id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
20,767 |
y \cdot x/100 = \frac{x}{100} \cdot y
|
-1,695 |
\pi*17/12 + \pi*\dfrac{11}{12} = \dfrac{7}{3}*\pi
|
21,296 |
|b_n a_n - ab| = |b_n a_n - ba + ba_n - a_n b|
|
10,767 |
x = x - \sum_{j=2}^n e_j*x_j + \sum_{j=2}^n e_j*x_j = \sum_{j=1}^n e_j*x_j
|
12,549 |
p^2 - p = p*(\left(-1\right) + p)
|
-7,737 |
\frac{1}{i\cdot 4 + 2}\cdot (-i\cdot 2 + 4)\cdot \tfrac{-i\cdot 4 + 2}{-i\cdot 4 + 2} = \frac{1}{2 + 4\cdot i}\cdot (4 - 2\cdot i)
|
36,798 |
-\frac{1}{15} \cdot 4 = -4/15
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30,284 |
\{\} = \left( \left(-1\right) + z_1, \alpha\right) \implies \{\} = [z_1, \alpha]
|
-7,766 |
\frac{1}{3 - i \cdot 3}(-i \cdot 3 + 3) \frac{-3 - 3i}{3 + i \cdot 3} = \frac{-i \cdot 3 - 3}{i \cdot 3 + 3}
|
28,461 |
26 = 5^2 + 1^2 = 4^2 + 3^2 + 1^2 = 3^2 + 3 \cdot 3 + 2^2 + 2^2
|
25,964 |
108124016 = \left(2002\cdot (-1) + 15504\right)\cdot (2002 + 6006)
|
-22,547 |
\tfrac{8}{9}\cdot \frac78 = 8\cdot 7/\left(9\cdot 8\right) = 56/72 = \frac{1}{9}\cdot 7
|
-5,925 |
\frac{2*g}{(2 + g)*(g + 6)} = \frac{g*2}{g * g + 8*g + 12}
|
-23,599 |
\frac{1/3*2}{7} = 2/21
|
11,167 |
n^2 + n*3 + 2 - n*3 + 3*(-1) = n^2 + (-1)
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24,533 |
\frac{1}{2} 109824 = 54912
|
15,694 |
(1 - q)^2 = 1 - 2q + q * q
|
-2,877 |
-(9*13)^{1/2} + (25*13)^{1/2} = 325^{1/2} - 117^{1/2}
|
21,892 |
\dfrac{1}{2} \cdot \left(2 + (-1) + 2 \cdot n + (-1)\right) = n
|
-25,952 |
0.58 = \tfrac{4.64}{8}
|
29,792 |
m \cdot (m + \left(-1\right))! = m!
|
21,276 |
0 = \frac1x rightarrow 1 = 0x
|
22,284 |
(3\cdot (-1) + x)\cdot (6\cdot (-1) + x) = 18 + x^2 - 9\cdot x
|
-13,838 |
\frac{72}{7 + 5} = \frac{72}{12} = \tfrac{72}{12} = 6
|
-20,843 |
-\frac{1}{7}\cdot 4\cdot \frac{4\cdot q}{4\cdot q} = ((-16)\cdot q)/(q\cdot 28)
|
6,615 |
\cos{x} = \sin{x}\Longrightarrow \frac12 \times \left(e^{x \times i} + e^{-i \times x}\right) = \frac{1}{2 \times i} \times (-e^{-i \times x} + e^{x \times i})
|
10,253 |
\dfrac{t_i - \frac{1}{t_i}}{t_i + (-1)} = 1 + \dfrac{1 - \dfrac{1}{t_i}}{t_i + (-1)} \geq 1 + \frac{1}{2 \times (t_i + (-1))}
|
25,978 |
(-1)^n\cdot \binom{-2}{n} = \binom{n + 1}{n} = \binom{n + 1}{1} = n + 1
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11,006 |
2 = \sin^2{F_2} + \sin^2{F_1} + \sin^2{C} \Rightarrow 1 - \cos^2{F_2} + 1 - -\sin^2{C} + \cos^2{F_1} = 2
|
29,145 |
50 K = \dfrac{1}{20} 1000 K
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24,255 |
\ln\left(r\right) + r = \int (r + 1)/r\,dr
|
15,584 |
\frac{1}{c*b} = \dfrac{1}{b*c}
|
18,935 |
\frac{1}{4}*5*t = 15 + t\Longrightarrow t = 60
|
30,197 |
x \cdot x \cdot x + (-1) = ((-1) + x) \cdot (1 + x^2 + x)
|
6,017 |
y = e^h + \left(-1\right) \implies \ln(1 + y) = h
|
32,390 |
k\cdot k! + k! = (k + 1)!
|
-15,682 |
\frac{1}{\frac{1}{\dfrac{1}{r^2} x^4}}x^4 = \frac{x^4}{r^2 \frac{1}{x^4}}
|
-23,721 |
\frac37 \cdot 3/4 = \tfrac{9}{28}
|
-6,094 |
\frac{3}{z^2 + 8*z + 9*(-1)} = \frac{3}{\left(z + 9\right)*(z + (-1))}
|
21,647 |
-\sin{s} \cos{x} + \cos{s} \sin{x} = \sin(-s + x)
|
15,102 |
w^9 = \left(w^3\right)^3
|
6,876 |
x^2 - 2\cdot x\cdot a + a^2 + b^2 = b^2 + (-a + x)^2
|
9,446 |
1 = x \cdot 12 + 5 \cdot y\Longrightarrow x = -2\wedge y = 5
|
12,908 |
\dfrac{v^2}{x^2} = (\frac{1}{x}\times v)^2
|
-26,582 |
\left(7x + 4\right) (-7x + 4) = 16 - 49 x^2
|
26,732 |
\frac{1}{4}\cdot π + \dfrac{π\cdot \left(-1\right)}{4} - q = -q
|
47,755 |
120^2\cdot 25\cdot 4 = 1440000
|
-1,856 |
7/12 \cdot π + \frac{π}{4} = 5/6 \cdot π
|
33,138 |
G_x\cdot G_\rho = G_\rho\cdot G_x
|
32,354 |
(x + z)^3 = (x + z) \cdot (x + z) \cdot (x + z) = (x + z) \cdot \left(x^2 + 2 \cdot x \cdot z + z \cdot z\right)
|
17,757 |
\left(3\cdot (-1) + y\right)\cdot (4\cdot (-1) + y)\cdot (y + 5\cdot (-1)) = 60\cdot (-1) + y^3 - 12\cdot y^2 + 47\cdot y
|
17,463 |
y^{\frac73} = y^{4/3 + \dfrac33} = y^{\dfrac43}*y^{\frac{3}{3}} = y^{\frac13*4}*y
|
28,283 |
\frac16 \cdot (-i + 6) = -\frac16 \cdot i + 1
|
6,470 |
\tan(y \cdot 3) = \tan\left(y \cdot 3\right)
|
19,282 |
z*H*x = H*z*x
|
32,066 |
4004001 = 2001 * 2001
|
45,117 |
x\cdot v = v\cdot x
|
31,602 |
\cos(-2 \cdot 2 + 2^2) = \cos\left(-2 \cdot 0 + 0^2\right)
|
33,181 |
L_k + L_l = L_l + L_k
|
40,019 |
25 = 68 + 43\times (-1)
|
14,631 |
1/7 + \dfrac{1}{42} = \frac{1}{6}
|
26,324 |
(g\cdot f)^2 \cdot (f\cdot g) = f \cdot f^2\cdot g^3
|
35,910 |
\frac{1}{24}7 = 91/24 + 2(-1) - 1^{-1} - 1/2
|
16,989 |
(x\times 3)^2 = 9\times x^2
|
498 |
6\cdot 252 = 1512
|
7,092 |
g^2 - b^2 = (g + b)*\left(-b + g\right)
|
12,926 |
0 = (c \cdot 2 + \left(-1\right)) \cdot 2 \Rightarrow \frac12 = c
|
8,009 |
\tfrac32\cdot 1/2\cdot 3 = \tfrac{9}{4}
|
974 |
\left(9 = y \times y \Rightarrow 9^{1/2} = y\right) \Rightarrow 3 = y
|
32,782 |
Z \cup Y \setminus Z = Z \cup \left(Y \cap Z^c\right) = (Y \cup Z) \cap (Z \cup Z^c) = Y \cup Z
|
-4,731 |
-\frac{1}{z + 3}\cdot 4 + \frac{2}{5\cdot (-1) + z} = \frac{26 - 2\cdot z}{z^2 - 2\cdot z + 15\cdot \left(-1\right)}
|
7,092 |
h \cdot h - g \cdot g = (g + h)\cdot (h - g)
|
19,131 |
(-8/3 + 3)^2*\frac{2}{9} = \frac{2}{81}
|
26,575 |
\frac124 = \frac21 = \frac{6}{3} = \dots
|
32,700 |
((1 + p)/2)^2 - \left(\dfrac{1}{2}\left(p + \left(-1\right)\right)\right)^2 = p
|
-24,660 |
\frac{12}{30} = \frac{2 \cdot 6}{6 \cdot 5}
|
18,102 |
N\cdot x\cdot b = b\cdot N\cdot N\cdot x
|
12,835 |
x^2 + x + 2(-1) + 2\sqrt{x^3 - x^2 - x + 1} = x * x * x \Rightarrow 4(x^3 - x^2 - x + 1) = (x^3 - x * x - x + 2) * (x^3 - x * x - x + 2)
|
3,293 |
-x^2 + (1 + x) * (1 + x) = 2*x + 1
|
4,106 |
(\int_0^1 (-\sigma + b)\,\text{d}\sigma) \cdot 2 = \frac{\partial}{\partial b} \int\limits_0^1 (\sigma - b)^2\,\text{d}\sigma
|
-14,041 |
7 + \frac{1}{5}50 = 7 + 10 = 17
|
20,269 |
(i + 1)! = i! (i + 1) < 2^i\cdot (i + 1)
|
39,323 |
4 \cdot (-1) + 3 + 1 = 0
|
1,404 |
5 \cdot y^3 + y^2 \cdot 20 - y \cdot 195 + 270 = (y + 9) \cdot (2 \cdot (-1) + y) \cdot (y + 3 \cdot (-1)) \cdot 5
|
5,467 |
-\tfrac{1}{2 + x} \cdot \left(2 \cdot \left(-1\right) + x\right) = \frac{1}{2 + x} \cdot \left(-x + 2\right)
|
17,482 |
-\left(a^2 + c \cdot c\right)^2 + (a^2 - c^2)^2 = -a^4 - 2\cdot a^2\cdot c^2 - c^4 + a^4 - 2\cdot a^2\cdot c^2 + c^4 = -4\cdot a^2\cdot c \cdot c
|
966 |
(2 \cdot (-1) + z) \cdot 5 = 10 \cdot \left(-1\right) + z \cdot 5
|
20,273 |
(-\sqrt{x^2 + 1} + t + x) \cdot (t + x + \sqrt{x \cdot x + 1}) = t \cdot t + 2 \cdot x \cdot t + (-1)
|
18,968 |
zz = z \cdot z = z + 1
|
27,569 |
d \cdot x \cdot f = d \cdot x \cdot f = \frac{d}{x \cdot f}
|
6,208 |
34658 = 1^3 + 14^3 + 17^3 + 30^2 \times 30
|
34,920 |
\sqrt{-4} = \sqrt{4}*\sqrt{-1} = 2i
|
5,919 |
258\cdot 4 + 147 \left(-7\right) = 3
|
1,423 |
\binom{5}{1} \times 6! \times 5! \times 2 = 864000
|
28,480 |
0 = \frac{z^2 - y^2}{z^2 + y \cdot y} \implies z \cdot z = y \cdot y
|
-30,287 |
\frac12(0 + 8) = \frac82 = 4
|
-26,654 |
3\times z^2 - z\times 20 + 7\times (-1) = (z\times 3 + 1)\times (z + 7\times (-1))
|
15,878 |
(n * n + \frac{n}{2})^2 = n^4 + n^3 + \tfrac{1}{4}n^2 < n^4 + n^3 + n * n + n + 1
|
-20,225 |
-\frac72\cdot (-\frac{1}{-9}\cdot 9) = \frac{63}{-18}
|
18,049 |
\frac{1}{2} \cdot (\frac{10303}{63} + 9 \cdot \left(-1\right)) = \dfrac{1}{63} \cdot 4868 \approx 77.27
|
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