id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
50,849 |
\binom{10}{3} = 5!
|
22,558 |
(z + y)^2 = z^2 + 2*z*y + y * y
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43,020 |
40000 = 6 \cdot z + 3 \cdot 0.3 \cdot z = 6 \cdot z + 0.9 \cdot z = 6.9 \cdot z
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24,928 |
e^{Y + B} = e^Y e^B
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23,745 |
|a + f|^2 = (a + f)\cdot \overline{a + f} = \left(a + f\right)\cdot (\overline{a} + \overline{f})
|
-4,201 |
\frac{1}{11} 88 \dfrac{1}{t} t = \dfrac{t*88}{t*11}
|
-10,386 |
\dfrac{1}{4}*4*\left(4*a + 5*(-1)\right)/a = \frac{1}{a*4}*(20*(-1) + 16*a)
|
26,185 |
\frac12\cdot (p + \left(-1\right))\cdot (p + \left(-1\right) + 1) = p\cdot (\left(-1\right) + p)/2
|
21,809 |
\frac{\sin^2(x)}{1 + \sin^2(x)} = 1 - \frac{1}{1 + \sin^2(x)} = 1 - \dfrac{\sec^2(x)}{2 \cdot \tan^2(x) + 1}
|
39,123 |
(g + f)^2 = g \cdot g + 2gf + f \cdot f \geq g^2 + f^2
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38,508 |
A^T \cdot A = A \cdot A^T
|
7,237 |
w^2 + w + 2(-1) = (w + (-1)) (w + 2)
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-9,204 |
-65\cdot x = -x\cdot 5\cdot 13
|
19,516 |
\frac{6}{50}*48/51 = \frac{1}{2550}288
|
1,713 |
\frac{\partial}{\partial x} \left(ze^{-x \cdot x}\right) = -e^{-x^2} z x \cdot 2 + e^{-x^2} \frac{\mathrm{d}z}{\mathrm{d}x}
|
31,391 |
\cos\left(x\right)\cdot \sin(x) = \sin(\pi/2 - x)\cdot \sin\left(x\right)
|
-28,767 |
\frac{x^3 + x}{1 + x} = x^2 - x + 2 - \frac{2}{x + 1}
|
8,876 |
\frac{1}{2}\cdot e^{((-1)\cdot x)/2} = \frac{\mathrm{d}}{\mathrm{d}x} (1 - e^{\frac{x\cdot (-1)}{2}})
|
-19,209 |
\frac{1}{18} = \frac{G_q}{9\cdot \pi}\cdot 9\cdot \pi = G_q
|
15,297 |
n\cdot y - (y + 2\cdot \left(-1\right))\cdot (n + (-1)) = y + 2\cdot ((-1) + n)
|
2,651 |
G \cdot 2 = G + G
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17,519 |
g^2 + g*z*2 + z^2 = (g + z) * (g + z)
|
28,319 |
\frac{1 - y^{a_j + 1}}{-y + 1} = 1 + y + \cdots*y^{a_j}
|
5,944 |
a^2 + 4 n^2 + 4 a n = (a + 2 n)^2
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-10,591 |
5 = 10 + 2*x + 16*\left(-1\right) = 2*x + 6*(-1)
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14,452 |
g \cdot N \cdot x = g \cdot x \cdot N
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4,930 |
(3 - \sqrt{3})^4 = 252 - 144*\sqrt{3}
|
-163 |
\frac{1}{3!\cdot (10 + 3\cdot (-1))!}\cdot 10! = \binom{10}{3}
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32,896 |
A_1 A_2 = A_1 A_2
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-10,021 |
0.01 (-84) = -\frac{1}{100} 84 = -0.84
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-681 |
(e^{\pi i*4/3})^{13} = e^{13 \dfrac{4 i \pi}{3} 1}
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55,494 |
\lfloor 5.2 \rfloor=5
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-9,349 |
-n\times 30 = -n\times 2\times 3\times 5
|
22,138 |
1 - -1 - 1 = 1 + 0
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-2,701 |
4\cdot 3^{\frac{1}{2}} - 3\cdot 3^{\frac{1}{2}} = -3^{\frac{1}{2}}\cdot 9^{\frac{1}{2}} + 16^{\frac{1}{2}}\cdot 3^{\frac{1}{2}}
|
-29,569 |
-2\cdot x^3 = -\dfrac{2}{x}\cdot x^4
|
11,694 |
2\cos^2{z} + \left(-1\right) = -\sin^2{z} + \cos^2{z}
|
1,274 |
1/a = \frac{1}{a} := \dfrac1a
|
150 |
\left(\varepsilon, 0 \leq x \implies \varepsilon \cdot 2 = x \cdot 2\right) \implies x = \varepsilon
|
18,634 |
e^{1 + |-z + x|} = e^{|x - z|} e^1
|
-4,327 |
\frac{49}{35} \cdot \frac{1}{n^2} \cdot n = \frac{49 \cdot n}{35 \cdot n^2}
|
3,983 |
x^8 + 1 = x^8 + 2 x^4 + 1 - 2 x^4 = \left(x^4 + 1\right)^2 - 2 x^4 = (x^4 + 2^{\frac{1}{2}} x^2 + 1) \left(x^4 - 2^{\frac{1}{2}} x^2 + 1\right)
|
32,027 |
x\cdot y\cdot r = y\cdot r\cdot x
|
-10,308 |
\frac{1}{i \cdot 6 + 6} \cdot (14 \cdot (-1) + 2 \cdot i) = 2/2 \cdot \tfrac{1}{i \cdot 3 + 3} \cdot (7 \cdot (-1) + i)
|
20,118 |
\sin^2(x) + \cos^2(x) + \tan^2\left(x\right) = d/dx \tan(x)
|
30,240 |
1^2 + 2^2 + 3^2 + 4^2 = \left(1 + 2 + 3 + 4\right)\cdot 3
|
26,216 |
-Q \times Q + z^2 = (z - Q)\times (z + Q)
|
14,089 |
\cos{b}\cdot \sin{a} + \sin{b}\cdot \cos{a} = \sin\left(b + a\right)
|
25,504 |
0 = (6 \cdot (-1) + 7 \cdot r) \cdot (r^2 + 3) \Rightarrow r = \frac17 \cdot 6
|
28,533 |
(-1) + 2\cdot \cos^2{Y} = \cos{Y\cdot 2}
|
8,288 |
B^6 = (B^2 \cdot B)^2
|
24,917 |
(a + b)*(b + b) = (a + b)*b + (a + b)*b = a*b + b^2 + a*b + b^2
|
8,740 |
c_1*a_1 + a_2*c_2 = a_1*c_1 + c_2*a_2
|
-23,146 |
-16/27 = -8/9 \cdot 2/3
|
14,608 |
1 = 7479 - 204 \cdot 37 + 14 \cdot \left(7479 - 202 \cdot 37\right)
|
21,489 |
(g^l)^1*1^{l + (-1)} = g^l
|
27,898 |
\dfrac{1}{x + 2 \cdot (-1)} \cdot (2^x - x^2) = \frac{1}{x + 2 \cdot (-1)} \cdot (2^x + 4 \cdot (-1) + 4 - x^2) = 4 \cdot \frac{1}{x + 2 \cdot (-1)} \cdot \left(2^{x + 2 \cdot \left(-1\right)} + \left(-1\right)\right) - x + 2
|
24,144 |
2^{n + 5 \cdot (-1)} = 2 \cdot 2^{n + 6 \cdot \left(-1\right)}
|
5,129 |
z + 3 - 4\cdot (z + (-1))^{1 / 2} = z + (-1) + 4 - 4\cdot (z + \left(-1\right))^{\frac{1}{2}} = z + \left(-1\right) - 4\cdot (z + (-1))^{1 / 2} + 4 = ((z + (-1))^{1 / 2} + 2\cdot (-1)) \cdot ((z + (-1))^{1 / 2} + 2\cdot (-1))
|
43,772 |
-5/3 = -\dfrac{1}{3}5
|
24,242 |
1007 = \frac12\left(2013 + 1\right)
|
-11,472 |
-i\cdot 5 - 3 = 0 + 3\cdot (-1) - i\cdot 5
|
25,060 |
I = L \cdot L^x rightarrow L \cdot L^x = I
|
-9,983 |
28\% = \dfrac{28}{100} = \dfrac{7}{25}
|
-24,806 |
199 = \frac{1}{3}\cdot 597
|
-25,231 |
\frac{\mathrm{d}}{\mathrm{d}y} \sqrt{y^3} = y\cdot 3/2
|
-22,281 |
35*(-1) + y^2 + y*2 = (y + 7)*(5*(-1) + y)
|
-20,243 |
\tfrac{64 + 48 q}{30 q + 40} = \frac85 \frac{q \cdot 6 + 8}{8 + 6q}
|
12,172 |
\sin(\alpha*0) - \cos(\alpha) = -\cos(\alpha)
|
-7,234 |
6/16*\frac{5}{15} = 1/8
|
13,126 |
\sin\left(z\right)/z = \frac1z\left(z - z^3/3! + z^5/5! - \dots\right) = 1 - \tfrac{z^2}{3!} + \frac{z^4}{5!} - \dots
|
5,913 |
\left(H\cdot x = x\cdot \lambda \Rightarrow H^2\cdot x = H\cdot x\cdot \lambda\right) \Rightarrow H\cdot x = \lambda\cdot H\cdot x = \lambda^2\cdot x
|
2,263 |
|5 + \pi |x| \cdot 3| = 3|x| \pi + 5
|
20,417 |
\frac12*(-1^{1/2} + (2*k + 1)^{1/2}) = \left((1 + 2*k)^{1/2} + (-1)\right)/2
|
22,455 |
1 - \frac{7}{18} = 11/18
|
-13,445 |
\dfrac{6}{10 + 4 \cdot (-1)} = 6/6 = 6/6 = 1
|
4,535 |
\frac{13}{24} = \frac16 \cdot 13/4
|
4,421 |
p^3 + (-1) = ((-1) + p)\cdot (p^2 + p + 1)
|
-18,214 |
22 = 32 (-1) + 54
|
10,116 |
\dfrac{1}{A*x} = 1/(x*A)
|
-18,476 |
3*l + 7 = 5*(l + 3*\left(-1\right)) = 5*l + 15*\left(-1\right)
|
-603 |
(e^{\pi i/2})^{11} = e^{11 \pi i/2}
|
-2,807 |
-\sqrt{16} \sqrt{2} + \sqrt{2} \sqrt{25} = -\sqrt{2} \cdot 4 + 5 \sqrt{2}
|
15,394 |
\frac{7^{55}}{5^{72}} = 7\cdot (\tfrac{1}{5^4}\cdot 7^2 \cdot 7)^{18}
|
9,782 |
(2\cdot x + 2\cdot \left(-1\right))! = \dfrac{1}{(-1) + 2\cdot x}\cdot (2\cdot x + \left(-1\right))!
|
23,676 |
E(Z_1 \cdot Z_2) = E(Z_2) \cdot E(Z_1)
|
4,380 |
(S + T)\times (v_1 + v_2) = v_1\times (S + T) + v_2\times \left(T + S\right)
|
-5,415 |
37.8 \cdot 10^{1 + 2} = 10^3 \cdot 37.8
|
34,707 |
\alpha^{1/2} = (-(-1) \cdot \alpha)^{1/2} = i \cdot \left(-\alpha\right)^{1/2}
|
17,368 |
{2 \times k \choose k} \times k!^2 = (2 \times k)!
|
49,989 |
\dfrac{1}{16} \cdot 5 = 0.3125
|
-26,471 |
(x \cdot 7 + 5)^2 = 25 + x \cdot 70 + 49 \cdot x^2
|
-23,496 |
\frac{1}{3} = \frac{5}{9}*3/5
|
-2,257 |
\dfrac{5}{18} - 3/18 = 2/18
|
17,747 |
\dfrac{1}{X^W*X} = \tfrac{1}{X^W*X}
|
10,552 |
\frac{1}{5 \cdot (-1) + n} \cdot 6 + 1 = \frac{1}{5 \cdot \left(-1\right) + n} \cdot (n + 1)
|
5,512 |
\tfrac{1}{-2^{\dfrac{1}{2}}*6 + 11} = \frac{1}{(3 - 2^{1 / 2})^2}
|
-20,554 |
\tfrac{1}{8 \times y} \times (7 \times y + 6) \times 10/10 = \frac{1}{80 \times y} \times (60 + 70 \times y)
|
-5,887 |
\tfrac{1}{(2*(-1) + p)*(p + 3*\left(-1\right))}*5*\frac{6}{6} = \frac{1}{6*(3*\left(-1\right) + p)*(p + 2*(-1))}*30
|
887 |
g + kq + f + xk = (q + x) k + f + g
|
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