id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
14,533 |
\dfrac{\dfrac{1}{6}}{4} = \frac{1}{24}
|
-2,474 |
-48^{1/2} + 75^{1/2} = -(16\cdot 3)^{1/2} + (25\cdot 3)^{1/2}
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-20,614 |
\frac{49 (-1) - 21 q}{-12 q + 28 (-1)} = \frac147 \frac{1}{7(-1) - q*3}(-3q + 7(-1))
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47,807 |
6*(-1) + 22.5 = 16.5
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30,517 |
0.637 = 1 - 0.3627 \cdot \dotsm
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14,913 |
\tfrac12 = \frac{1}{1 - -1}
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-5,695 |
\frac{1/4 \cdot 4}{(m + 1) \cdot (m + 9)} = \frac{1}{4 \cdot (9 + m) \cdot (m + 1)} \cdot 4
|
20,723 |
|w + \left(-1\right)| + |x + (-1)| = |w| + |x| = |w + 1| + |x + 1|
|
15,398 |
\sin(\dfrac{4\cdot \pi}{3}) = -\sin(\pi/3)
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41,574 |
{360\over120} = 3
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6,193 |
-\frac{1}{\left(2\times (-1) + m\right)^2} = \frac{\mathrm{d}}{\mathrm{d}m} \dfrac{1}{m + 2\times (-1)}
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-13,968 |
5 + (\dfrac{40}{5}) = 5 + (8) = 5 + 8 = 13
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3,339 |
\mathbb{E}\left(G \times v\right) = G \times G \times v = G \times v = G \times v
|
-3,172 |
5^{\frac{1}{2}}\cdot (4\cdot (-1) + 5) = 5^{\frac{1}{2}}
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14,204 |
\left(B_2*3 - \frac{3}{2} + 1 = 0 \implies B_2*3 = 1/2\right) \implies B_2 = 1/6
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20,708 |
\overline{F \cup \overline{H}} = H \cap \overline{F} = H \backslash F
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23,402 |
c \cdot b = b/c = b \cdot c^7
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-8,520 |
\frac149 - \frac{5}{12} = \frac{9*3}{4*3} - \dfrac{5}{12}1 = 27/12 - 5/12 = \frac{1}{12}(27 + 5(-1)) = \dfrac{22}{12}
|
24,240 |
(y + x)^2 = x \cdot x + 2xy + y^2
|
19,946 |
2 \cdot l! = 2 \cdot 1 \cdot 2 \cdot \cdots \cdot l = 2 \cdot 4 \cdot \cdots \cdot 2 \cdot l
|
35,133 |
(-a)^{2k} = (-1)^{2k} a^{2k} = 1^k a^{2k} = a^{2k}
|
895 |
x_m + h_m = x_m + h_m
|
-1,202 |
2/3 \cdot \left(-4/7\right) = \frac{\frac17 \cdot (-4)}{3 \cdot \frac{1}{2}}
|
44,540 |
\frac{π}{2} + \frac{1}{2}*π = π
|
11,679 |
4\cdot a\cdot 4\cdot a\cdot 1/2 = 8\cdot a^2
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10,384 |
2^{1 / 2} \approx 1.41\cdot \dots < 1.44 = 1.2 \cdot 1.2 = (5/4) \cdot (5/4)
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47,304 |
5! = 5\times 4\times 3\times 2
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6,674 |
\left(2 + a = |a \cdot 2 - i \cdot a| \Rightarrow 2 + 5^{\frac{1}{2}} \cdot a + a = 0\right) \Rightarrow a = -\frac{2}{5^{\frac{1}{2}} + 1}
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1,543 |
\mathbb{E}(V) \cdot \mathbb{E}(X) = \mathbb{E}(X \cdot V)
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-7,594 |
\frac{-25 + i*20}{5 - 4i} = \frac{-25 + i*20}{5 - 4i} \dfrac{1}{5 + 4i}(5 + i*4)
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28,750 |
\mathbb{E}\left(b\right)\cdot \mathbb{E}\left(f\right) = \mathbb{E}\left(b\cdot f\right) = 0 \implies 0 = b\cdot f
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19,399 |
x^2 - x + 2\cdot \left(-1\right) = (1 + x)\cdot (x + 2\cdot \left(-1\right))
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4,174 |
2\cdot \pi\cdot r^3 = \dfrac23\cdot \pi\cdot R^3 \Rightarrow r = \frac{1}{3^{\frac13}}\cdot R
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-17,777 |
12 + 10 \cdot (-1) = 2
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-20,971 |
\frac{1}{-q*7 + 4}*(-q*7 + 4)*(-\frac{5}{6}) = \frac{1}{-42*q + 24}*\left(35*q + 20*(-1)\right)
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4,378 |
2*x + 2 + 3 = 5 + x*2
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32,393 |
24 - 24*(-1) + 47 = 24*2 + 47*(-1)
|
19,990 |
97 = 0 \cdot 5! + 4! \cdot 4 + 0 \cdot 3! + 0 \cdot 2! + 0 \cdot 1! + 0!
|
3,092 |
\frac12 \cdot (a + b) = \dfrac{1}{2} \cdot (a + b)
|
23,355 |
m^3 \leq m^3\times 2 + 5\times (-1) \Rightarrow m^3 \geq 5
|
5,041 |
\frac{1}{2009} + 2/2008*\frac{2008}{2009} = 3/2009
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31,105 |
\frac{\text{d}}{\text{d}a} \tan^{-1}{a} = \dfrac{1}{1 + a^2}
|
29,551 |
a^4\cdot x = x = a^3\cdot x
|
-8,877 |
0\cdot 0\cdot 0\cdot 0\cdot 0 = 0^5
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-25,025 |
-\frac{4}{1 + x^2\cdot 16} = -4 + 64\cdot x^2 - 1024\cdot x^4 + x^6\cdot 16384 - \ldots
|
832 |
x - h - h + e - 2x = -h \cdot 2 + x \cdot 3 - e
|
7,165 |
x^{m\cdot 5} + x + 1 + x^{5\cdot m + 3} - x^{m\cdot 5} = x^{3 + m\cdot 5} + x + 1
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31,440 |
0 > z \implies |z| = -z
|
13,866 |
-\frac{4}{2} + 4/2 + \frac{1}{4} \cdot 18 = \dfrac{9}{2}
|
14,120 |
2 \cdot (2 \cdot a^2 + a \cdot 2 + 37) = 73 + (2 \cdot a + 1)^2
|
24,008 |
\dfrac{38}{7} = \frac{1}{14}*(21 + 30 + 10 + 12 + 3)
|
15,660 |
\binom{2 + 4}{4} = \binom{6}{2}
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11,536 |
\left(\left(z^2 - y^2\right)^2 + \left(2\cdot z\cdot y\right)^2\right)^{1/2} = \left((z^2 + y^2)^2\right)^{1/2} = z^2 + y \cdot y
|
-24,089 |
\frac{1}{6 + 10}\cdot 32 = 32/16 = 32/16 = 2
|
14,982 |
(-1) + 2*x = x^2 - (1 - x)^2
|
-1,707 |
\tfrac{1}{12} \cdot 29 \cdot \pi = 3/4 \cdot \pi + \tfrac{5}{3} \cdot \pi
|
27,376 |
-z\cdot \tan{a} + \tan(c + a)\cdot z = y \Rightarrow z = \dfrac{y}{\tan(a + c) - \tan{a}}
|
11,893 |
13 \cdot x = 4 + x \cdot 5 + x \cdot 8 + 4 \cdot (-1)
|
-29,497 |
10 - 9 \cdot (-6) = 10 + 54 = 64
|
1,095 |
2*f - f + 1 = 2*f - f + (-1) = f + (-1)
|
6,288 |
\cos{y} = \cos{\frac{y}{2} \cdot 2}
|
-3,664 |
\frac{9}{x^2}\cdot 1/5 = \frac{9}{5\cdot x^2}
|
-23,396 |
0.83\cdot 0.689 = 0.83\cdot 0.83\cdot 0.83 = 0.83^3
|
29,063 |
x_{l*2} = -1/(2*l) rightarrow \lim_{l \to \infty} x_{2*l} = 0
|
9,499 |
\tfrac{\frac{1}{36}*7}{\frac14} = \frac79
|
1,184 |
x/\pi \cdot \pi = x
|
20,439 |
\|\varphi_1 + \cdots + \varphi_l + \varphi_{l + 1}\| = \|\varphi_1 + \cdots + \varphi_l + \varphi_{l + 1}\|
|
27,607 |
0\cdot \cot(0) = 0 = 0
|
3,327 |
\left|{x}\right| = \left|{Z}\right| \cdot \frac{\left|{x}\right|}{\left|{Z}\right|} = \left|{Z}\right| \cdot \left|{x}\right| \cdot \left|{1/Z}\right| = \left|{Z \cdot x/Z}\right|
|
6,162 |
(q + (-1))\cdot ((-1) + p) = p\cdot q - p - q + 1
|
4,724 |
(dr)^3 = 3375 \implies 15 = dr
|
47,756 |
\frac{5^{\tfrac{1}{5}} + (5 \cdot 5)^{1/5} + ... + (5^n)^{\frac15}}{\frac{1}{5^{1/5}} + \frac{...}{\left(5^2\right)^{\frac{1}{5}}} + \dfrac{1}{\left(5^n\right)^{\frac{1}{5}}}} = \dfrac{(5^{n + 1})^{\frac{1}{5}}}{\dfrac{1}{5^{1/5}} + \frac{...}{(5^2)^{1/5}} + \frac{1}{(5^n)^{\frac{1}{5}}}}\cdot (\frac{1}{5^{1/5}} + \frac{...}{(5 \cdot 5)^{1/5}} + \frac{1}{(5^n)^{1/5}}) = (5^{n + 1})^{1/5}
|
22,264 |
1^3 = 1^2\Longrightarrow 3 = 2
|
4,460 |
6 \cdot \sqrt{34} + 35 = \frac{6 + \sqrt{34}}{-\sqrt{34} + 6}
|
42,268 |
73 = (214\cdot (-1) + 360)/2
|
8,013 |
0 = h^l = h^{l + 2 \cdot (-1)} \cdot h^2 = h^{l + 2 \cdot \left(-1\right)} \cdot h = h^{l + (-1)}
|
16,582 |
h^2 - g \times g = (g + h)\times (h - g)
|
3,580 |
4 \cdot l^2 \cdot m^2 - l \cdot l \cdot m^2 \cdot 2 = m^2 \cdot l^2 \cdot 2
|
2,615 |
(z \cdot z - \sqrt{2}) \cdot \left(\sqrt{2} + z^2\right) = z^4 + 2 \cdot (-1)
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-20,467 |
-9/2 \cdot \frac{1}{\left(-1\right) - 9 \cdot \mu} \cdot \left(-\mu \cdot 9 + \left(-1\right)\right) = \tfrac{81 \cdot \mu + 9}{2 \cdot (-1) - 18 \cdot \mu}
|
20,290 |
1.6^{\left(-1\right) + n} = 1.6 \times 1.6^{n + 2 \times \left(-1\right)}
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-22,289 |
(2*(-1) + p)*(6 + p) = p^2 + 4*p + 12*\left(-1\right)
|
977 |
x^{b + d} = x^b\times x^d
|
-3,207 |
\sqrt{7}\cdot 8 = (4 + 5 + (-1)) \sqrt{7}
|
34,707 |
x^{1/2} = (-\left(-1\right) \cdot x)^{1/2} = i \cdot (-x)^{1/2}
|
25,436 |
x^3 - y^3 + x - y = (x - y)*(1 + x^2 + x*y + y^2)
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-13,102 |
\left((-10.6)\cdot 1/(-5)\right)/(-0.4) = -\frac{1}{(-5)\cdot (-0.4)}\cdot 10.6 = -10.6/2
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6,778 |
2*(-1) + (\frac1x + x) * (\frac1x + x) = x * x + \frac{1}{x^2}
|
-6,752 |
\dfrac{2}{100} + \frac{1}{100}*70 = 2/100 + 7/10
|
32,290 |
\sin\left(E_1 + E_2\right) = \cos(E_2) \cdot \sin\left(E_1\right) + \cos(E_1) \cdot \sin(E_2)
|
-2,110 |
-5/3*\pi + \pi*17/12 = -\frac{\pi}{4}
|
6,070 |
1/\left(C_2\right) - \tfrac{1}{C_1} = \frac{C_1 - C_2}{C_1 \cdot C_2}
|
-713 |
(e^{\frac13 \cdot 5 \cdot \pi \cdot i})^{15} = e^{\dfrac{5}{3} \cdot i \cdot \pi \cdot 15}
|
-29,149 |
-16 = 0 \cdot 4 + 3 \cdot (-2) + 5 \cdot (-2)
|
15,714 |
\cos(\arctan{\zeta}) = \frac{1}{(\zeta^2 + 1)^{\frac{1}{2}}}
|
2,487 |
g^2 - f \cdot f = \left(g + f\right) \cdot (g - f)
|
5,947 |
-2\cdot y = 6\cdot e^{(-5 - 2\cdot y)/2} = 6\cdot \frac{1}{e^{5/2}}\cdot e^{-y}
|
18,121 |
D \cdot 3 + 2 - 2 \cdot D + 2 \cdot \left(-1\right) = D
|
2,061 |
\frac{\sin(z)}{\frac{1}{\cos(z)}}\tfrac{1}{\cos(z)} = \frac{\tan(z)}{\sec(z)}
|
-1,599 |
\frac{\pi}{2} - \pi/4 = \dfrac14 \cdot \pi
|
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