id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-10,599 |
\dfrac{\frac{1}{3}\cdot 3}{s + 3 (-1)} = \dfrac{3}{s\cdot 3 + 9 (-1)}
|
45,025 |
3 \cdot 18 - 2 \cdot 26 = 2
|
12,732 |
-2 \times 8 + 17 = 1
|
19,067 |
2.5 = \frac14 + \frac14*2 + 3*1/4 + 1/4*4
|
24,324 |
\frac{1}{(1 + 5 + 4 \cdot (-1)) \cdot 3} \cdot 18 = 3
|
29,663 |
4464 = 9000 - 9 \cdot 9 \cdot 8 \cdot 7
|
-20,067 |
7 p \cdot 1/(7 p)/8 = \frac{p \cdot 7}{p \cdot 56}
|
13,814 |
\dfrac{1}{-1/D + 1/B} = D*(\frac{1}{-B + D} - 1/D)*D
|
3,198 |
166 = -\binom{7 + 4 + (-1)}{4 + (-1)} + \binom{(-1) + 10 + 4}{4 + \left(-1\right)}
|
-30,294 |
4\cdot \pi/3 = \pi + \pi/3
|
18,214 |
120 = g^2 - b^2 = (g + b) \times (g - b)
|
31,052 |
(y^4 + 1 - y^2) \cdot (1 + y \cdot y) = 1 + y^6
|
14,286 |
-1 = \cos(r) + \cos\left(2*r\right) = \cos(r) + 2*\cos^2\left(r\right) + (-1)
|
14,589 |
\frac{1/x\cdot f_1}{f_2\cdot \frac1g} = f_1\cdot g/(x\cdot f_2)
|
4,627 |
3\cdot (-1) + (2\cdot (-1) + \mathbb{E}(2^{-\rho}))^2 = 0 \Rightarrow \mathbb{E}(2^{-\rho}) = -\sqrt{3} + 2
|
-30,343 |
0 = (x \cdot p_0)^2 + 3 \cdot x \cdot p_0 + 18 \cdot (-1) = (x \cdot p_0 + 6) \cdot (x \cdot p_0 + 3 \cdot (-1))
|
18,953 |
(-1) + 29^{32} = (1 + 29^{16}) (\left(-1\right) + 29^{16})
|
-18,966 |
\dfrac{1}{18}*7 = \dfrac{A_s}{100*\pi}*100*\pi = A_s
|
-5,904 |
\dfrac{1}{p^2 - 5\cdot p + 6}\cdot 5 = \frac{5}{\left(p + 3\cdot (-1)\right)\cdot (2\cdot (-1) + p)}
|
30,655 |
(g + c)^2 = 2*c*g + g^2 + c^2
|
21,517 |
328125000 = 1^3\cdot 5^4\cdot 4200\cdot 5^3
|
24,591 |
(5 + x) \times (1 + 2 \times x) = 2 \times x \times x + 11 \times x + 5
|
-20,565 |
\frac{9 + 4*a}{-3*a + 6}*\frac55 = \frac{45 + a*20}{-a*15 + 30}
|
30,834 |
\operatorname{atan}(-\infty) = -\frac{1}{2}\times \pi
|
20,652 |
s^2 - q^2 = (s - q) (q + s)
|
-20,764 |
7/7 \cdot \frac{1}{s + 4} \cdot (s + 7) = \dfrac{49 + 7 \cdot s}{7 \cdot s + 28}
|
9,284 |
\frac{h \cdot g_2}{x \cdot g_1} = h/(g_1) \cdot g_2/x
|
4,786 |
\tfrac{\frac{1}{2}*\pi^2}{\pi} = \pi/2
|
1,899 |
a^2 + b + 2*a*\sqrt{b} - 2*a*\sqrt{b} + a^2*2 = -a^2 + b
|
-19,428 |
\frac15*7/(\frac{1}{5}*7) = \frac{7}{5}*5/7
|
-10,481 |
-\tfrac{1}{15 + q\cdot 6}\cdot \left(6 + 15\cdot q\right) = 3/3\cdot (-\frac{2 + q\cdot 5}{5 + 2\cdot q})
|
24,317 |
g/d + a/b = 0 + \frac{1}{d b} (d a + b g)
|
15,626 |
1885 = 6^2 + 43^2 = 21 \cdot 21 + 38 \cdot 38 = 11 \cdot 11 + 42 \cdot 42 = 27^2 + 34^2
|
30,518 |
(1 - h^2)^{\frac{1}{2}}\cdot 9^{\frac{1}{2}} = \left(9 - 9\cdot h^2\right)^{\frac{1}{2}}
|
9,217 |
0 < -t \Rightarrow 0 > t
|
11,918 |
x*Y = (x^{1/2}*Y^{1/2})^2
|
31,612 |
0 = m^2 - m*12 + 32 \Rightarrow m = 4,8
|
32,889 |
\mathbb{E}\left[Y \cdot X\right] = \mathbb{E}\left[X\right] \cdot \mathbb{E}\left[Y\right]
|
20,087 |
{4 \choose 2} \cdot 2 \cdot 9! - 24 \cdot 8! = 84 \cdot 8!
|
2,936 |
\frac{1}{2}(-d^2 + g \cdot g) = \dfrac{g^2}{2} - d^2/2
|
16,936 |
(a + x)*(a - x) = -x^2 + a * a
|
18,404 |
5^2 \times \binom{6}{2} \times 5^4 = 5^6 \times \binom{6}{2}
|
-20,061 |
\frac{p \cdot (-8)}{(-8) \cdot p} \cdot (-\frac31) = \dfrac{24 \cdot p}{\left(-8\right) \cdot p}
|
1,598 |
\binom{x}{x - i} = \frac{x!}{(x - i)!\cdot (x - x - i)!} = \tfrac{x!}{(x - i)!\cdot i!} = \binom{x}{i}
|
7,712 |
\tfrac{2}{5} = \frac{1}{50}\cdot 20
|
-4,712 |
-\frac{2}{(-1) + z} - \frac{3}{z + 2} = \frac{(-1) - z\cdot 5}{z \cdot z + z + 2\cdot (-1)}
|
14,480 |
X \cdot Y = A \Rightarrow A = X \cdot Y
|
-11,903 |
\frac{9.797}{100} = 9.797*0.01
|
14,598 |
|z + 2 \cdot (-1)| \cdot 4 = |8 \cdot (-1) + 4 \cdot z|
|
997 |
c^2*a^2 = (a*c)^2
|
6,675 |
(f + g)^2 = g^2 + f \cdot f + 2 \cdot f \cdot g
|
-18,334 |
\frac{a\cdot (a + 9)}{(9 + a)\cdot (a + 9\cdot (-1))} = \frac{9\cdot a + a^2}{81\cdot (-1) + a^2}
|
17,279 |
\left(z^2 - 2 \times z + 4 \times \left(-1\right)\right) \times (z + 2) = z^3 - 8 \times z + 8 \times (-1)
|
15,981 |
1 - \sin(x) = 1 - \cos(\pi/2 - x) \approx \frac{1}{2} \cdot (x - \pi/2) \cdot (x - \pi/2)
|
1,522 |
(z_2 - z_1) \left(z_2^{(-1) + m} + z_1 z_2^{2(-1) + m} + \dotsm + z_2 z_1^{m + 2\left(-1\right)} + z_1^{m + \left(-1\right)}\right) = -z_1^m + z_2^m
|
7,358 |
\left(k + 2\right)! = (k + 1 + 1)\cdot (k + 1)!
|
29,053 |
\frac{9}{2 \cdot \dfrac15} \cdot 1/40 = \frac{45}{80} = \dfrac{9}{16}
|
-28,767 |
-\frac{2}{1 + x} + x^2 - x + 2 = \dfrac{1}{1 + x}\cdot (x + x^3)
|
12,380 |
2 \cdot I = \pi \Rightarrow \pi/2 = I
|
34,026 |
(m + 1)\cdot m! = (1 + m)!
|
-5,142 |
10^7 \cdot 38.8 = 38.8 \cdot 10^{3 + 4}
|
-27,579 |
\frac{\text{d}z}{\text{d}x} = \tfrac{(-1) \cdot \left(6 \cdot x^2 - 5 \cdot z\right)}{(-1) \cdot (5 \cdot x + 2 \cdot z)} = \frac{6 \cdot x^2 - 5 \cdot z}{5 \cdot x + 2 \cdot z}
|
11,689 |
2\cdot 2^k=2^{k+1}\;...)\implies
|
39,623 |
\mathbb{P}\left(B\right) = \mathbb{P}\left(B\right)
|
15,676 |
a^{\frac{1}{6}}\cdot a^{\frac{1}{3}} = a^{1/6}\cdot a^{\tfrac{1}{3}} = \sqrt{a}
|
113 |
4\cdot (1!\cdot \binom{9}{1} + 2!\cdot \binom{9}{2} + \dotsm + 9!\cdot \binom{9}{9}) = 3945636
|
-15,234 |
\dfrac{x^8}{c^2 \cdot \frac{1}{x^5}} = \frac{1}{\dfrac{1}{x^5} \cdot c \cdot c \cdot \frac{1}{x^8}}
|
34,924 |
\vartheta_{x_i}/2 = \vartheta_{x_i}
|
16,173 |
\sin(\frac{π}{6}) = \dfrac12
|
14,269 |
3\cdot 33 + 3/3 + \frac{3}{3} - \tfrac{3}{3} = 99 + 1 + 1 + (-1) = 100
|
255 |
\left((-1) + 3\right)\cdot 2^1 = 4
|
5,059 |
\frac1q \cdot ((-1) \cdot p) = -\frac{p}{q}
|
33,454 |
\left|{A \cdot B}\right| = \left|{A}\right| \cdot \left|{B}\right| = \left|{B \cdot A}\right|
|
-3,413 |
(5 + 3 + 2)\cdot 7^{1/2} = 10\cdot 7^{1/2}
|
23,425 |
\cos\left(v - x\right) - \cos(x + v) = 2\cdot \sin{v}\cdot \sin{x}
|
-25,470 |
\frac{\mathrm{d}}{\mathrm{d}x} (-x \cdot 7 + \cos{x}) = -\sin{x} + 7 \cdot (-1)
|
3,736 |
\frac{12}{30} = \dfrac25
|
25,681 |
\frac{1}{4} (\pi \cdot (-1)) = \tan^{-1}(-1)
|
21,736 |
\gamma = q\gamma_1 n + \gamma_2 n rightarrow \frac{\gamma}{n} = \gamma_2 + \gamma_1 q
|
2,843 |
4/2 + 8/2 = \frac{1}{2} \cdot (4 + 8) = 12/2
|
8,713 |
994 = \frac{1}{2 + \left(-1\right)} \cdot \left(1000 + 6 \cdot (-1)\right)
|
27,794 |
l*0 = l + (-1)^l*0 = l = 0 + (-1)^0 l = 0l
|
-14,838 |
83 + 88 + 87 + 93 + 79 = 430
|
10,590 |
(z + 1/z)^3 - 3\cdot (z + 1/z) = z^3 + \frac{1}{z^3}
|
12,554 |
\frac{1}{\sqrt{1 + p} + 1} = (\sqrt{1 + p} + (-1))/p
|
32,847 |
z^4 + 1 = \left(1 + z^2 - 2^{\frac{1}{2}} z\right) (1 + z^2 + 2^{1 / 2} z)
|
9,961 |
-\cos(x) = \int \sin\left(x\right)\,\mathrm{d}x
|
7,459 |
3*2*π/5 + 2*π/5*2 = π*2
|
-29,460 |
10 - 3*2 = 10 + 6*\left(-1\right) = 4
|
25,575 |
4 (-1) + a_n^2 = 2 (-1) + a_{1 + n} \Rightarrow \tfrac{2 (-1) + a_{n + 1}}{2 (-1) + a_n} = a_n + 2
|
-7,787 |
(28 - 44\cdot i - 56\cdot i + 88\cdot \left(-1\right))/20 = \frac{1}{20}\cdot \left(-60 - 100\cdot i\right) = -3 - 5\cdot i
|
12,121 |
2*x/(3*x) - \dfrac{1}{x*3}*6 = \frac13*2 - 2/x
|
-18,555 |
5y + 9(-1) = 2*\left(4y + 3(-1)\right) = 8y + 6\left(-1\right)
|
3,893 |
0 = 6\cdot x + c_1\cdot 3 \Rightarrow c_1 = -x\cdot 2
|
10,603 |
\dfrac{u}{u + 3 \cdot \left(-1\right)} = \frac{u + 3 \cdot \left(-1\right) + 3}{u + 3 \cdot (-1)} = 1 + \dfrac{3}{u + 3 \cdot (-1)}
|
35,513 |
3 = 2 + \cos{2\cdot \pi\cdot 4}
|
-4,838 |
10^2 \cdot 10\cdot 4.0 = 4\cdot 10^{4 - 1}
|
-1,641 |
\frac14 \cdot 3 \cdot \pi = \pi \cdot \frac{11}{4} - \pi \cdot 2
|
1,226 |
1/9 = \frac122/3 \cdot 1/3
|
34,389 |
x \cdot 6 + 6 = x \cdot 6 + 3 \cdot 2
|
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