id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-29,588 |
\frac{\mathrm{d}}{\mathrm{d}z} (2\cdot z^2 - 6\cdot z + 5) = 6\cdot (-1) + z\cdot 4
|
39,123 |
(a + d)^2 = a^2 + 2*a*d + d * d \geq a * a + d * d
|
41,171 |
10^{15} + (-1) = 9\cdot 111\cdot 1001001001001
|
-5,490 |
\frac{1}{(7 + q)\cdot (2 + q)\cdot 2}\cdot 6 = \frac12\cdot 2\cdot \frac{1}{(q + 2)\cdot (q + 7)}\cdot 3
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42,486 |
4*11 + 3*4 = 56
|
30,223 |
\tfrac{1}{2}(5 + 15) = 10
|
-5,581 |
\dfrac{4 \cdot (y + 4 \cdot (-1)) - 5 \cdot \left(y + 6 \cdot (-1)\right) + (-1)}{\left(y + 4 \cdot (-1)\right) \cdot (6 \cdot (-1) + y)} = \dfrac{4}{\left(y + 4 \cdot (-1)\right) \cdot \left(6 \cdot (-1) + y\right)} \cdot (y + 4 \cdot (-1)) - \frac{5 \cdot (y + 6 \cdot (-1))}{(4 \cdot (-1) + y) \cdot (y + 6 \cdot (-1))} - \frac{1}{(4 \cdot (-1) + y) \cdot \left(y + 6 \cdot (-1)\right)}
|
21,892 |
n = (2 + \left(-1\right) + n \cdot 2 + (-1))/2
|
-11,536 |
10 \cdot i + 40 = 25 + 15 + 10 \cdot i
|
12,552 |
(0*(-1) + z)*(z + 0*\left(-1\right)) = z^2
|
18,954 |
\frac{\frac{5}{18}}{\frac{7}{9}} = \frac{5}{14}
|
26,598 |
l/h = 1/(1/l*h)
|
28,132 |
(V + X)^2 - X^2 - V^2 = V*X + X*V
|
22,691 |
x-\frac{1}{2}=\frac{2x-1}{2}
|
-1,387 |
-\frac{1}{9}\cdot \tfrac79 = (1/9 \left(-1\right))/(1/7\cdot 9)
|
-20,173 |
10/(-70) = -1/7*(-\frac{1}{-10}*10)
|
18,418 |
|x \cdot T| = |T| \cdot |x|
|
-2,257 |
\dfrac{2}{18} = 5/18 - \frac{3}{18}
|
13,796 |
z^{\frac32} = (1 + z + (-1))^{\dfrac32}
|
14,557 |
y = \tfrac{y}{|y|}\cdot |y|
|
4,682 |
4 \cdot (\frac{1}{5} \cdot 2)^{n + (-1)} = \frac{1}{5^{n + (-1)}} \cdot 2^{n + (-1)} \cdot 2 \cdot 2
|
16,391 |
\frac{1}{y + 4} \cdot y = \frac{1}{y - i + 4 + i} \cdot y
|
-4,794 |
6.3 \times 10 = \frac{63.0}{10000} \times 1 = 6.3/1000
|
-10,357 |
-\frac{9}{12\cdot n}\cdot 3/3 = -27/(n\cdot 36)
|
526 |
(1 - q)^7 - 7*(1 - q)^6*q = \left(1 - q\right)^6*\left(1 - q - 7*q\right) = (1 - q)^6*(1 - 8*q)
|
-26,288 |
5 = Y \cdot e^{\left(-2\right) \cdot 0} = Y
|
-24,883 |
\frac{11}{12} = \dfrac{x}{12 \cdot \pi} \cdot 12 \cdot \pi = x
|
-13,896 |
10 + 6 \cdot 16/2 = 10 + 6 \cdot 8 = 10 + 6 \cdot 8 = 10 + 48 = 58
|
4,466 |
\left(\delta - g\right)^2 = \delta^2 - 2\cdot \delta\cdot g + g^2 = \delta^2 - g \cdot g
|
-549 |
\left(e^{19*i*\pi/12}\right)^6 = e^{19*\pi*i/12*6}
|
30,534 |
i = 2^{2\cdot \left(L + 1\right)} + (-1) = 4\cdot 4^L + \left(-1\right)
|
31,204 |
\overline{x} = \frac1x = x^4
|
-11,970 |
\frac12 = \dfrac{p}{8\pi}*8\pi = p
|
8,550 |
(z + x) r = x r + z r
|
28,068 |
0 = e^{\sin{z \cdot Q}} + z^2 - 2 \cdot Q + (-1) \approx z \cdot Q + z^2 - 2 \cdot Q
|
18,877 |
(1324*H)^2 = 1324^2*H = 12*34*H = H
|
-23,991 |
10 + \left(\dfrac{4}{4}\right)= 10 + (1) = 10 + 1 = 11
|
22,498 |
z \cdot 0 = (z + 0) \cdot (0 + 0) = z \cdot 0 + z \cdot 0 \Rightarrow 0 = z \cdot 0
|
51,797 |
1/7893600 = 1/23\times 1/25\times \frac{1}{26}/24/22
|
21,403 |
1 - 3*2/21 = 15/21 = \frac{5}{7}
|
18,571 |
H^\vartheta*G = G*H^\vartheta
|
29,301 |
10152 = 3^3 \cdot 2^3 \cdot 47
|
2,291 |
{n \choose 2}\times 2 + {n \choose 0}\times 2 = n^2 - n + 2
|
-613 |
-4 \pi + \frac{1}{2} 11 \pi = \pi \frac{3}{2}
|
-10,435 |
-\dfrac{5}{2\cdot (-1) + 4\cdot q}\cdot \frac55 = -\tfrac{1}{q\cdot 20 + 10\cdot (-1)}\cdot 25
|
11,231 |
1^2 \times 2 - 4 + 3 = 1
|
7,883 |
\frac{1}{2^{1 + n}}(n + 1) = \frac{1}{2^{n + 1}}\left(3(-1) + 2n + 4 - n\right)
|
26,494 |
-p \cdot p + h^2 = (p + h) \cdot \left(-p + h\right)
|
6,016 |
\frac{\partial}{\partial t} (zy) = z\frac{\mathrm{d}y}{\mathrm{d}t} + y\frac{\mathrm{d}z}{\mathrm{d}t}
|
-22,958 |
\dfrac{1}{30}*42 = 7*6/(5*6)
|
-9,243 |
-60*y + 90 = 2*3*3*5 - 2*2*3*5*y
|
13,699 |
y^4*y*2 = 2*y^5
|
25,188 |
a\cdot m + m\cdot b = m\cdot \left(b + a\right)
|
-14,535 |
\frac{10}{4 + 2 \cdot (-1)} = 10/2 = \dfrac{10}{2} = 5
|
-22,969 |
\dfrac{20}{24} = \dfrac{20}{6*4}1
|
50,356 |
(x - x_0)^2 / a^2 + (y-y_0)^2 / b^2 = 1\implies (x - x_0)^2 / a^2 + (y-y_0)^2 / b^2 - 1=0
|
29,722 |
d\cdot x\cdot z = x\cdot z = x\cdot z = d\cdot x\cdot z
|
-29,593 |
d/dz (-2z^4) = -2d/dz z^4 = -2 \cdot 4z^3 = -8z^3
|
-20,927 |
-\frac37 \frac{q + 2 (-1)}{q + 2 (-1)} = \frac{6 - 3 q}{7 q + 14 (-1)}
|
884 |
1 = \left|{\frac{X}{X}}\right| = \left|{X}\right|\cdot \left|{\frac1X}\right|
|
4,368 |
C_1\cdot C_3\cdot f\cdot C_2 = C_3\cdot C_2\cdot C_1\cdot f
|
20,319 |
i\times \sin(\pi\times 5/4) + \cos(5\times \pi/4) = \left(\sqrt{2}\times \left(-1\right)\times (i + 1)\right)/2
|
-26,950 |
\sum_{k=1}^\infty \frac{(3 + 4)^k}{k \cdot 7^k} \cdot \left(k + 6\right) = \sum_{k=1}^\infty \frac{\left(k + 6\right) \cdot 7^k}{k \cdot 7^k} = \sum_{k=1}^\infty \frac1k \cdot (k + 6)
|
-29,591 |
d/dy \left(2 y^2 - 6 y + 5\right) = y\cdot 4 + 6 \left(-1\right)
|
-15,900 |
\dfrac{20}{10} = -\frac{5}{10}\cdot 5 + 9\cdot \frac{1}{10}\cdot 5
|
21,089 |
\frac{b^2}{c^2} = \frac14\cdot 3^{1/2} \Rightarrow b = 3^{1/2},c = 2
|
6,129 |
1/3 + \frac{1}{4*3} = -\frac{1}{3*4} + \dfrac12
|
-123 |
4\cdot (-1) - 21 = -25
|
37,370 |
36 + \left(2\cdot 6 + 9\right)\cdot 2 = 78
|
19,334 |
(x - a) \cdot \left(x + a\right) = x^2 - a^2 = x^2 + 1 - a \cdot a + 1
|
36,360 |
a^{l + 1} = a^l*a
|
390 |
e^{2*y + \left(-1\right)}*2 = d/dy (e^{y*2 + (-1)} + 1)
|
1,476 |
\left(-y*3 + 4 = 7\Longrightarrow -y*3 = 3\right)\Longrightarrow y = -1 = 7
|
17,368 |
(n*2)! = {2n \choose n} n!^2
|
7,718 |
\frac1yx yx = x\frac{y}{y}x
|
12,883 |
|a| = |a - g + g| \leq |a - g| + |a|
|
46,547 |
\frac{\mathrm{d}x}{\mathrm{d}x} = \frac{\mathrm{d}x}{\mathrm{d}x}
|
2,804 |
\left(t + (-1)\right) \cdot ((-1) + t^2 - 2 \cdot t) = t^3 - t^2 \cdot 3 + t + 1
|
16,567 |
\sin{2y} = \sin{y} \cos{y}\cdot 2
|
34,921 |
J + I = A \Rightarrow A = \sqrt{J} + \sqrt{I}
|
30,847 |
60 = 150/5 \times (3 + \left(-1\right))
|
-14,279 |
9 + (6 - 4)\cdot 9 = 9 + (6 + 4\cdot (-1))\cdot 9 = 9 + 2\cdot 9 = 9 + 18 = 27
|
14,158 |
(z*\sqrt{k} + Z)*(Z - \sqrt{k}*z) = Z^2 - k*z^2
|
24,101 |
(x + 1)! - x! = (x + 1) x! - x! = \left(x + 1 + (-1)\right) x! = xx!
|
14,196 |
\cos(\pi + i) = -\cos{i} = -\left(e^{i^2} + e^{-i^2}\right)/2 = -\frac{1}{2}\cdot (e + \frac{1}{e})
|
819 |
2\cdot R - R = R
|
6,593 |
-m^2 + 8 \cdot m + 18 = -(m^2 - 8 \cdot m + 18 \cdot (-1)) = -((m + 4 \cdot (-1))^2 + 34 \cdot \left(-1\right)) = -(m + 4 \cdot \left(-1\right) - \sqrt{34}) \cdot (m + 4 \cdot \left(-1\right) + \sqrt{34})
|
33,417 |
\frac{\partial}{\partial z} z^k = z^{k + (-1)} \cdot k
|
15,654 |
{n \choose r} = \frac{n!}{r! (n - r)!}
|
3,660 |
(x^2 + xb + b^2) (-b + x) = -b \cdot b \cdot b + x^3
|
-4,093 |
6/5 x^3 = 6x^3/5
|
15,977 |
1 + z^2 + z = \frac{z^3 + (-1)}{\left(-1\right) + z}
|
22,267 |
-\sin{\frac13\pi} = \sin{\frac43\pi}
|
31,876 |
z \cdot z + 8 \cdot z + 7 = (z + 1) \cdot (7 + z)
|
23,219 |
\frac{(2\cdot n + 1)\cdot (1 + n)}{(2\cdot n + 1)\cdot \left(3 + n\cdot 2\right)} = \frac{1 + n}{3 + n\cdot 2}
|
-6,730 |
\frac{1}{100} \cdot 3 + 3/10 = \frac{30}{100} + \frac{3}{100}
|
-6,699 |
\dfrac{0}{100} + \frac{9}{100} = \frac{0}{10} + \frac{9}{100}
|
8,030 |
\frac14 \cdot \pi + \frac{1}{3} \cdot \pi = \frac{7}{12} \cdot \pi
|
33,371 |
48\times 6 + 2\times3 + 6\times1= 300
|
29,750 |
\left(y^2 - z * z + y*4 + 4 = 0 \Rightarrow 0 = -z^2 + (y + 2)^2\right) \Rightarrow (y + 2 + z)*(y + 2 - z) = 0
|
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