id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-20,377 |
\frac{20 + l\cdot 4}{25 + l\cdot 5} = \frac{l + 5}{l + 5}\cdot \frac45
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4,308 |
\binom{k}{2} = \dfrac{1}{2! \cdot (k + 2 \cdot (-1))!} \cdot k! = \frac{k}{2} \cdot (k + \left(-1\right))
|
34,798 |
\binom{m + 1}{b + 1} = \binom{m}{b + 1} + \binom{m}{b}
|
-10,651 |
\frac{36}{12\cdot \epsilon^2} = \dfrac{4}{4}\cdot \frac{9}{\epsilon \cdot \epsilon\cdot 3}
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-11,557 |
i \cdot 18 - 5 + 8 \cdot (-1) = -13 + 18 \cdot i
|
27,550 |
V_{x \cdot l} \cdot \beta_l \cdot V_{q \cdot x} = V_{q \cdot x} \cdot V_{l \cdot x} \cdot \beta_l
|
31,819 |
e^q = 1 + q + \frac{1}{2!} \cdot q^2 + \dotsm \gt q^2/2
|
5,145 |
3^{f + (-1)} = \dfrac133^f = 3^f/3 = \frac{1}{3}3^f
|
18,669 |
(y + 3 \cdot (-1)) \cdot (y + 5) - (y + 4) \cdot (y + 5 \cdot (-1)) = y^2 + 2 \cdot y + 15 \cdot \left(-1\right) - y^2 - y + 20 \cdot (-1) = 3 \cdot y + 5
|
37,118 |
{3 \choose 1} = \dfrac{3!}{1! \cdot 2!} = 3
|
15,665 |
\cos^2(w)\cdot 2 + (-1) = \cos(2w)
|
9,476 |
2^{\frac{1}{8}\cdot (m + 1)} = 2^{\dfrac18}\cdot 2^{\frac{m}{8}} > 2^{1/8}\cdot m
|
13,760 |
3^3 + 2 (-1) = 25 = 5 5
|
-15,721 |
\frac{x}{\left(k^3\cdot x^5\right)^2} = \frac{x}{k^6\cdot x^{10}}
|
31,938 |
2*B = B + B
|
-13,919 |
\frac{2}{4 + 3 \cdot (-1)} = \frac{1}{1} \cdot 2 = \dfrac{2}{1} = 2
|
14,093 |
7 + 1/8 = \frac{57}{8}
|
8,272 |
\frac{1}{1 + y^2 \times n \times n} \times n = \frac{\partial}{\partial y} \tan^{-1}(y \times n)
|
25,848 |
\mathbb{E}(Y)\cdot \mathbb{E}(X) = \mathbb{E}(Y\cdot \mathbb{E}(X))
|
-25,830 |
\frac{1}{x + 3\cdot (-1)}\cdot (x \cdot x^2 - x\cdot 4 + 15\cdot (-1)) = x^2 + 3\cdot x + 5
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-24,466 |
6 + \frac14 \cdot 36 = 6 + 9 = 6 + 9 = 15
|
8,617 |
2 \cdot (f^2 + b^2 + x^2 + (-1)) = 2 \cdot (f \cdot f + b^2 + x^2 - f \cdot b - b \cdot x - f \cdot x) = (f - b)^2 + (b - x)^2 + (x - f)^2
|
155 |
\frac{1}{b}\left((-1) a\right) = -a/b = a/((-1) b)
|
13,404 |
z^3 - 2z + (-1) = ((-1) + z^2 - z) \left(z + 1\right)
|
6,364 |
-1 \times 1 + 2^2 = 3
|
2,564 |
(k\cdot 2)^2 + (2\cdot h) \cdot (2\cdot h) = 10 \cdot 10 rightarrow 5^2 = k^2 + h^2
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29,983 |
11=0\times25+11
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-9,317 |
5a * a - a*35 = -5*7 a + 5a a
|
4,802 |
4/100\cdot z = 0.04\cdot z
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31,348 |
\dfrac{1}{10000}\cdot 9360 = 0.936 = 117/125
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6,870 |
\frac{1}{((-1) + M)!}(U - M + M + (-1))! = \frac{((-1) + U)!}{\left((-1) + M\right)!}
|
24,258 |
\int z \times z^2\times \sqrt{-z^2 + 4}\,\text{d}z = \int \sqrt{4 - z^2}\times z \times z\times z\,\text{d}z
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11,792 |
\sqrt{7} - \sqrt{6} - \sqrt{6} - \sqrt{5} = -\sqrt{6}\cdot 2 + \sqrt{5} + \sqrt{7}
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34,081 |
\cos{2*z} = \cos^2{z} - \sin^2{z} = 2*\cos^2{z} + \left(-1\right)
|
3,840 |
1 - a \cdot y \cdot y = \frac{1}{1/a} \cdot (\frac{1}{a} - y^2)
|
5,202 |
\cos(\arcsin{x}) = (1 - x^2)^{\frac{1}{2}}
|
-30,924 |
24 = -3\cdot 8 + 48
|
10,186 |
(-10 z + 7x) (7x + z*10) = 49 x^2 - z^2*100
|
-2,734 |
6^{1/2} \cdot (5 + 2 \cdot (-1)) = 6^{1/2} \cdot 3
|
10,399 |
f*D^n = D^0*D^n*f
|
13,280 |
\frac{1}{3} + 1/4 + 1/5 = 47/60
|
28,842 |
19 = 26 - (-1) + 2^2 2
|
24,873 |
\dfrac{1}{16}(1 - x) + x = 1/16 + x\cdot 15/16
|
18,621 |
\frac13 = \dfrac{1}{3}*2/2
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-20,029 |
\frac{-q*9 + 2}{5*(-1) + q*10}*\frac{1}{7}*7 = \frac{14 - q*63}{70*q + 35*(-1)}
|
16,491 |
-\frac{20}{3}\cdot y^2 + 6 + -\frac{1}{3}\cdot y\cdot (3\cdot y^2 - 17\cdot y + 24\cdot (-1)) = -y^3 - y \cdot y + 8\cdot y + 6
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-19,014 |
2/15 = \frac{D_s}{36\cdot π}\cdot 36\cdot π = D_s
|
-3,567 |
r^5/r\cdot \dfrac{96}{64} = 96\cdot r^5/(64\cdot r)
|
5,109 |
7 = 7 + 0 \cdot 3
|
52,852 |
0.35*0.28 = 0.098 = 0.98
|
-7,010 |
\frac{6}{14}*2/13 = \tfrac{6}{91}
|
10,002 |
n^{n + (-1)} + (-1) = ((-1) + n) (n^{2(-1) + n} + n^{n + 3(-1)} + ... + n + 1)
|
13,918 |
8 + y^3 = (y + 2)\cdot (4 + y \cdot y - y\cdot 2)
|
15,344 |
x - \sqrt{26} \leq 0 \Rightarrow \sqrt{26} \geq x
|
16,590 |
((-1) + y)*((-1) + x) + (-1) = y*x - x - y
|
17,712 |
l^2 - l - l + (-1) = l^2 - 2l + 1 = (l + (-1)) \cdot (l + (-1))
|
4,410 |
0 = l \Rightarrow 0 \gt \left(-1\right) + 4 l
|
2,376 |
(d + d + d)*\left(b + b + b\right) = 3*d*3*b = 3*3*d*b = 9*d*b
|
25,310 |
y = \sqrt{y}\cdot \sqrt{y} = \left(\sqrt{y}\right)^2 = y
|
26,424 |
2 + 8 + 24 + 64 + \cdots + 2^m*m = 2*((m + (-1))*2^m + 1)
|
-20,004 |
8/8 \frac{9z}{-7z + 5\left(-1\right)} = \frac{z\cdot 72}{40 \left(-1\right) - z\cdot 56}
|
16,996 |
2^{546}+1=(2^{182}+1)(2^{364}-2^{182}+1)
|
12,200 |
\frac{1}{2(x + 1)} + \tfrac{1}{2 \cdot \left(1 - x\right)} = \dfrac{1}{1 - x^2}
|
-6,482 |
\frac{1}{8}\cdot 8\cdot \frac{2}{(t + 4)\cdot (8 + t)} = \tfrac{16}{8\cdot (t + 4)\cdot (t + 8)}
|
641 |
a + a*2 + 3*a + 10 = 250 \Rightarrow a = 40
|
18,961 |
(f + 11)\cdot (u + 11) - f\cdot u = f\cdot u + 11\cdot f + 11\cdot u + 11\cdot 11 - f\cdot u = 11\cdot f + 11\cdot u + 121
|
25,585 |
w + m + x = m + x + w
|
-5,622 |
\tfrac{4}{\left(9\cdot (-1) + q\right)\cdot 3} = \frac{4}{27\cdot (-1) + q\cdot 3}
|
-3,659 |
\dfrac{5}{6\cdot q} = \frac{5}{q}\cdot 1/6
|
4,734 |
2/1 \cdot \dfrac{1}{-4} \cdot \frac{2}{1} = \tfrac{4}{-4} = -1
|
7,582 |
\sin^2(x) = \sin^2\left(x\right) = \sin(\sin(x))
|
16,934 |
1 + z\cdot y = z\cdot y + 1
|
21,474 |
\mathbb{E}[-2\cdot Z_2\cdot Z_1 + Z_1^2 + Z_2^2] = \mathbb{E}[(-Z_1 + Z_2)^2]
|
19,832 |
\frac{h*x}{d} = x*\frac{h}{d}
|
24,116 |
-e^{x + \left(-1\right)}/2 = \frac{1}{2\cdot (\left(-1\right) + x)}\cdot e^{x + (-1)}\cdot (1 - x)
|
-20,520 |
\tfrac{1}{10} 10 \left(-\dfrac{6}{5}\right) = -\frac{1}{50} 60
|
3,607 |
\dfrac{y^n}{7 + y^n} = \frac{1}{1 + \dfrac{1}{y^n}\cdot 7}
|
-27,398 |
4 \left(-1\right) + 154 = 150
|
7,212 |
e^{1 + |x - z|} = e^1 e^{|x - z|}
|
-8,996 |
13.3\% = \frac{1}{100}13.3
|
10,293 |
1587/12167 = \frac{1}{x\cdot y\cdot z}\cdot \left(x\cdot y + y\cdot z + x\cdot z\right) = \frac1x + 1/y + 1/z
|
23,388 |
\frac{1}{\frac23\cdot 3} = 1/2\cdot 3/3
|
-1,333 |
(\left(-2\right)*1/9)/(3*1/2) = \tfrac{2}{3}*\left(-\frac{2}{9}\right)
|
27,481 |
p^3 - p^2 + p^2 - p + p + \left(-1\right) + 1 = p^3
|
19,829 |
y * y + 5*y + 1 = y^2 - 6*y + 9 + 8*(-1) = (y + 3*\left(-1\right))^2 + 8*(-1)
|
20,553 |
\left(-2\right)\cdot (-1) = 2 \implies (-2)\cdot \left(-2\right) = 4
|
13,554 |
12 = -84\cdot 2 + 3\cdot \left(-84 + 144\right)
|
16,859 |
(3 + 2*l)*l + 1 = 1 + 2*l * l + l*3
|
17,861 |
\frac{1}{0\cdot (-1) + 2} = 1/2
|
12,409 |
{52 \choose 13} = \dfrac{1}{13} 52 {51 \choose 12} = 4 {51 \choose 12}
|
29,176 |
\frac{1}{14} = \frac{216}{3024}
|
14,186 |
2 \times a + c - a = c + a
|
32,637 |
0 = a^7 + 1 = \left(a + 1\right)*(a^6 - a^5 + a^4 - a^3 + a^2 - a + 1)
|
4,544 |
X \cdot n \cdot z_2 + X \cdot n \cdot z_1 \cdot a = \left(z_1 \cdot n \cdot a + z_2 \cdot n\right) \cdot X
|
16,565 |
5/2*\dfrac{2}{3} = \dfrac{1}{3}*5
|
-6,111 |
\dfrac{5}{3(q + 8)} \times \dfrac{q + 10}{q + 10} = \dfrac{5(q + 10)}{3(q + 8)(q + 10)}
|
-3,722 |
\tfrac{q^3}{q^2} = q\cdot q\cdot q/(q\cdot q) = q
|
22,778 |
\dfrac13\cdot 2 = \frac{1}{45}\cdot 30
|
17,349 |
4^{k + 1} + 4^2\cdot ((-1) + 4^{k + (-1)})/3 = 4 \cdot 4\cdot ((-1) + 4^k)/3
|
25,070 |
\left(l + \left(-1\right)\right)\cdot \left(l + \left(-1\right)\right) = l^2 - 2\cdot l + 1 > l
|
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