id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
17,102 |
(a - b) \cdot (a - b) = b \cdot b + a \cdot a - 2\cdot a\cdot b
|
20,075 |
x + (-1) = x + 2\cdot (-1) + 1
|
14,258 |
\left(2*m + 3\right)*m + 1 = 2*m * m + 3*m + 1 = (2*m + 1)*\left(m + 1\right)
|
-4,565 |
x^2 + x*5 + 6 = (2 + x) (x + 3)
|
41,381 |
1*23 + 4(-1) + 5 + 6(-1) + 7(-1) = 11
|
38,448 |
\sin{z} = \cos(-\frac{1}{2}\cdot \pi + z)
|
9,859 |
T - X \lt X \Rightarrow T \lt 2 X
|
-7,956 |
\dfrac{-2 - i}{-i - 2}\times \dfrac{1}{-2 + i}\times \left(i + 8\right) = \frac{1}{i - 2}\times \left(8 + i\right)
|
8,351 |
\frac{h}{d} + x/d = \frac1d \cdot \left(h + x\right)
|
38,583 |
64232 = 39 * 39^2 + 17^3
|
-20,186 |
-4/7*9/9 = -36/63
|
778 |
\dfrac{8(-1) + 120}{5 + (-1)} = 28
|
26,596 |
2 + x^2 - x*3 = (\left(-1\right) + x)*\left(2*(-1) + x\right)
|
21,531 |
\frac{1}{y \cdot y + 1}\cdot y^2 = \frac{y^2 + 1 + (-1)}{y \cdot y + 1} = 1 - \dfrac{1}{y^2 + 1}
|
-20,435 |
\frac{4*(-1) + s}{s*7 + (-1)}*\dfrac14*4 = \dfrac{16*(-1) + s*4}{s*28 + 4*(-1)}
|
-19,720 |
6\cdot 6/(7) = \frac{1}{7}\cdot 36
|
5,096 |
N*2^{N + (-1)} = \dfrac{2^{N + (-1)}}{(-1) + 2^N}N*((-1) + 2^N)
|
17,632 |
\mathbb{E}\left[B_1 + B_2 + B_3\right] = \mathbb{E}\left[B_3\right] + \mathbb{E}\left[B_1\right] + \mathbb{E}\left[B_2\right]
|
5,219 |
\left(A + 2*\left(-1\right)\right)*(A + 1) = 2*(-1) + A^2 - A
|
21,205 |
\frac{1}{k^{1/2} + (k + 1)^{1/2}} = \left(1 + k\right)^{1/2} - k^{1/2}
|
-13,343 |
\dfrac{12}{9 + 3\cdot (-1)} = \dfrac{12}{6} = 12/6 = 2
|
-30,263 |
(y + 7)\cdot (y + 7\cdot (-1)) = y^2 + 49\cdot (-1)
|
30,303 |
\mathbb{E}\left[X\right] \cdot \mathbb{E}\left[B\right] = \mathbb{E}\left[X \cdot B\right]
|
29,319 |
a^x*\ln(a) = \frac{\partial}{\partial x} a^x
|
12,339 |
n = \left\{\dotsm, 1, n\right\}
|
-4,244 |
\frac{63 \cdot n}{n^5 \cdot 54} \cdot 1 = 63/54 \cdot \dfrac{1}{n^5} \cdot n
|
4,421 |
\left(r + (-1)\right) (1 + r^2 + r) = r^3 + \left(-1\right)
|
21,904 |
E\left(A\right)\cdot E\left(H\right) = E\left(H\cdot A\right)
|
20,156 |
u_x + f\cdot u_y = 0 = \left( 1, f\right)\cdot ( u_x, u_y)
|
1,858 |
\|t - r\|^2 = \|t - x + x - r\|^2 = \|t - x\|^2 + \|x - r\|^2 + 2
|
-4,884 |
10^{1 + 3}*15 = 15*10^4
|
5,927 |
((-1) + z^2) \cdot \left(1 + z^4 + z^2\right) = (-1) + z^6
|
16,587 |
(x + 0) \left(x^2 + 2x + 2\right) = 0 + x^3 + 2x^2 + 2x
|
14,449 |
0 = (-1) + 4\cdot x \Rightarrow 1/4 = x
|
24,934 |
\frac{\partial}{\partial x} x^{\tfrac{1}{q}} = \tfrac1q\times x^{(1 - q)/q} = \tfrac{1}{q}\times x^{1/q + (-1)}
|
4,685 |
-8 \geq \frac6y \implies y \geq -6/8 = -3/4
|
23,766 |
y^{\frac1e} = y^{1/e}
|
2,616 |
\frac{1}{6^3}(6 + 54 + 18) = 78/216 = \frac{13}{36} \approx 0.361
|
31,877 |
212/39 = \frac{1}{39}17 + 5
|
-1,116 |
-40/42 = ((-40) \dfrac{1}{2})/\left(42*1/2\right) = -20/21
|
11,137 |
c_1^{c_2}\cdot c_1^d = c_1^{c_2 + d}
|
2,270 |
x^2 - z^2 = x*x - z*z = \left(x + z\right)*\left(x - z\right)
|
-8,506 |
\frac{1}{-9} \cdot 9 = -1
|
9,301 |
AG_{11} = G_{11} A
|
16,663 |
\binom{2}{1} \binom{3}{1} \binom{3}{2} \binom{6}{3} = 6*5*4*3
|
21,829 |
\left(n = 6 \Leftrightarrow 2 + n = 8, 4 n + 1 = 25\right) \implies \left( 2 + n, 1 + 4 n\right) = 1
|
28,545 |
2 = 1 - 2 + 3*(-1)
|
10,273 |
\dfrac12 = (-1) - 1 + \frac{1}{2} + 2
|
22,112 |
2\times \cos{z} = e^{i\times z} + e^{-i\times z} = e^{i\times z} + e^{-i\times z} = 2\times \cosh{i\times z}
|
26,599 |
\tfrac12\cdot \left(\cos(x\cdot 2) + 1\right) = \cos^2\left(x\right)
|
-8,085 |
\frac{1}{i\cdot 5 + 3}\cdot (2 - 8\cdot i) = \dfrac{1}{i\cdot 5 + 3}\cdot (2 - i\cdot 8)\cdot \frac{3 - 5\cdot i}{3 - i\cdot 5}
|
34,360 |
-p + p^3 + p^2 = (-1) + p^2 + p^2 - p + p^2 - p + p^2 - p \cdot 2 + 1 + p^3 - 3 \cdot p^2 + p \cdot 3
|
8,979 |
20538 = 2 \cdot 3^2 \cdot 7 \cdot 163
|
8,745 |
c = a \Rightarrow a^2 = c^2
|
13,321 |
-\frac{1}{2 + x^2} + 1 = \dfrac{1 + x^2}{x^2 + 2}
|
11,601 |
(n + \left(-1\right))!\cdot (n + 1)! = (n + 1)/n\cdot n!^2 > n!^2
|
31,858 |
12\cdot (-1) + 6 = -6
|
29,602 |
\sin(\alpha + \frac{\pi\cdot 3}{2}) = -\cos\left(\alpha\right)
|
27,725 |
|A \cap F| = |A \cap F|
|
48,776 |
2^1*5 + 1 = 11
|
29,115 |
c + 3\cdot z\cdot b = 0 \Rightarrow -\frac{c}{b\cdot 3} = z
|
6,473 |
\frac{1 + 2 \cdot z}{2 + 2 \cdot k} = \dfrac{1}{2} \cdot \left(\dfrac{z + 1}{k + 1} + \dfrac{z}{k + 1}\right)
|
-11,971 |
71/90 = p/(12*\pi)*12*\pi = p
|
32,210 |
\binom{2 + k}{1 + k} = 1 + \binom{k + 1}{k}
|
24,502 |
-l^2 + x^2 = (l + x) (-l + x)
|
32,384 |
15\times3=45
|
-1,858 |
\pi \cdot \frac{13}{12} = \dfrac{1}{4} \cdot 3 \cdot \pi + \frac{\pi}{3}
|
-5,742 |
\frac{5*p}{8 + p^2 - p*9} = \tfrac{1}{(p + 8*(-1))*((-1) + p)}*5*p
|
12,973 |
a + z - a = a + y - a \Rightarrow -a + a + z = y - a + a
|
-20,802 |
4/1 \cdot \frac{9 + 10 \cdot k}{9 + k \cdot 10} = \frac{40 \cdot k + 36}{10 \cdot k + 9}
|
-29,357 |
(2 + Y)*(2 - Y) = 2^2 - Y^2 = 4 - Y^2
|
10,999 |
\int (1 - e^{-z}) \cdot e^{e^z}\,dz = \int (e^z + \left(-1\right)) \cdot e^{-z} \cdot e^{e^z}\,dz = \int \left(e^z + (-1)\right) \cdot e^{e^z - z}\,dz
|
-2,188 |
-3/12 + \dfrac{7}{12} = 4/12
|
13,956 |
f_1 \cdot z_0 + z_1 = z_1 + z_0 \cdot f_1
|
31,804 |
c*b*a = (a + i)*10 * 10 + b*10 + c - i = a*10^2 + b*10 + c + i*10^2 - i = a*10 * 10 + b*10 + c + 99*i
|
-3,118 |
12 \cdot 2^{1/2} = 2^{1/2} \cdot (4 + 3 + 5)
|
3,389 |
1/4 + 1/3 + 1/2 = \frac{13}{12}
|
19,879 |
6^2*4 = 4^2 + 8^2 + 8 * 8
|
4,522 |
\frac{1}{29}\cdot 9 = 9/29
|
24,957 |
y^{a - h} = \frac{y^a}{y^h}
|
12,863 |
-6 = \sqrt{2} + 3*(-1) - \sqrt{2} + 3*\left(-1\right)
|
45,656 |
(\sqrt{c})^2 + (\frac{1}{\sqrt{c}})^2 + 2 = (\sqrt{c} + \frac{1}{\sqrt{c}}) \cdot (\sqrt{c} + \frac{1}{\sqrt{c}}) = \left(c + 1\right)^2/c
|
-6,667 |
\dfrac{5}{3x + 12 (-1)} = \tfrac{5}{3(4(-1) + x)}
|
35,084 |
\cos{\alpha} \sin{\alpha}\cdot 2 = \sin{2\alpha}
|
30,489 |
z + 3 < 0 \implies -3 \gt z
|
8,777 |
a^2 \cdot a + b^3 + c^3 - 3\cdot a\cdot b\cdot c = (c + a + b)\cdot (a^2 + b^2 + c^2 - a\cdot b - c\cdot b - a\cdot c)
|
28,667 |
k + (-1) = j \Rightarrow k = j + 1
|
19,648 |
(-\mathrm{i} + 1) (\mathrm{i} + 1) = 2
|
10,772 |
-2x + x \cdot x = (-1) + ((-1) + x)^2
|
7,571 |
60 (-1) + 1024 + 4 (-1) = 960
|
-4,459 |
x \cdot x + 3 \cdot x + 10 \cdot (-1) = \left(x + 5\right) \cdot (2 \cdot (-1) + x)
|
-20,557 |
\frac{1}{(-5)*y}*\left((-1) - 9*y\right)*\frac12*2 = (-y*18 + 2*(-1))/(\left(-10\right)*y)
|
-18,274 |
\frac{-g\cdot 5 + g \cdot g}{g^2 + 4\cdot g + 45\cdot \left(-1\right)} = \frac{1}{(g + 5\cdot \left(-1\right))\cdot (9 + g)}\cdot g\cdot \left(5\cdot (-1) + g\right)
|
52,970 |
\int\frac{x^2}{\tan{x}-x}dx=\int\left(\frac{x^2}{\tan{x}-x}+x-x\right)dx=\int\frac{x\sin{x}}{\sin{x}-x\cos{x}}dx-\frac{x^2}{2}
|
16,445 |
A^{\frac12}\cdot A^{1/2} = A
|
13,491 |
v_3\cdot v_1\cdot v_2 = v_3\cdot v_1\cdot v_2
|
409 |
4y = y \cdot 2 \cdot 2
|
13,375 |
(r + 1)/2 = r - \dfrac{1}{2}\cdot ((-1) + r)
|
4,874 |
2^{\frac{1}{3} \cdot (m + 1)} = 2^{1/3} \cdot 2^{m/3} > m \cdot 2^{\dfrac{1}{3}}
|
15,052 |
-\binom{10}{1} + 2^{10} + (-1) = 2^{10} + 11 \times (-1)
|
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