id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-7,435 |
6/10*2/11 = \frac{6}{55}
|
13,405 |
2\cdot l = q \cdot q + q\Longrightarrow l = \tfrac{1}{2}\cdot (q^2 + q)
|
-3,512 |
\frac{1}{100} \cdot 8 = \dfrac{2 \cdot 4}{2 \cdot 50}
|
-20,002 |
-7/4 \cdot \frac{3 \cdot (-1) - x \cdot 2}{3 \cdot (-1) - 2 \cdot x} = \frac{21 + 14 \cdot x}{12 \cdot (-1) - 8 \cdot x}
|
15,836 |
a + b + a + \left(n + 2 \cdot (-1)\right) \cdot b = a \cdot 2 + b \cdot (\left(-1\right) + n)
|
10,559 |
1 + 2^{1 + n} n = 1 + 2^{n + 1} n
|
23,301 |
z\cdot 2 = \frac4z \implies 2\cdot z^2 = 4
|
-4,148 |
96 l^3/(12 l) = \tfrac{96}{12} l^3/l
|
-16,351 |
\sqrt{44}\cdot 3 = \sqrt{4\cdot 11}\cdot 3
|
20,509 |
e^{z'}\cdot e^z = e^{z + z'}
|
-7,235 |
\frac{2*1/3}{6} = \frac19
|
-30,252 |
\frac{1}{z + 2}\cdot (z^2 + 11\cdot z + 18) = \frac{1}{z + 2}\cdot (z + 2)\cdot (z + 9) = z + 9
|
-24,692 |
27\cdot i + 7 = -11 + 23\cdot i + 18 + 4\cdot i
|
30,769 |
\frac{88236750}{50^6}*1 = 352947/62500000 = 0.005647152
|
19,682 |
d/dz (\arctan(2*z)/3) = \frac{2}{3}*\dfrac{1}{1 + (2*z)^2}
|
-12,028 |
3/4 = \frac{s}{4\cdot \pi}\cdot 4\cdot \pi = s
|
49,189 |
-32 = \left(-48\right)\cdot (-1) - 80
|
37,889 |
\|-z\| = |-1| \|z\| = \|z\|
|
-19,518 |
\frac15\cdot 7/\left(1/4\cdot 9\right) = 7/5\cdot 4/9
|
42,035 |
0 \cdot 0 \cdot 3 = 0
|
6,251 |
\frac{\frac{1}{4!*1!*1!*1!*4!}*11!}{2} = 34650
|
-4,178 |
\frac{22\cdot a^3}{a^3\cdot 12} = \frac{1}{a^3}\cdot a^3\cdot \frac{22}{12}
|
22,508 |
(y + 0) \cdot (y^2 + y \cdot 0 + 1) = 0 + y^3 + 0 \cdot y^2 + y
|
10,559 |
1 + n \cdot 2^{n + 1} = 2^{n + 1} \cdot n + 1
|
17,766 |
x^5 = 1 + x^5 + (-1) = 1 + \left(x + (-1)\right)\cdot \left(x^4 + x^3 + x^2 + x + 1\right)
|
-23,286 |
4/7 \cdot \frac{1}{8} \cdot 3 = \frac{3}{14}
|
18,550 |
\binom{6}{2} \cdot 3 = 45
|
16,040 |
s^2 - s*(\lambda_1 + \lambda_2) + \lambda_1*\lambda_2 = (s - \lambda_2)*\left(s - \lambda_1\right)
|
9,156 |
a b = a^3 b^3 = (b a)^3 = b a
|
11,303 |
\frac{c}{g^2} = \frac{c}{g^2}
|
6,403 |
d + \frac{1}{d}(8m + (-1)) = (m*8 + d^2 + (-1))/d
|
-1,688 |
-\pi\cdot \frac56 = \pi\cdot 5/12 - \frac14\cdot 5\cdot \pi
|
21,614 |
25 \cdot u^2 - 10 \cdot u + 1 = ((-1) + 5 \cdot u)^2
|
-10,784 |
\frac{1}{16 \cdot z^3} \cdot 8 \cdot \frac55 = \frac{40}{z^3 \cdot 80}
|
14,734 |
3 \cdot y + 4 = 1 + \left(1 + y\right) \cdot 3
|
11,038 |
584640 = \dfrac{1}{2!*2!}*10! - \frac{9!}{2!} + 9!/2! + 8!
|
15,646 |
\frac{1}{y + 2} = \frac{y + 2*(-1)}{4*(-1) + y^2}
|
12,318 |
|\xi| \gt \frac{\mathrm{d}z}{\mathrm{d}t} = 0 \implies \xi = z
|
15,373 |
\sqrt{\frac{1}{2}\cdot 3} = \frac{\sqrt{6}}{2}
|
-4,319 |
\dfrac{3}{3 \cdot 4} \dfrac{n^4}{n} = 3/12 n^4/n
|
512 |
\cos{A} \cdot \sin{X} + \cos{X} \cdot \sin{A} = \sin(X + A)
|
27,410 |
f = f\cdot f\cdot h \implies f = h
|
24,752 |
-3/a + \frac8x = 1 \implies -x*3 + 8a = xa
|
18,562 |
f^5 = d^4 \Rightarrow f = (\frac{d}{f})^4
|
49,318 |
1 + 1/2 + 1/3 + \frac14 + 1/5 + \frac16 + 17 + 1/8 + ... ... \geq 1 + \frac12 + \frac14 + 1/4 + \dfrac18 + 1/8 + 1/8 + \frac{1}{8} + ... = 1 + \frac{1}{2} + 1/2 + 1/2 + ... = \infty
|
-24,892 |
\frac{2}{15} = \dfrac{1}{12 \pi}s*12 \pi = s
|
5,049 |
4\cdot l + 64 + 48\cdot (-1) rightarrow l = -4
|
9,059 |
(g + d)*\left(g - d\right) = g^2 - d^2
|
31,351 |
\pi\cdot 2\cdot (1 - 1/2) = \pi
|
-562 |
(e^{\pi \times i/3})^3 = e^{3 \times \pi \times i/3}
|
13,415 |
(-1/2)^{1/(\dfrac{1}{2})} = (-\frac12)^{\frac{1}{\dfrac{1}{2}}} = (-1/2)^2 = \dfrac14
|
-19,467 |
\frac{3 \cdot \frac12}{1/3 \cdot 8} = \dfrac{3}{2} \cdot \frac{3}{8}
|
-2,889 |
3 \sqrt{11} = \left(5 + 2 (-1)\right) \sqrt{11}
|
32,349 |
0 = e^2\cdot 0
|
7,736 |
7/11 = 1 - \frac{4}{11}
|
-23,013 |
\dfrac{50}{40} = \frac{10 \cdot 5}{10 \cdot 4}
|
23,496 |
\sin(-x + q) = -\sin(x)\cdot \cos\left(q\right) + \sin(q)\cdot \cos\left(x\right)
|
-18,372 |
\dfrac{1}{7X + X^2}\left(7 + X^2 + X\cdot 8\right) = \frac{1}{X\cdot \left(X + 7\right)}(X + 1) (X + 7)
|
31,988 |
4*\frac{1}{1 + 3*\left(-1\right)}*(1 - 3^m) = 4*\frac12*(3^m + \left(-1\right)) = 2*3^m + 2*(-1)
|
683 |
x^2 + 4\cdot x + 5\cdot \left(-1\right) = x^2 + 4\cdot x + 4 + 9\cdot (-1) = (x + 2)^2 + 9\cdot (-1) = (x + 2)^2 - 3 \cdot 3
|
6,333 |
a\cdot f\cdot c = (a + f + 2\cdot a\cdot f)\cdot c = a + f + 2\cdot a\cdot f + c + 2\cdot a\cdot c + 2\cdot f\cdot c + 4\cdot a\cdot f\cdot c
|
23,621 |
1 + \left(-1\right) + 2 \cdot \cos^2(x) = 0 + 2 \cdot \cos^2(x) = 2 \cdot \cos^2(x)
|
-1,987 |
\pi = 5/12\times \pi + 7/12\times \pi
|
15,935 |
0 = \frac{1}{0 + 2}\times (2^0 + (-1))
|
19,635 |
\frac{\pi}{3} + \pi = \pi*4/3
|
37,952 |
\left(3\cdot y^3\right)^{10} = 3^{10}\cdot y^{30}
|
33,608 |
(\left(-1\right) + 6^2)/12 = 35/12
|
-20,955 |
100/70 = \frac{10}{10}*\tfrac{1}{7}*10
|
26,200 |
1/(z*x) = \frac{1}{x*z}
|
-13,016 |
5\times (-1) + 18 = 13
|
-25,292 |
-\frac{1}{x^{10}} \cdot 9 = \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{x^9}
|
8,888 |
(1 + n)*\left((-1) + n\right) = n^2 + (-1)
|
-9,144 |
z^2*20 = z*2*2*5*z
|
21,275 |
\left(x + 1\right)! = \left(x + 1\right)\cdot x\cdot ...\cdot 2
|
9,361 |
E(Z\times C) = 0 = 0\times E(C) = E(Z)\times E(C)
|
39,953 |
37928 = 2 \cdot 2 \cdot 2 + 7^3 + 25^3 + 28^3
|
35,512 |
56 = \binom{8}{3}\cdot \binom{2}{0}
|
6,615 |
\cos{z} = \sin{z} \implies (e^{i\cdot z} - e^{-z\cdot i})/(2\cdot i) = \left(e^{-z\cdot i} + e^{i\cdot z}\right)/2
|
9,896 |
-a + a*a*g = \frac{1}{-\frac1a + \dfrac{1}{a - 1/g}}
|
-5,648 |
\frac{3}{2 \cdot t + 18 \cdot \left(-1\right)} = \frac{3}{\left(t + 9 \cdot (-1)\right) \cdot 2}
|
34,949 |
190 = \frac{19}{2} \cdot 20
|
24,145 |
-8 = a + b \Rightarrow -2 = a - b
|
23,918 |
\frac{1}{400}*300 = 300*1/100/(400*\dfrac{1}{100}) = \frac{3}{4}
|
8,256 |
26 = \frac{1}{2 + (-1)}\times (30 + 4\times \left(-1\right))
|
8,566 |
5^{x \cdot 2} - 5^x = 6 \Rightarrow 6 = 5^x \cdot (5^x + (-1))
|
11,981 |
\sin{3*x} = -4*\sin^3{x} + 3*\sin{x}
|
-25,502 |
\frac{d}{dt} (-\cos(\pi \cdot t) \cdot 2) = 2 \cdot \sin(t \cdot \pi) \cdot \pi
|
27,241 |
2 \cdot 4 \cdot 6 \cdot \dotsm \cdot 2 \cdot x = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot \dotsm \cdot 2 \cdot x
|
1,335 |
\dfrac{1}{z^r} = z^{-r}
|
9,000 |
\sqrt{z \cdot z - 5\cdot z + 4} = \sqrt{(z + (-1))\cdot (z + 4\cdot (-1))} = \sqrt{z + (-1)}\cdot \sqrt{z + 4\cdot (-1)}
|
1,747 |
3 \times \left(-1\right) + k^2 + k \times 2 = \left((-1) + k\right) \times (k + 3)
|
-1,868 |
0 = -\frac{19}{12}\cdot \pi + \pi\cdot \frac{19}{12}
|
36,499 |
c_G = c_G
|
17,384 |
1 + z^2 - z = \left(z - 1/2\right) \cdot \left(z - 1/2\right) + \frac34
|
43,418 |
90720 = 105840 + 15120 \cdot (-1)
|
26,502 |
x*e = h_2*h_1 \implies h_1 = x,h_2 = e
|
3,592 |
\sin{Y} \cdot \cos{30} \cdot Z \cdot 2 = x_3 - x_1\Longrightarrow \frac{1}{3^{1/2}} \cdot (x_3 - x_1) = Z \cdot \sin{Y}
|
-24,648 |
45 = 44 + 1
|
-15,857 |
-\frac{1}{10}80 = 10/10 - \tfrac{9}{10}*10
|
-29,339 |
(2 \cdot x + 5) \cdot \left(2 \cdot x + 5 \cdot (-1)\right) = (2 \cdot x)^2 - 5^2 = 4 \cdot x^2 + 25 \cdot (-1)
|
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