id
int64 -30,985
55.9k
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|---|---|
-27,733 |
\frac{\mathrm{d}}{\mathrm{d}z} \sec{z} = \sec{z}*\tan{z}
|
28,232 |
\left(a^m + z^m \Leftrightarrow a + z = 0\right) \implies a^m + z^m = 0
|
-4,840 |
\tfrac{7.2}{10} = 7.2/10
|
3,579 |
4*x + 24 = 0 \implies x = -6
|
30,671 |
0 = \tilde{c}^n rightarrow c^n = 0
|
-30,713 |
5\cdot (-1) + 20\cdot x = 5\cdot (x\cdot 4 + (-1))
|
-18,154 |
13*(-1) + 63 = 50
|
6,661 |
w\cdot 2\cdot x\cdot 3 = 6\cdot x\cdot w
|
-8,005 |
\frac{1}{32} \cdot (-80 + 80 \cdot i + 80 \cdot i + 80) = \left(0 + 160 \cdot i\right)/32 = 5 \cdot i
|
-5,023 |
2.01*10 = \frac{20.1}{10}1 = 2.01*10^0
|
28,603 |
t^2 - y^2 = \left(t - y\right)\cdot (y + t)
|
10,872 |
33! = 2^{2 (-1) + 33}*4043484860477916195764296875
|
14,677 |
\arctan(\infty/(\sqrt{2})) = \frac{\pi}{2}
|
33,036 |
-1.625 = -\frac1813
|
26,592 |
a^2 - f^2 = (a - f)\cdot \left(f + a\right)
|
6,836 |
\frac{1}{x\alpha} = 1/(x\alpha)
|
29,821 |
5!*4!*4315*6! = 8947584000
|
14,748 |
-80*2^2 * 2 + 3 * 3 * 3*24 = 2^3
|
10,388 |
\frac{3^3}{3} + 3^2 + \frac{6}{3} \cdot 1 = 20
|
17,934 |
\left(y = 1^{\tfrac1n} \Rightarrow y^n = 1\right) \Rightarrow 0 = y^n + \left(-1\right)
|
29,045 |
\dfrac{1}{y^6} = (\frac{1}{y})^6
|
40,192 |
|A \cdot B - I \cdot \lambda| = |A \cdot B - \lambda \cdot I|
|
17,169 |
\frac{\mathrm{d}v}{\mathrm{d}t} = a\Longrightarrow 2av = 2v\frac{\mathrm{d}v}{\mathrm{d}t}
|
274 |
\dfrac{1}{k!} (2 (1/2 + (-1)) (2 (-1) + 1/2) \ldots\cdot \left(\frac12 - k + 1\right))^{-1} = \binom{\frac{1}{2}}{k}
|
8,233 |
2 = e + b \implies e - b = 8
|
10,019 |
p\cdot p^{m + \left(-1\right)} = p^m
|
30,706 |
y = x rightarrow y = x
|
110 |
(h + a)^2 = 2 \times a \times h + a \times a + h^2
|
24,710 |
2 (-1) + y^2 + y = (2 + y) ((-1) + y)
|
24,489 |
6\cdot \left(-1\right) + 20 = 14
|
13,600 |
1/3 + \dfrac{2}{9} = \frac39 + \frac29 = 5/9
|
28,247 |
2^{2 \cdot l} = (2^2)^l = 4^l
|
-10,423 |
\frac{3 \cdot n + 1}{n \cdot 2} \cdot \frac55 = \frac{5 + n \cdot 15}{n \cdot 10}
|
19,917 |
1 + z^2 + z = (\frac12 + z)^2 + 3/4
|
-4,292 |
\frac{10}{x}\times 1/9 = \frac{10}{9\times x}
|
-23,510 |
\tfrac{5 / 7}{3}\cdot 1 = \dfrac{5}{21}
|
19,943 |
x = F\Longrightarrow \frac{x}{F} = 1
|
13,180 |
\tfrac1dx = (1 + 4l)^{1/2} \Rightarrow \tfrac{x^2}{d \cdot d} = 2 + 4l
|
-28,410 |
x \cdot x + 10 x + 41 = x^2 + 10 x + 25 + 16 = (x + 5)^2 + 16 = (x + 5)^2 + 4^2
|
29,061 |
n\times 3 + n = 4\times n
|
-20,978 |
\dfrac{3}{3}*\frac{-4*t + 5}{-7*t + 4} = \frac{15 - t*12}{-21*t + 12}
|
37,319 |
0 = 0C = C
|
7,095 |
1/3 (2/3) \cdot (2/3) \cdot (2/3) = 8/81
|
25,669 |
{52 \choose 5} = 49\cdot 48\cdot 50\cdot 51\cdot 52/5!
|
34,596 |
119^2 + 120 * 120 = 169^2
|
7,889 |
fb = \frac{1}{fb} = 1/\left(bf\right) = bf
|
37,668 |
1/(k*x) = \dfrac{1}{k*x}
|
12,852 |
c_2 \cdot c_2 + c_1\cdot c_2\cdot 2 + c_1^2 = (c_2 + c_1) \cdot (c_2 + c_1)
|
21,027 |
4 \cdot g + 2 \cdot (-1) \gt 0 \Rightarrow 2^{4 \cdot g + 2 \cdot \left(-1\right)} > 2^0 = 1
|
5,531 |
z^2 + z*2 + 2 = (z + 1)^2 + 1
|
-16,037 |
9*8*7*6*5 = \frac{9!}{(9 + 5*(-1))!} = 15120
|
21,731 |
1 = a \cdot b\Longrightarrow 1 = a \cdot b
|
26,341 |
(c^2 + h^2 - c \cdot h) \cdot (h + c) = c^3 + h^3
|
36,511 |
-\cos(\phi) = \cos(\pi - \phi)
|
5,887 |
exp(\ln(e)) = e
|
3,344 |
\|g\| = \|\frac{1}{\lambda - A}\cdot g\cdot (\lambda - A)\| \leq \|(\lambda - A)\cdot g\|
|
-30,270 |
(y + 3\cdot (-1))\cdot \left(3 + y\right) = y^2 + 9\cdot (-1)
|
4,851 |
\mu*\frac{\partial}{\partial \mu} \sum_{i=1}^n \mu^i = \sum_{i=1}^n i*\mu^i
|
8,872 |
\frac{1}{3}*3^{-j} = 3^{-(j + 1)}
|
19,600 |
W\cdot (C - B)\cdot r = -r\cdot B\cdot W + r\cdot C\cdot W
|
32,878 |
(1 + z) \cdot ((-1) + z) = z^2 + (-1)
|
19,163 |
-4 \cdot a \cdot b + (a + b)^2 = (a - b) \cdot (a - b)
|
48,330 |
3^2 = 2 + 7
|
3,738 |
a^2/2 = a*1/2*a
|
8,600 |
b \cdot a \cdot b = b^2 \cdot b \cdot a/b
|
7,732 |
\sin(B + Y) = \sin(Y)*\cos(B) + \cos(Y)*\sin(B)
|
-27,498 |
f\cdot f\cdot 7\cdot 5 = 35\cdot f^2
|
10,001 |
-3\cdot (x + 2\cdot (-1))^2 = -3\cdot \left(2\cdot (-1) + x\right)\cdot (x + 2\cdot \left(-1\right))
|
-10,727 |
\frac55 \times \left(-\frac{10 + y}{y^2 \times 5}\right) = -\frac{50 + y \times 5}{y \times y \times 25}
|
33,102 |
x^2 \cdot x_\alpha \cdot \psi = x_\alpha \cdot x^2 \cdot \psi = x_\alpha \cdot k \cdot (k + 1) \cdot \psi = k \cdot (k + 1) \cdot x_\alpha \cdot \psi
|
-29,828 |
\frac{\mathrm{d}}{\mathrm{d}x} \left(x^3 - x^2*4 + 3x\right) = 3 + x^2*3 - 8x
|
-1,604 |
-\pi/3 + 2\pi = \pi \frac53
|
41,251 |
\frac{1 - \sqrt{5}}{2} = \frac{1}{2} - \frac{\sqrt{5}}{2}
|
24,067 |
75 - 81*12 + 75*12 = 75 - (81 + 75*(-1))*12
|
-9,642 |
0.01\cdot (-92) = -\dfrac{92}{100} = -0.92
|
24,393 |
b^x = b^x
|
3,126 |
x^2 + \epsilon \cdot \epsilon + A^2 = (x + 2 \cdot \left(-1\right)) \cdot (x + 2 \cdot \left(-1\right)) + (\epsilon + 4 \cdot (-1))^2 + \left(A + 3 \cdot (-1)\right)^2 = \left(x + 10 \cdot (-1)\right) \cdot \left(x + 10 \cdot (-1)\right) + (\epsilon + 8 \cdot \left(-1\right))^2 + (A + 9 \cdot (-1))^2
|
10,500 |
x*(1 + l) = x + x*l
|
15,028 |
\left((-d + a)^2 + \left(d - c\right)^2 + (c - a)^2\right)/2 = a^2 + d \cdot d + c^2 - a \cdot d - c \cdot d - a \cdot c
|
5,258 |
1/6 \times {2 \choose 1}/6 = \frac{1}{18}
|
-13,884 |
(9 + 1 \times 2) - 1 \times 8 = (9 + 2) - 1 \times 8 = 11 - 1 \times 8 = 11 - 8 = 3
|
6,390 |
5 + 12\cdot i = \left(2\cdot i + 3\right)^2
|
3,777 |
d/dx y \cdot y \cdot y = 3 \cdot y^2 \cdot \frac{dy}{dx}
|
25,839 |
E(x) E(Y) = E(Yx)
|
10,056 |
\dfrac{1}{3}\left(3l + 3(-1)\right) + \frac{1}{3}(3l \cdot l + 3l + 1) = (3l^2 + 6l + 2(-1))/3 = l^2 + 2l - 2/3
|
23,388 |
3 \cdot \frac12/3 = \dfrac{1}{\frac{1}{3}2 \cdot 3}
|
-18,277 |
\dfrac{1}{(y + 4) \cdot (y + 9)} \cdot \left(y + 4\right) \cdot (y + 7 \cdot (-1)) = \frac{y^2 - 3 \cdot y + 28 \cdot (-1)}{y \cdot y + 13 \cdot y + 36}
|
6,193 |
\frac{\mathrm{d}}{\mathrm{d}k} \frac{1}{2\cdot (-1) + k} = -\dfrac{1}{(2\cdot (-1) + k)^2}
|
12,287 |
\dfrac{1}{2} \cdot (-\sqrt{3} + 1) = 1/2 - \sqrt{3}/2
|
4,606 |
R/I \cdot x = R \cdot x/I
|
25,107 |
1 - y \cdot 8 + y^2 \cdot 12 = (2 \cdot y + (-1)) \cdot ((-1) + y \cdot 6)
|
4,988 |
\dfrac12\cdot \left(1 + 2017\right) = 1009
|
1,606 |
a^f/a = a^{(-1) + f}
|
1,303 |
\dfrac{2\cdot \tan{x}}{1 + \tan^2{x}} = \sin{x\cdot 2}
|
21,576 |
a \cdot b = (a \cdot b + b \cdot a)/2 = b \cdot a
|
13,291 |
\sum_{k=1}^x (1 + k) \cdot (k + (-1)) = \sum_{k=1}^x (1 + k) \cdot ((-1) + k)
|
-1,138 |
-8/7*5/6 = (1/7 (-8))/(6*1/5)
|
-12,107 |
\frac{1}{45} \cdot 44 = \frac{s}{18 \cdot \pi} \cdot 18 \cdot \pi = s
|
14,078 |
21 = a + b + d + h + 5\cdot (-1) + 5 + h = a + b + d + 2\cdot h
|
25,370 |
\left(2 + s\right)^2 + 1^2 = 5 + s^2 + s*4
|
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