id
int64 -30,985
55.9k
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stringlengths 5
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|---|---|
-20,091 |
45\cdot y/\left(y\cdot (-35)\right) = -\frac17\cdot 9\cdot \dfrac{y\cdot (-5)}{\left(-5\right)\cdot y}
|
-25,998 |
-5 = \frac{1}{-2} \cdot 10
|
34,389 |
6\cdot l + 6 = 6\cdot l + 3\cdot 2
|
-7,172 |
\tfrac{1}{9} \cdot 4 = 4/9
|
-20,778 |
\frac{7}{n + 4}\cdot 5/5 = \frac{1}{5n + 20}35
|
17,795 |
\dfrac{\dfrac{g_1}{x} + y}{y + g_2/c}\cdot \frac1c\cdot x = \frac{g_1 + y\cdot x}{y\cdot c + g_2}
|
17,900 |
(h^x Xc)^x = c^x X^x h = c^x Xh
|
-20,580 |
5/5*\dfrac{3*(-1) + n}{n*2 + 2*(-1)} = \frac{5*n + 15*(-1)}{10*n + 10*\left(-1\right)}
|
33,700 |
\binom{(-1) + S + 8 \left(-1\right) + 4}{(-1) + 4} = \binom{5 (-1) + S}{3}
|
21,683 |
2x=0\Rightarrow x=0\\y=3-x\\y=0
|
19,366 |
|z| \gt 1 \Rightarrow 1 > 1/|z|
|
22,154 |
y_2/6 + \frac{1}{10}*Y + \frac{1}{7.5}*y_1 = 3 \Rightarrow 90 = y_2*5 + Y*3 + 4*y_1
|
-19,669 |
\tfrac{10}{5} = 10/5
|
22,756 |
|x_1|/|x_2| = |\frac{1}{x_2} \cdot x_1|
|
126 |
\cos{\theta/2} = \frac{\sin{\theta}}{\sin{\theta/2} \cdot 2}
|
20,447 |
x \cdot a_1 \cdot a_2 = a_1 \cdot a_2 \cdot x
|
12,755 |
n^4 + \left(-1\right) = (n^2 + 1)\cdot ((-1) + n^2)
|
18,296 |
t/x\cdot \binom{\left(-1\right) + t}{x + (-1)} = \binom{t}{x}
|
-2,110 |
\pi \tfrac{1}{12}17 - \pi \frac{1}{3}5 = -\frac{\pi}{4}
|
31,713 |
2 = -2 z + y \Rightarrow -2 = -y + z\cdot 2
|
-23,493 |
\dfrac{4}{5}\cdot 5/6 = \frac23
|
5,897 |
3*(x + 3) = x*3 + 3*3
|
34,858 |
10^{\left(k + 1\right)^2} = 10^{k^2 + 2\cdot k + 1} = 10^{k \cdot k}\cdot 10^{2\cdot k + 1}
|
293 |
7 = 5\cdot y + 20 - 24\cdot y rightarrow 7 = -y\cdot 19 + 20
|
37,854 |
1/9 = \dfrac{1}{10} + \tfrac{1}{100} + 1/1000 + \dots
|
4,345 |
i\cdot \sin{x} + \cos{x} = e^{x\cdot i} \Rightarrow \left(e^{-i\cdot x} + e^{x\cdot i}\right)/2 = \cos{x}
|
4,388 |
\tfrac{1}{g_2} - \tfrac{1}{g_1} = g_1/(g_2\cdot g_1) - \frac{1}{g_2\cdot g_1}\cdot g_2 = \frac{g_1 - g_2}{g_2\cdot g_1}
|
13,574 |
(\sqrt{3} - 1)/4 = -1/4 + \tfrac{1}{4}\times \sqrt{3}
|
14,920 |
d/dx (-x^2) = -2 \cdot x
|
26,314 |
-\frac{1}{a} = \frac{1}{(-1) a}
|
17,425 |
\frac{1}{m + 1} m + m^2 - m = \frac{m m^2}{m + 1}
|
16,266 |
5\cdot \tan^2(π/10) + 10\cdot \left(-1\right) + \cot^2(\frac{π}{10}) = 0
|
1,205 |
\sin{z} = \tan{z} \times \cos{z}
|
-16,550 |
7 \cdot \sqrt{99} = \sqrt{9 \cdot 11} \cdot 7
|
34,573 |
B^k \cdot A^0 \cdot B^0 \cdot A^l = B^k \cdot A^l
|
-20,524 |
\frac{1}{(-3) \cdot p} \cdot (4 \cdot p + 10 \cdot (-1)) \cdot \frac33 = \frac{1}{(-9) \cdot p} \cdot \left(p \cdot 12 + 30 \cdot \left(-1\right)\right)
|
-1,834 |
\pi\times \dfrac{1}{12}\times 13 + 11/6\times \pi = 35/12\times \pi
|
18,500 |
l\cdot \binom{p}{l} = p\cdot \binom{p + (-1)}{\left(-1\right) + l}
|
16,941 |
0 = -\tfrac{7*6}{7} + 6
|
-10,317 |
-\dfrac{40 + 40 \cdot m}{30 \cdot (-1) + m \cdot 30} = -\frac{4 \cdot m + 4}{m \cdot 3 + 3 \cdot (-1)} \cdot 10/10
|
20,523 |
\frac14 \cdot \pi + 3 \cdot \pi/2 = \dfrac{7}{4} \cdot \pi
|
-3,657 |
\frac{x^4}{x^2 * x} = \frac{x*x*x*x}{x*x*x} = x
|
30,500 |
\left\lceil{x + \left(-1\right)}\right\rceil = \left\lceil{x}\right\rceil + (-1)
|
23,899 |
\frac{a}{a} = \frac1a*a = a
|
5,871 |
x/(y\cdot 1/z) = z\cdot x/y
|
6,396 |
(\frac{v b}{v})^x = b^x v^x v^{-x}
|
21,090 |
\frac{1}{7 \cdot 1/2} = \frac{1}{7} \cdot 2 \approx 0.285714
|
2,117 |
h + 1 - j + \left(-1\right) = 2 + h - j
|
38,391 |
2^2 \cdot 2 \cdot 37 = 296
|
12,558 |
60 = 30\cdot q \Rightarrow q = 2
|
14,299 |
{6 \choose 2} \times {4 \choose 1} \times 3! \times {5 \choose 2} = 3600
|
13,502 |
\tfrac{1}{x^2} = \frac{1}{x^2 * x}*x
|
23,953 |
30 + 20 + 12 - 10 + 6 + 4 + 2 = 62 + 20*(-1) + 2 = 44
|
4,758 |
\frac{h + s/2}{1/2 \cdot s} = \frac{1}{s} \cdot (2 \cdot h + s)
|
3,122 |
\dfrac{\sqrt{17}}{2}*\left(10 + 12\right) = 11*\sqrt{17}
|
-20,891 |
-\dfrac94 \frac{-8x + 7(-1)}{-x\cdot 8 + 7(-1)} = \frac{63 + 72 x}{28 (-1) - x\cdot 32}
|
3,900 |
\frac{1}{y \times y + 4}\times 2 = \frac{8}{64 + y \times y} \Rightarrow y = 4
|
28,252 |
\cos{2 \cdot (y + (-1))} = \cos(2 \cdot \left(-1\right) + 2 \cdot y)
|
-21,969 |
-\dfrac{5}{2} - 6/10 = -5\cdot 5/(2\cdot 5) - 6/(10) = -25/10 - 6/10 = -(25 + 6\cdot \left(-1\right))/10 = -\tfrac{31}{10}
|
13,902 |
\tfrac{21}{7} = 3
|
21,159 |
\cos{\theta\cdot 2} = -\sin^2{\theta} + \cos^2{\theta}
|
30,831 |
44 = 4 \cdot 4\cdot 1/4\cdot 11
|
12,012 |
-\frac{-1}{2\cdot (1 + 1 + 1)} + 1 - -\dfrac{1}{2\cdot (1 + \left(-1\right) + 1)} = \dfrac53
|
11,333 |
|E \cdot B| = |B| \cdot |E|
|
15,473 |
(z^3)^2 = z^6 = z^2 \cdot z^2 \cdot z^2
|
32,502 |
21 = {2 + 6 + \left(-1\right) \choose \left(-1\right) + 6}
|
26,113 |
X^{2001} = (X^3)^{667}
|
18,354 |
\cos(2\cdot y) = \cos^2(y) - \sin^2\left(y\right) = 2\cdot \cos^2(y) + (-1) = 1 - 2\cdot \sin^2(y)
|
-3,614 |
\dfrac{1}{q \cdot q}\cdot q^5\cdot 16/4 = \frac{16}{q^2\cdot 4}\cdot q^5
|
13,307 |
(\sqrt{5} + 1)/2 = \dfrac12 \cdot \sqrt{5} + \dfrac12
|
26,162 |
9 = 9 + 0 \cdot 3^{1/2}
|
28,748 |
g + g - h = 2\cdot g - h
|
-11,580 |
-8 - i\cdot 6 = -9 + 1 - i\cdot 6
|
-207 |
\frac{1}{(7 + 4\cdot (-1))!}\cdot 7! = 7\cdot 6\cdot 5\cdot 4
|
24,027 |
\frac{\left(-1\right) + x}{x + 4} = \frac{4 + x}{4 + x} - \frac{1}{x + 4} \cdot 5
|
8,423 |
0 = 32*x^4 + 16*x^3 - 12*x^2 - 4*x + 1 = (2*x + 1)*\left(2*x + \left(-1\right)\right)*(8*x^2 + 4*x + (-1))
|
-8,498 |
-\frac{16}{2} = -8
|
28,362 |
x*(b + d) = d*x + b*x
|
35,379 |
(0.23\%) * (0.23\%) = 0.0023^2 = 5.29*10^{-6}
|
3,066 |
{n + 2 \choose 2} = \frac{1}{2}(n + 1) (n + 2) = \frac12\left(n^2 + 3n + 2\right)
|
-7,226 |
0 = \dfrac38\times 0
|
23,218 |
\left|{A}\right|\cdot \left|{A}\right| = \left|{A}\right|^2
|
17,687 |
5^5 = 5^4 \cdot 5
|
14,637 |
\frac{1}{|z|^n \cdot (|z|^n + (-1))} + \frac{1}{|z|^n} = \frac{1}{(-1) + |z|^n}
|
5,921 |
((-1) + 5 + 3)*G*5 = G*5*7
|
37,976 |
\left(1 + 2^{29}\right)/3 = 178956971
|
22,967 |
n\cdot 2 - n + (-1) = n + 1
|
-511 |
e^{7\dfrac{11}{12}\pi i} = (e^{11 \pi i/12})^7
|
15,775 |
1/(1/a) = \frac{1}{\dfrac1a}
|
21,912 |
(h/1000)^2\cdot 0.25\cdot 1000 = h^2/4000
|
33,585 |
(-1) + 7 = 3 + (-1) + 5 + (-1)
|
10,134 |
|w_0| = (\frac{2l}{l + 1}1)^{\frac{1}{2}} \Rightarrow l = \dfrac{w_0 * w_0}{-w_0^2 + 2}
|
-20,264 |
\dfrac{1}{-20\cdot p + 30}\cdot \left(36\cdot (-1) + 24\cdot p\right) = \dfrac{1}{6 - 4\cdot p}\cdot \left(6 - 4\cdot p\right)\cdot (-\frac{6}{5})
|
-27,707 |
\frac{\text{d}}{\text{d}z} \sin(z) = \cos\left(z\right)
|
5,090 |
2 \times \cos(\theta/2) \times \sin(\theta/2) = \sin(\theta)
|
9,968 |
26/\left(1/3*52\right) = 3/2
|
-15,682 |
\frac{z^4}{\frac{1}{z^4\cdot \dfrac{1}{r^2}}} = \frac{z^4}{\frac{1}{z^4}\cdot r^2}
|
31,506 |
\dfrac{n + (-1)}{2 \cdot n} = \frac{1}{2} \cdot (1 - \frac{1}{n}) = 1/2 - \frac{1}{2 \cdot n}
|
-3,664 |
\dfrac{9}{5\cdot n^2} = \frac{\frac15}{n^2}\cdot 9
|
-24,445 |
\frac{98}{5 + 9} = 98/14 = \frac{1}{14}98 = 7
|
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