id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
26,684 |
\frac{\dfrac13*2*x}{\dfrac{\sqrt{1463}}{108}*2} = 36/(\sqrt{1463})*x
|
7,688 |
1/y = \overline{y}*1/\overline{y}/y = \dfrac{\overline{y}}{|y|^2}
|
18,878 |
\tfrac{5}{21} = \frac{1}{{7 \choose 2}}\left({2 \choose 2} + {2 \choose 2} + {3 \choose 2}\right)
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-20,287 |
-\dfrac{1}{r + 4} \cdot 9 \cdot 4/4 = -\frac{1}{r \cdot 4 + 16} \cdot 36
|
3,714 |
\dfrac{n!}{\left(n - -r + n\right)!\cdot (n - r)!} = \frac{n!}{(n - r)!\cdot r!}
|
36,020 |
\frac{1}{15 + 2 + 7}*15 = \frac{15}{24}
|
11,641 |
3 \cdot (-1) + 31 + 21 \cdot (-1) + 19 \cdot \left(-1\right) + 17 + 13 + 11 \cdot (-1) + 7 + 5 \cdot (-1) = 9
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-8,335 |
-12 \div -3 = 4
|
24,360 |
5 = (4^2 + 3^2)^{\frac{1}{2}}
|
12,003 |
x = \operatorname{asin}(s) = s + \dfrac{s^3}{2}*1/3 + 3/(2*4)*\frac{1}{5}*x^5
|
8,154 |
-i = \sin(\frac{\pi*3}{2}) i + \cos(3\pi/2)
|
5,736 |
\left(\dfrac14\right)^{\frac{1}{2}} = 1/2 \gt \frac14
|
3,611 |
a_{i \cdot i} = -a_{i \cdot i}\Longrightarrow 0 = a_{i \cdot i}
|
25,919 |
n^7 - n = n^7 - n^5 + n^5 - n^3 + n^3 - n = (n^4 + n^2 + 1)\cdot (n \cdot n \cdot n - n)
|
24,610 |
\tfrac{89}{55} = 1 + \frac{34}{55}
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30,192 |
20683 = 10^3 + 27^2 \cdot 27 = 19^3 + 24^3
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-6,253 |
\dfrac{t}{2*(9 + t)*(5*(-1) + t)}*2 = \frac{t}{(9 + t)*(t + 5*\left(-1\right))}*\frac{2}{2}
|
-1,634 |
-\pi*3/4 = \pi - \pi \frac74
|
17,849 |
y^{1/3} = y^{2/6}
|
-1,082 |
\frac{4}{24} = 4\cdot \frac{1}{4}/(24\cdot 1/4) = 1/6
|
6,054 |
y^3 + y^2 + y*2 + 0 = (0 + y) (y^2 + y + 2)
|
6,068 |
n \leq 4 \cdot (\sqrt{n + (-1)} + (-1))^2 = 4 \cdot \left(n + (-1) - 2 \cdot \sqrt{n + (-1)} + 1\right) = 4 \cdot n - 8 \cdot \sqrt{n + \left(-1\right)}
|
-2,273 |
\frac{1}{12}*2 = -1/12 + \tfrac{1}{12}*3
|
8,704 |
\cos(-y + z) = \cos(y)\times \cos(z) + \sin(z)\times \sin\left(y\right)
|
15,385 |
R_\lambda \cdot R_x = R_x \cdot R_\lambda = \dfrac{R_x - R_\lambda}{\lambda - x}
|
13,165 |
1729 = 10^3 + 9^2 \cdot 9 = 12^3 + 1 \cdot 1 \cdot 1
|
1,128 |
u_x + h\cdot u_W = 1 = \left( 1, h\right)\cdot ( u_x, u_W)
|
2,939 |
|7\cdot (-1) + 2| = 5
|
-10,589 |
9 = 8 \cdot x + 12 + 28 \cdot (-1) = 8 \cdot x + 16 \cdot \left(-1\right)
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46,551 |
3*1/3 = 1
|
19,809 |
\frac1y + \frac{1}{y} - \frac{1}{y^2} = \frac{2}{y} - \dfrac{1}{y \times y} < \frac{1}{y}\times 2
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51,602 |
\frac{n!}{n^n} = 2/n\cdot \dotsm\cdot (n + (-1))/n\cdot \frac{n}{n}/n \leq 1/n
|
19,187 |
\int\limits_{-h_1}^{h_1} h_2\,\text{d}z = 2\cdot \int_0^{h_1} h_2\,\text{d}z
|
-6,471 |
\tfrac{1}{\left(z + 5\right) (2(-1) + z)}4 = \frac{1}{z^2 + 3z + 10 (-1)}4
|
2,292 |
\frac{a_m \dfrac{1}{a_m}}{1/\left(a_m\right) + 1} = \frac{a_m}{1 + a_m}
|
18,593 |
1/(D\cdot t) = 1/(t\cdot D)
|
34,139 |
g*z + z*f = z*\left(f + g\right)
|
27,764 |
1 + \dfrac{1}{2}\cdot (5^{\tfrac{1}{3}} - 1) = \dfrac{1}{2} + 5^{\frac{1}{3}}/2
|
11,488 |
\|\omega \cdot x\| = \|\omega \cdot x - V \cdot x + V \cdot x\| \leq \|\omega \cdot x - V \cdot x\| + \|V \cdot x\|
|
15,398 |
\sin{4\cdot π/3} = -\sin{\frac{π}{3}}
|
21,686 |
x_r \rho_r = ((x_r + \rho_r)^2 - (x_r - \rho_r) (x_r - \rho_r))/4
|
32,713 |
3 + q^2 + (-1) = 2 + q^2
|
-7,597 |
\frac{-6\cdot i - 9}{-i\cdot 2 - 3} = \frac{-6\cdot i - 9}{-2\cdot i - 3}\cdot \dfrac{i\cdot 2 - 3}{-3 + 2\cdot i}
|
26,377 |
(x + 1)*(-x*3 + (1 + x)^2) = 1 + x^3
|
-22,248 |
x^2 - 12x + 20 = (x - 10)(x - 2)
|
5,510 |
\frac{1}{2^{(-1) + n}} = \frac{1}{2^n}*(2 + 0*(-1))
|
-5,852 |
\dfrac{5}{x\cdot 3 + 12} = \dfrac{1}{3\cdot (x + 4)}\cdot 5
|
-7,394 |
\frac{5}{39} = \tfrac{4}{13}\cdot \frac{1}{12}\cdot 5
|
18,405 |
6 = 2.3 = \left(1 + (-5)^{1 / 2}\right)*\left(1 - (-5)^{1 / 2}\right)
|
-20,506 |
-1/5*\dfrac{(-10)*k}{(-10)*k} = \dfrac{10*k}{k*(-50)}
|
-23,817 |
7 + \frac{1}{3} \cdot 21 = 7 + 7 = 14
|
17,973 |
\sin(\cos^{-1}(d)) = (1 - d * d)^{1/2}
|
10,877 |
\frac1y x = \tfrac{1}{y*1/x}
|
14,158 |
(-\sqrt{m} \cdot y + z) \cdot (\sqrt{m} \cdot y + z) = z^2 - y^2 \cdot m
|
24,678 |
1 = -(-\cosh{x} + \sinh{x}) \cdot (\sinh{x} + \cosh{x}) \Rightarrow 5 \cdot (\sinh{x} + \cosh{x}) = 1
|
13,945 |
f^y = (1/f)^{-y} = (\frac1f)^{-y}
|
737 |
b = e b e = \frac{b}{e} e
|
-15,722 |
\dfrac{{(a^{-3})^{-2}}}{{a^{5}y^{5}}} = \dfrac{{a^{6}}}{{a^{5}y^{5}}}
|
7,399 |
56 = -3 \cdot 62 + 242
|
6,706 |
(x - b)^2 = s - \tfrac{1}{s} \Rightarrow \sqrt{s - \frac{1}{s}} = |x - b|
|
9,041 |
c\frac1cb = bc/c
|
14,991 |
c\cdot b < b^2 + c^2 - b\cdot c\Longrightarrow b^3 + c^3 > b\cdot c\cdot (b + c) = b^2\cdot c + b\cdot c^2
|
7,075 |
\frac{3\cdot 17}{17\cdot 4} = \frac{51}{68}
|
17,935 |
25 + 20 (-1) = 5
|
32,657 |
-(n + \left(-1\right)) * (n + \left(-1\right)) + n^2 = (-1) + n*2
|
16,976 |
y' = 1 + x + z + x \cdot z = 1 + x + (1 + x) \cdot z \Rightarrow -(1 + x) \cdot z + y' = x + 1
|
-2,888 |
5 \cdot 3^{\frac{1}{2}} = 3^{1 / 2} \cdot \left(1 + 4\right)
|
15,213 |
A' + x = A'\times x
|
11,296 |
x^2 + v^2\cdot 3 = \left(x + v\right)^2 + \left(-x + v\right) (v + x) + (-x + v)^2
|
22,691 |
-1/2 + x = \left((-1) + 2*x\right)/2
|
658 |
\frac{x^m - j^m}{x - j} = x^{(-1) + m} + \cdots + x \cdot x\cdot j^{3\cdot (-1) + m} + j^{2\cdot (-1) + m}\cdot x + j^{m + (-1)}
|
17,565 |
4 = \left(7\times \left(-1\right) + \sqrt{65}\right)\times (\sqrt{65} + 7)/2/2
|
2,955 |
c*d + G*c = (d + G)*c
|
30,119 |
x^2 - y^2 = (x+y)(x-y)
|
-26,657 |
\left(4y + 3\right) (2 + 3y) = 6 + y^2*12 + 17 y
|
-11,081 |
(x + 10 \cdot (-1))^2 + h = (x + 10 \cdot (-1)) \cdot (x + 10 \cdot (-1)) + h = x \cdot x - 20 \cdot x + 100 + h
|
51,618 |
-7 = 1 + 8 \cdot (-1)
|
13,371 |
x*4 - 2*y = 4 \implies 2*x - y = 2
|
-20,962 |
\dfrac{5}{9} \times \dfrac{-10}{-10} = \dfrac{-50}{-90}
|
29,748 |
\frac{9900}{2} \times 1 = 4950
|
3,324 |
(x + 1)^n = (x + 1)^2\cdot \left(1 + x\right)^{2\cdot \left(-1\right) + n}
|
2,869 |
|A| = B\Longrightarrow A^2 = |A| |A| = B B = B^2
|
13,918 |
8 + y^3 = (y + 2) \cdot (y^2 - y \cdot 2 + 4)
|
10,960 |
(-\sqrt{y} + 1) \cdot (1 + \sqrt{y}) = 1 - y
|
-1,993 |
-\frac{\pi}{12} + \pi\cdot 19/12 = 3/2\cdot \pi
|
48,010 |
\sqrt{x} \sqrt{x} = x
|
3,331 |
c*h/g = \frac{c}{g}*h
|
3,422 |
e^{-\int_t^V q*p\,\mathrm{d}p} = e^{-\int_t^V p*q\,\mathrm{d}p}
|
-20,313 |
\frac{1}{28 + 20 \cdot t} \cdot \left(t \cdot \left(-20\right)\right) = \frac{1}{4} \cdot 4 \cdot \dfrac{1}{7 + t \cdot 5} \cdot (\left(-5\right) \cdot t)
|
7,039 |
\cos\left(-a + \pi/2\right) = \sin(a)
|
-18,331 |
\frac{t^2 + t \cdot 4 + 32 \cdot (-1)}{t^2 - t \cdot 4} = \frac{(8 + t) \cdot (t + 4 \cdot \left(-1\right))}{t \cdot (4 \cdot (-1) + t)}
|
-14,823 |
320 \div 4 = 80
|
24,726 |
13/204 = \frac{13}{52} \times \dfrac{1}{51} \times 13
|
12,243 |
(a - h)*(a^n + h*a^{(-1) + n} + \dotsm + a*h^{(-1) + n} + h^n) = a^{n + 1} - h^{n + 1}
|
20,568 |
(\frac12*(1 + 1) + \frac{2}{1} + 2/1)/3 = 5/3
|
19,804 |
2^4 + 2^2 + 2^2 = 2 \cdot 2 \cdot 2 + 2^3 + 2 \cdot 2^2
|
5,013 |
1*2 \ldots*((-1) + l) l*(l + 1) = (1 + l)!
|
13,428 |
h^2 + b^2 + h \cdot b \cdot 2 = (h + b) \cdot (h + b)
|
-10,737 |
-3 = 12 - 8r + 10 \left(-1\right) = -8r + 2
|
21,835 |
4^{10} = 2^{20} = 1048576 < 1.05*10^6
|
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