac11 \cdot (-1)^{1 + 1} = 1
|
11,759 |
\dfrac{1 + 2 + 3 + 4 + 5}{1 + 1 + 1 + 1 + 1} = \dfrac1515 = 3
|
25,458 |
B^X*B = B*B^X
|
-20,862 |
-1/6*\frac{1}{6*(-1) + z*3}*(6*(-1) + 3*z) = \frac{1}{18*z + 36*(-1)}*(-3*z + 6)
|
122 |
108 = (2 + 1) \cdot (1 + 2) \cdot (1 + 2) \cdot (3 + 1)
|
364 |
(s + s \cdot 2) \cdot \cot{\frac{1}{4} \cdot \pi} = s \cdot 3
|
14,291 |
x^2 - \left(x + \left(-1\right)\right)^2 = 2 \cdot x + (-1)
|
25,434 |
-x/2 + 3/x = \frac{1}{x} \cdot 3 - \frac{x}{2}
|
34,421 |
\binom{6+3-1}{3} = \binom{8}{3} = 56
|
7,493 |
\mu = p \cdot 0 + (1 - p) \cdot (1 + \mu) = (1 - p) \cdot (1 + \mu)
|
22,452 |
d^g = (e^{\ln(d)})^g = e^{g\cdot \ln(d)}
|
-23,027 |
\frac{1}{10 \times 9} \times 70 = 70/90
|
34,709 |
120*\tfrac{1}{30} = 4
|
-15,403 |
\frac{1}{\frac{p^{12}}{y^{20}} p^{15}} = \frac{1}{(\frac{1}{y^5}p * p^2)^4 p^{15}}
|
29,881 |
\sin(-\phi) = -\sin(\phi)
|
-2,744 |
7\cdot 7^{\frac{1}{2}} = 7^{\frac{1}{2}}\cdot (5 + 2)
|
-25,046 |
2 \cdot 1/6/5 = \dfrac{2}{30} = 1/15
|
2,195 |
\ln(2) = 1/2 + \frac{1}{6} + 1/30 + \frac{1}{56} + \dots \leq 1 + \frac14 + \frac{1}{25} + 1/49 + \dots
|
1,880 |
\int \sqrt{2^2 - y^2} \cdot y \cdot y \cdot y\,\mathrm{d}y = \int \sqrt{(2 + y) \cdot \left(2 - y\right)} \cdot y^3\,\mathrm{d}y
|
9,294 |
t^4 - t^2*2 + 1 = (1 - t * t)^2
|
24,843 |
b^2 - 3\cdot b + 19\cdot (-1) = \left(b + 7\right)^2 - 17\cdot (b + 4)
|
-11,896 |
\dfrac{3.609}{1000} = 3.609*0.001
|
21,760 |
\tan(\frac{\pi}{2} - x) = 1/\tan{x}
|
7,697 |
\lim_{z \to -3} \tfrac{3 + z}{9 \cdot (-1) + z^2} = \lim_{z \to -3} \dfrac{z + 3}{(z + 3 \cdot \left(-1\right)) \cdot (z + 3)}
|
-22,740 |
\frac{1}{90}\cdot 40 = 2\cdot 20/(2\cdot 45) = \frac{2\cdot 5\cdot 4}{2\cdot 5\cdot 9} = 4/9
|
-20,018 |
\frac{1}{5x + 45 \left(-1\right)}(30 + 5x) = 5/5 \frac{x + 6}{9\left(-1\right) + x}
|
29,362 |
\frac{z^2 + 9 (-1)}{3 (-1) + z} = 3 + z
|
26,518 |
e^{rx} r = \frac{\partial}{\partial x} e^{xr}
|
4,858 |
\frac{1 + x}{x + \left(-1\right)} = \dfrac{2}{x + (-1)} + 1
|
27,620 |
1/4 \cdot 3/2 = \frac183
|
5,091 |
3/x - 1/2 = \dfrac{6}{x*2} - x/(2*x)
|
-5,142 |
38.8 \times 10^{4 + 3} = 38.8 \times 10^7
|
6,536 |
x = x/4 + \frac{x}{4} + \frac14 \cdot x + \tfrac{x}{4}
|
5,242 |
\left(s - q\right) \cdot \binom{s}{q} = \binom{s}{q + 1} \cdot (1 + q)
|
10,356 |
\left(\frac{1}{A} = 3\cdot A rightarrow A^2\cdot 3 = I\right) rightarrow A^2 = I/3
|
8,443 |
\dfrac{1}{15} = \frac{8\cdot 3!}{10!}\cdot 7!
|
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