id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
15,752 |
h - h\cdot x\cdot h = h - h\cdot x\cdot h
|
-2,349 |
9/12 - \dfrac{1}{12}8 = 1/12
|
22,636 |
e^{-1/4} > e^0 - 1/4 = \tfrac34 > 0.7 = \frac{3.5}{5} \gt \frac{1}{5} \cdot \pi
|
15,342 |
|c\cdot i| = \sqrt{0^2 + c^2} = c
|
1,475 |
x/z = zx^i y^j z^{k + \left(-1\right)} = x^{2i} y^j z^k
|
32,542 |
x + N = x + N
|
774 |
-n\cdot 8 + c = 2\Longrightarrow c = 8\cdot n + 2
|
-362 |
\frac{8!}{3!*(3*\left(-1\right) + 8)!} = {8 \choose 3}
|
20,409 |
(-1) + p^3 = (1 + p^2 + p)*(p + (-1))
|
-18,925 |
\frac{1}{24}\times 23 = A_s/(9\times \pi)\times 9\times \pi = A_s
|
17,594 |
7/x = 1/12 \implies x = 84
|
6,613 |
(a + c)^2 = a * a + c*a*2 + c^2
|
29,194 |
3 = 5 + 6 + 8*(-1)
|
-30,747 |
z^2*9 + 18 (-1) = (z * z + 2(-1))*9
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32,007 |
17 * 17*13^4*5^6 = 128970765625
|
20,191 |
\dfrac{1}{4} = 16/64
|
16,516 |
(z + 2)*(z + 2*(-1)) = z * z + 4*(-1)
|
-5,653 |
\dfrac{1}{(s + 9\cdot (-1))\cdot (2\cdot \left(-1\right) + s)}\cdot 3 = \dfrac{1}{s^2 - 11\cdot s + 18}\cdot 3
|
9,519 |
g^3\times d^3 = (d\times g)^3
|
12,114 |
y'^2 - y'*y + z = 0 \implies (y \pm \sqrt{y^2 - 4*z})/2 = y'
|
985 |
c^{x_1 + x_2 + \cdots + x_k} = c^{x_2}\times c^{x_1}\times \cdots\times c^{x_k}
|
26,097 |
\left(i + 1\right)^2 - i^2 = 1 + 2 i
|
-9,344 |
60 \cdot (-1) - k \cdot 90 = -k \cdot 2 \cdot 3 \cdot 3 \cdot 5 - 2 \cdot 2 \cdot 3 \cdot 5
|
14,024 |
-\frac{1}{\tau} = 5i = 25 \tau
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26,661 |
\frac{24}{64} = \frac{1}{4^4} \cdot 3! \cdot 4^{4 + 3 \cdot (-1)} \cdot {4 \choose 3}
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31,420 |
A - A - E = A \cap \overline{A \cap \overline{E}} = A \cap (E \cup \overline{A}) = A \cap E
|
17,739 |
(1 + 99 + 10 (-1)) \left(9 + 0(-1) + 1\right) (1 + 99 + 10 (-1)) = 81000
|
14,169 |
l + 4 \cdot (-1) = -7 \Rightarrow l = -3
|
45,368 |
4400 + 219 (-1) = 4181
|
11,300 |
e^{Q_1}*e^{Q_2} = e^{Q_2 + Q_1}
|
-25,802 |
\tfrac{5}{21} = \frac57 \frac{1}{3}
|
-20,324 |
\frac{z + 4 \cdot (-1)}{4 \cdot \left(-1\right) + z} \cdot (-3/2) = \frac{12 - z \cdot 3}{8 \cdot (-1) + z \cdot 2}
|
-681 |
(e^{\frac{\pi*i*4}{3}})^{13} = e^{4*\pi*i/3*13}
|
27,344 |
\cos{\frac{\pi}{4}} = \sin{\pi/4} = 1/\left(\sqrt{2}\right)
|
13,825 |
2^l + 2^{(-1) + l}\cdot \frac1p\cdot l = 2^{(-1) + l}\cdot (l + p\cdot 2)/p
|
26,935 |
\pi \cdot (z^2 + 3 \cdot z + 18 \cdot (-1)) \cdot (z + 3)/1 = (18 \cdot (-1) + z^2 + z \cdot 3) \cdot \pi \cdot \left(z + 3\right)
|
280 |
(ag)^2 = a^2 g * g
|
31,090 |
d + e = 2\cdot e + d - e
|
26,644 |
\left(2 \cdot 5 \cdot t\right)^2 + 2 \cdot 5 \cdot t = 100 \cdot t^2 + 10 \cdot t = 10 \cdot \left(10 \cdot t^2 + t\right)
|
27,471 |
2 \cdot k = \left(k + 1\right)^2 - k^2 - 1^2
|
6,099 |
1 = \frac12 + \frac{1}{3} + 1/7 + \frac{1}{42}
|
190 |
1 + \pi = \cos(\frac{1}{2}\times \pi) + \left(\frac{\pi}{2}\right)^3\times \frac{1}{\pi^3}\times 8 + 2\times \frac{\pi}{2}
|
14,338 |
-4 = 6\cdot \left(-1\right) + y\Longrightarrow 2 = y
|
22,802 |
((-8) * (-8) + 8^2 + 4^2)^{1/2} = 12
|
1,587 |
1 = -3 \cdot (1 - 1/2)^2 + 2 - 2 \cdot (-1/2 + 1)^3
|
5,337 |
\|-T_\alpha Ex/E + \frac{x}{E}\| = \|\frac{x}{E} - T_\alpha x\|
|
3,698 |
8\cdot \pi\cdot t = 2\cdot t\cdot 4\cdot \pi
|
1,309 |
\frac{z}{2 + m} = \frac{z^{m + 2}}{z^{m + 1}\cdot \frac{1}{(1 + m)!}}\cdot \dfrac{1}{(m + 2)!}
|
-1,292 |
-3/5\times 7/4 = ((-3)\times \dfrac{1}{5})/(4\times \frac{1}{7})
|
-6,702 |
20/100 + 1/100 = 1/100 + \frac{2}{10}
|
18,041 |
1 = F_2*F_1 rightarrow 1 = F_1*F_2
|
3,651 |
\theta \cdot \sigma_x = \theta \cdot \sigma_x
|
-17,333 |
0.654 = 65.4/100
|
22,338 |
(\sqrt{g} + \sqrt{c})^2 = g + c + 2 \cdot \sqrt{g \cdot c} \gt g + c
|
22,726 |
(a + b) N = aN + bN
|
13,124 |
\frac{1}{168}*5 - \dfrac{1}{40} = \tfrac{1}{840}*(25 + 21*(-1)) = \frac{1}{210}
|
-7,848 |
\tfrac{1 + 2\cdot i}{2\cdot i + 1}\cdot \frac{1}{1 - i\cdot 2}\cdot (-11 - i\cdot 3) = \frac{1}{1 - 2\cdot i}\cdot (-3\cdot i - 11)
|
6,924 |
t_i m_i = t_i m_i
|
33,200 |
2\cdot 7 = \left(\sqrt{-13} + 1\right)\cdot (-\sqrt{-13} + 1)
|
16,254 |
4 = \frac{1}{2}((-1) + 9)
|
9,117 |
1/8 + \frac{1}{2} + \frac18 + 1/4 = 1
|
10,701 |
4 + (n + 2*\left(-1\right))/2 = \frac{n}{2} + 3
|
17,108 |
\cos(2z) = (-1) + 2\cos^2(z)
|
-5,649 |
\dfrac{1}{20 \cdot (-1) + 2 \cdot p} \cdot 2 = \frac{2}{2 \cdot (10 \cdot (-1) + p)}
|
3,900 |
\frac{2}{4 + y^2} = \frac{1}{64 + y^2}\cdot 8 \implies y = 4
|
37,812 |
9/6 = \frac{3}{2 \cdot 3} \cdot 3 = \frac{3}{2}
|
52,211 |
32 = 2^{6 + \left(-1\right)}
|
21,992 |
(y \cdot 4 + 12)^{\dfrac{1}{2}} = 2 \cdot (y + 3)^{\frac{1}{2}}
|
-5,804 |
\frac{z \times 4 + 12}{36 + 3 \times z^2 - z \times 21} = \frac{1}{36 + 3 \times z^2 - 21 \times z} \times (z \times 4 + 12 \times (-1) - 6 \times z + 24 + 6 \times z)
|
25,039 |
E \cdot Z = Z - E = Z \cdot E
|
17,118 |
(n + 1) \times \left(n + (-1)\right) = n^2 + (-1)
|
-15,319 |
\frac{1}{\frac{1}{\frac{1}{k^2} \cdot p^4} \cdot p^2} = \frac{1}{p^2 \cdot \frac{1}{p^4} \cdot k \cdot k}
|
571 |
\binom{2^n}{2} + \left(-1\right) = 2^n \cdot \left(2^n + (-1)\right)/2 + (-1) = \left(2^{2 \cdot n} - 2^n + 2 \cdot (-1)\right)/2
|
12,597 |
y^d\cdot y^b = y^{b + d}
|
24,381 |
|x_1\times x_2| = |x_2|\times |x_1|
|
4,010 |
\cos{\frac{2\pi}{4}1} = 0
|
245 |
\dfrac{1}{z + 2} = y \implies z = \frac{1}{y}(1 - y*2)
|
-19,172 |
\frac{7}{24} = \dfrac{A_x}{36*\pi}*36*\pi = A_x
|
40,819 |
0.625 \cdot 2 = 1.25
|
28,283 |
-i/6 + 1 = \left(-i + 6\right)/6
|
-9,943 |
\phantom{ -\dfrac{7}{25} \times -\dfrac{1}{4} } = \dfrac{-7 \times -1 }{25 \times 4 } = \dfrac{7}{100}
|
26,829 |
\alpha \beta x = \beta \alpha x
|
-9,482 |
x*2*2*3 + 3 (-1) = 3 (-1) + x*12
|
-5,887 |
\dfrac{30}{6(3\left(-1\right) + q) (2(-1) + q)} = \frac{5}{(q + 3(-1)) (q + 2(-1))} \frac{1}{6}6
|
10,460 |
5/8 + c_2 + 1/4 = 1 \Rightarrow \frac18 = c_2
|
19,309 |
1 + \dfrac{1}{x + (-1)} = \frac{x + \left(-1\right) + 1}{x + \left(-1\right)} = \frac{1}{x + \left(-1\right)}\cdot x
|
30,093 |
3 \times 3 \times 3 + 1^3 + 5^3 = 153
|
10,384 |
\sqrt{2} \approx 1.41 \times \dotsm \lt 1.44 = 1.2^2 = \left(\tfrac{5}{4}\right)^2
|
-19,617 |
\frac{70}{9} = \tfrac{10}{9}\times 7
|
576 |
b - a = \frac14 \cdot (4 \cdot b - 4 \cdot a)
|
-1,203 |
\frac{1/7 \cdot (-9)}{8 \cdot \frac{1}{3}} = -9/7 \cdot 3/8
|
14,948 |
\tfrac{\dfrac{1}{6}/6\cdot 5}{6} = 5/216
|
-6,683 |
\frac{4}{100} + 6/10 = \frac{60}{100} + \frac{1}{100} \cdot 4
|
-10,743 |
-\tfrac{7}{5*(-1) + 3*p}*3/3 = -\tfrac{21}{15*(-1) + 9*p}
|
15,886 |
1 + 3*(x*2 + (-1)) = 6*x + 2*(-1)
|
14,060 |
N = \left\{\cdots, N, 1\right\}
|
-22,303 |
t \cdot t - 6\cdot t + 8 = (t + 4\cdot (-1))\cdot (2\cdot (-1) + t)
|
-2,267 |
\frac{5}{20} - 3/20 = \frac{2}{20}
|
485 |
(x + (-1)) (1 + x \cdot x + x) = x^3 + (-1)
|
-2,442 |
\left(4\cdot (-1) + 5 + 2\right)\cdot 7^{1/2} = 3\cdot 7^{1/2}
|
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