id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-3,033 |
3 \cdot \sqrt{11} = (1 + 2) \cdot \sqrt{11}
|
-5,131 |
\frac{0.84}{10} = \frac{1}{10}\cdot 0.84
|
29,002 |
0 = z_2 + z_3 + z_4 \Rightarrow -z_4 - z_3 = z_2
|
18,635 |
54912 = \binom{12}{2} \times \binom{4}{3} \times 13 \times 4 \times 4
|
5,472 |
(-\left(f - x\right)^2 + (f + x) \cdot (f + x))/4 = f \cdot x
|
18,120 |
\dfrac{3!}{(3 + 2 \times (-1))!} = 6
|
-744 |
e^{i \cdot \pi \cdot 7/12 \cdot 13} = (e^{7 \cdot i \cdot \pi/12})^{13}
|
-24,529 |
3 + \left(\dfrac{40}{5}\right)= 3 + (8) = 3 + 8 = 11
|
22,181 |
2\cdot (m + 1)^3 \lt 2\cdot (2\cdot m) \cdot (2\cdot m)^2 = 8\cdot 2\cdot m \cdot m^2 \leq (m + 1)\cdot 2\cdot m^3
|
-26,419 |
1/\left(390625*9765625\right) = 5^{-8 - 10} = 5^{-8 + 10 \left(-1\right)} = 1/3814697265625
|
13,023 |
3 = \dfrac{4!}{2^2\cdot 2!}
|
7,911 |
\frac{2}{3} = 2/3 \cdot (\frac{1 + 0}{1 + 0})^0
|
14,017 |
y_6 = y_5\cdot y_3 \Rightarrow |y_5\cdot y_3| = |y_6|
|
24,482 |
\sin\left(π + z\right) = \sin(π) \cos(z) + \sin(z) \cos(π)
|
9,303 |
y^3 - 4*y + 4*(-1) = (y + 3*(-1))*(y^2 + 3*y + 5) = (y + 3*(-1))*(y * y - 8*y + 5) = (y + 3*(-1))*(y + 4*(-1))^2
|
34,430 |
\frac{1}{y^l} = y^{-l}
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-20,006 |
\frac{z \cdot 80 + 48 \cdot (-1)}{z \cdot 90 + 54 \cdot (-1)} = \dfrac{8}{9} \cdot \tfrac{6 \cdot (-1) + z \cdot 10}{10 \cdot z + 6 \cdot (-1)}
|
5,636 |
(y + 3) \left(y + 2\right) \left(1 + y\right) = y \cdot y \cdot y + y^2\cdot 6 + 11 y + 6
|
6,183 |
\frac{1}{C_1\cdot C_2} = 1/\left(C_2\cdot C_1\right)
|
7,016 |
f^{x - h} = \tfrac{1}{f^h}f^x
|
8,488 |
\cos^2{\theta} = \tfrac{\cos{2\theta}}{2} + \frac12
|
24,556 |
(x^5 + x^4 + x^3 + x^2 + x^1 + x^0)\cdot (x + (-1)) = x^6 + (-1)
|
16,469 |
96 = 24 \cdot (-1) + 120
|
11,683 |
1 = |\dfrac{m_1 + 1}{1 - m_1}|\Longrightarrow 0 = m_1
|
30,411 |
\operatorname{E}\left[X - x\right]^2 = \operatorname{E}\left[X^2\right] - x \cdot \operatorname{E}\left[X\right] \cdot 2 + x^2
|
-10,287 |
\frac44\cdot \frac{10}{5\cdot (-1) + 2\cdot z} = \dfrac{40}{20\cdot \left(-1\right) + z\cdot 8}
|
-10,628 |
-\dfrac{1}{100 + 60 \cdot r} \cdot 30 = -\frac{3}{6 \cdot r + 10} \cdot 10/10
|
25,413 |
0 = z - z = z - z = \zeta - z = \zeta - z
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-6,526 |
\dfrac{2}{36 \cdot (-1) + 4 \cdot x} = \frac{2}{(x + 9 \cdot (-1)) \cdot 4}
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25,464 |
\tfrac{1}{n \cdot n + 4\cdot \left(-1\right)}\cdot 4 = \frac{n + 2 - n + 2\cdot (-1)}{(n + 2)\cdot (n + 2\cdot (-1))} = \dfrac{1}{n + 2\cdot (-1)} - \frac{1}{n + 2}
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-18,314 |
\frac{(n + 1) (3(-1) + n)}{(n + 1) (7\left(-1\right) + n)} = \dfrac{n^2 - n\cdot 2 + 3(-1)}{n^2 - n\cdot 6 + 7(-1)}
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-5,530 |
\frac{3}{(10 \cdot (-1) + t) \cdot 3} = \frac{1}{30 \cdot (-1) + t \cdot 3} \cdot 3
|
-3,435 |
\sqrt{27} - \sqrt{3} = \sqrt{9*3} - \sqrt{3}
|
4,896 |
-2/16 + q^2/4 = -1/8 + q^2/4
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-11,449 |
-8\times g - 4\times i = -4\times (-5\times g - x) = 20\times g + 4\times x
|
16,090 |
\left\lfloor{n/2}\right\rfloor = \left\lceil{\tfrac{n}{2}}\right\rceil = n/2
|
-6,352 |
\frac{3}{4 (2 \left(-1\right) + p)} = \dfrac{3}{4 p + 8 \left(-1\right)}
|
24,446 |
-1 + \dfrac{1}{\pi^2}6 = -1 + \tfrac{6}{\pi \cdot \pi}
|
28,156 |
\dfrac{1/(\sqrt{2})}{\sqrt{2}}\sqrt{2} = \frac{\sqrt{2}}{2}
|
8,277 |
e + x + b'' = e + x + b''
|
11,696 |
2 \cdot (-E[R]^2 + E[R^2]) = Var[R] \cdot 2
|
-3,561 |
\frac{\mu}{\mu^2}\cdot 6/12 = \frac{6\cdot \mu}{\mu^2\cdot 12}
|
38,207 |
24 = {3 \choose 1}*{2 \choose 1}*{4 \choose 1}
|
-20,648 |
-\tfrac{48}{-60 \cdot p + 24} = \frac{6}{6} \cdot (-\dfrac{8}{-10 \cdot p + 4})
|
17,123 |
5/6 - 1/5 = \dfrac{1}{30}*19
|
14,228 |
f - B = \frac{f^3 - B^3}{B^2 + f^2 + B*f}
|
44,667 |
\int\limits_{-\infty}^\infty e^{-y^2 - y}\,\mathrm{d}y = \int\limits_{-\infty}^\infty e^{-(y + 1/2)^2 + 1/4}\,\mathrm{d}y = e^{1/4}*\int\limits_{-\infty}^\infty e^{-(y + 1/2)^2}\,\mathrm{d}y
|
3,185 |
3\times 16 = 48
|
-4,703 |
\frac{9 - y\cdot 5}{y^2 - 3\cdot y + 2} = -\dfrac{4}{y + (-1)} - \dfrac{1}{y + 2\cdot \left(-1\right)}
|
4,066 |
\frac{x}{1 + x} + x + \dfrac{1}{x + 1} = 1 + x
|
-2,577 |
2*\sqrt{7} + \sqrt{7}*4 = \sqrt{7}*\sqrt{4} + \sqrt{7}*\sqrt{16}
|
-11,627 |
21\cdot i + 3 = -9 + 12 + i\cdot 21
|
23,286 |
\cos\left(l \times x\right) \times (1 + i \times \tan\left(l \times x\right)) = e^{i \times l \times x} = \left(e^{i \times x}\right)^l
|
-9,628 |
8\% = \dfrac{8}{100} = \tfrac{2}{25}
|
30,957 |
\sqrt{x^2 + y^2 + |y|} \cdot \|( x, y)\| = \sqrt{(x^2 + y^2 + |y|) \cdot (x^2 + y^2)} = \sqrt{x^4 + 2 \cdot x^2 \cdot y^2 + y^4 + x^2 \cdot |y \cdot |y^2| \cdot y|}
|
18,085 |
f^3 + g^3 + g^2\cdot f\cdot 3 + 3\cdot g\cdot f^2 = (f + g)^3
|
4,871 |
a_1 \cdot \frac{1}{x_1 \cdot a_1} \cdot x_1 = \frac{1}{x_1 \cdot a_1} \cdot x_1 \cdot a_1
|
8,315 |
\left((-1) + m\right)! = \tfrac{m!}{m}
|
3,827 |
\mathbb{P}(t) = t^2 + t + 1 = (t - e^{\frac23\cdot \pi\cdot i})\cdot (t - e^{((-2)\cdot \pi\cdot i)/3})
|
21,869 |
\tfrac{240}{3600} = \dfrac{1}{16} \cdot \frac{1}{15} + \frac{1}{16}
|
-16,055 |
7 \cdot 6 \cdot 5 \cdot 4 = \frac{1}{(7 + 4 \cdot (-1))!} \cdot 7! = 840
|
20,558 |
\cos(2 \times x) = 1 - 2 \times \sin^2(x)
|
-27,759 |
\frac{\mathrm{d}}{\mathrm{d}z} (2\times \tan{z}) = 2\times \frac{\mathrm{d}}{\mathrm{d}z} \tan{z} = 2\times \sec^2{z}
|
-4,641 |
\frac{1}{20 + y^2 + 9 y} (2 y + 13) = \frac{5}{4 + y} - \frac{3}{5 + y}
|
10,703 |
1 - \dfrac{1}{p + 1} = 1/(2) + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{p \cdot (1 + p)}
|
25,647 |
300 - 90 + 180 rightarrow 280*(-1) + 300 = 20
|
10,106 |
k + k \cdot k = (k^2 \cdot 4 + 4k)/4
|
-2,845 |
2^{1/2} = (3\times (-1) + 4)\times 2^{1/2}
|
12,755 |
(-1) + n^4 = ((-1) + n^2)\cdot (n^2 + 1)
|
-1,611 |
\pi\cdot \frac{1}{12}\cdot 31 = 17/12\cdot \pi + \dfrac16\cdot 7\cdot \pi
|
-1,137 |
\dfrac{\dfrac{1}{8} \cdot (-7)}{\left(-3\right) \cdot \dfrac18} = -\frac83 \cdot (-\frac78)
|
-13,790 |
6 + \tfrac12 \cdot 20 = 6 + 10 = 6 + 10 = 16
|
34,603 |
\tan{x} = 1 \implies \frac{\pi}{4} = x
|
15,879 |
\frac{\mathrm{d}}{\mathrm{d}x} (\cos(x) + \sin(x)) = -\sin(x) + \cos(x) = u \Rightarrow -\sin\left(2*x\right) + 1 = u^2
|
12,396 |
1/k * 1/k*(\dfrac{1}{k}\left((-1) + k\right))^1*2 = \frac{1}{k^3}(k*2 + 2(-1))
|
9,727 |
x^3 + a^3 + h^2 \cdot h - a\cdot h\cdot x\cdot 3 = (x^2 + a^2 + h^2 - x\cdot a - h\cdot x - h\cdot a)\cdot (h + x + a)
|
-3,567 |
\frac{p^5}{p}*\frac{96}{64} = \frac{96*p^5}{p*64}
|
27,048 |
2/3\cdot 12/17 = \frac{1}{17}\cdot 8
|
20,256 |
\cos{\pi/5} = -2*(\left(\sqrt{5} + (-1)\right)/4)^2 + 1
|
-1,375 |
-8/1 \cdot \frac75 = \dfrac{\frac{1}{5} \cdot 7}{(-1) \cdot \frac{1}{8}}
|
-17,324 |
0.174 = 17.4/100
|
11,513 |
\frac{d}{du} \tan^{-1}{u} = \frac{1}{\sec^2(\tan^{-1}{u})}
|
-22,306 |
(y + 6\cdot (-1))\cdot (5\cdot (-1) + y) = 30 + y^2 - 11\cdot y
|
10,940 |
\frac{1}{1/2\cdot \sqrt{n}}\cdot \left(-\frac{n}{2} + W_n\right) = (-n + W_n\cdot 2)/(\sqrt{n})
|
-6,517 |
\frac{1}{36 (-1) + z^2 + 5z}4 = \frac{1}{(4(-1) + z) (9 + z)}4
|
37,931 |
x\binom{\theta}{x} = \binom{\theta + (-1)}{x + \left(-1\right)} \theta
|
-1,464 |
\frac{1}{\frac14} \cdot ((-1) \cdot \frac{1}{3}) = -\frac{1}{3} \cdot \frac{1}{1} \cdot 4
|
39,833 |
2^2 \cdot 139 = 556
|
-16,003 |
9 \cdot 4/10 - \dfrac{1}{10} \cdot 6 \cdot 6 = 0
|
-15,779 |
-5/10 = -5/10 \cdot 6 + 5/10 \cdot 5
|
-19,661 |
\frac{28}{8} = \dfrac{7\cdot 4}{8}
|
3,955 |
1 \times 2 \times 3 \times 4 \times 5 = 2^2 \times 2 \times 5 \times 3
|
8,058 |
(a + \sqrt{T} \cdot b)^2 = a \cdot a + b^2 \cdot T + 2 \cdot b \cdot \sqrt{T} \cdot a
|
9,278 |
4 - 4\sqrt{x-4} + |x - 4| = 4 - 4\sqrt{x-4} + (x - 4) = x - 4\sqrt{x-4}
|
26,645 |
\cos{2\cdot y} = \cos{-2\cdot y}
|
-24,754 |
\sin(7 \pi/12) = (\sqrt{2} + \sqrt{6})/4
|
11,314 |
\cos(z) = 1 - 2\sin^2(z/2)
|
5,763 |
1/20 + \frac{1}{3} + \frac14 + \frac{1}{5} + \frac{1}{6} = 1
|
24,757 |
(-4)^2 = 4^2 = 16 = \left((-16)^{\frac{1}{2}} (-1)^{1 / 2}\right)^2
|
23,323 |
2^{1/3} = 2^{\frac{1}{3}} = \left(2^2\right)^{1/6}
|
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