id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-8,090
|
\frac{1}{26} (115 + 75 i - 23 i + 15) = \frac{1}{26} (130 + 52 i) = 5 + 2 i
|
10,888
|
\dfrac{1}{(z_1 + 2 \cdot (-1)) \cdot (z_2 + 2 \cdot (-1))} \cdot ((-5) \cdot (-z_1 + z_2)) = \dfrac{1}{(2 \cdot (-1) + z_2) \cdot (2 \cdot (-1) + z_1)} \cdot (-(3 \cdot (-1) + 4 \cdot z_1) \cdot \left(2 \cdot (-1) + z_2\right) + \left(3 \cdot (-1) + 4 \cdot z_2\right) \cdot \left(2 \cdot (-1) + z_1\right))
|
14,231
|
bw + dw = w*(b + d)
|
-6,349
|
\frac{x \cdot 2}{x^2 + x \cdot 12 + 35} \cdot 1 = \tfrac{x \cdot 2}{(5 + x) \cdot \left(x + 7\right)}
|
23,187
|
\lambda_i \cdot (j - k) = j \cdot \lambda_i - k \cdot \lambda_i
|
23,553
|
\left(-y + 1\right) \cdot \left(y + 1\right) = -y^2 + 1
|
8,990
|
\left\{256, \ldots, 129130\right\} = F_1 \Rightarrow |F_1| = 128
|
21,849
|
\sqrt{\sin^2(t) + \cos^2(t)} td a = td a
|
-10,084
|
0.01 \cdot (-99) = -99/100 = -0.99
|
47,607
|
\sin(x)=2\,{\frac {\tan \left( x/2 \right) }{1+ \left( \tan \left( x/2 \right) \right) ^{2}}}
|
19,450
|
\frac{269}{8} + \frac18 \cdot (5 \cdot (-1) + 2 \cdot x) \cdot (x^2 \cdot 4 + x \cdot 10 + 49) = x^3 + x \cdot 6 + 3
|
17,141
|
a - D - c = a - D - c
|
25,176
|
(x+x^2+\cdots+x^6)^3= (x+x^2+\cdots+x^6) (x+x^2+\cdots+x^6) (x+x^2+\cdots+x^6)
|
17,785
|
p = 1/2 = 1 - p
|
5,644
|
-\dfrac{1}{(x + 1) \cdot (x + 1)} = d/dx \frac{1}{1 + x}
|
5,422
|
-y + y \cdot y = y\cdot (y + \left(-1\right))
|
26,094
|
(a + b)^2 = a \cdot a + b \cdot b + 2\cdot a\cdot b = a^2 + b^2 + a\cdot b = a + b + a\cdot b = a\cdot b
|
7,476
|
n\cdot \frac{1}{3}\cdot 17 - 14/3 = 5/3\cdot n - 14/3 + 12/3\cdot n
|
10,523
|
6666 \cdot \dfrac12 \cdot 120 = 6666 \cdot 60
|
33,888
|
\sin^2\phi=1-\cos^2\phi
|
-20,482
|
-1/7 \frac{n \cdot 10 + 4}{n \cdot 10 + 4} = \frac{1}{28 + 70 n}(4(-1) - n \cdot 10)
|
-1,373
|
(\frac16\times \left(-5\right))/(1/4\times 9) = -5/6\times 4/9
|
5,783
|
-(m + \left(-1\right))^2 = -m^2 + 4*m + (-1) - 2*m
|
-19,305
|
\frac{\frac{1}{4} \cdot 5}{3 \cdot \frac{1}{5}} = \frac{5}{3} \cdot \frac{5}{4}
|
49,147
|
42=7\cdot6
|
8,896
|
5\cdot i^2 + i^2\cdot 3 + i^2 = 9\cdot i \cdot i
|
-11,982
|
1/2 = r/(4\cdot \pi)\cdot 4\cdot \pi = r
|
16,335
|
q \cdot (e^2 - e) = 0 = (q \cdot e - q) \cdot e
|
7,844
|
\frac{1}{l + l^2} = \frac1l - \frac{1}{1 + l}
|
22,868
|
\cos\left(x\right) = (-1) + 2\cdot \cos^2(\dfrac{x}{2})
|
6,789
|
y_p\cdot y_l = y_l\cdot y_p
|
2,289
|
2^i = 2\cdot 2^{i + (-1)}
|
29,350
|
\left(x - f\right) * \left(x - f\right) = (x - f)*(x - f)
|
14,970
|
120\cdot x + x\cdot 22 = 142\cdot x
|
26,019
|
\frac1n \cdot (n + 1) \cdot x = \frac{x^{1 + n}}{n \cdot x^n} \cdot (1 + n)
|
6,555
|
\dfrac{3}{2} = 3/2 = 2\cdot 3/4
|
10,129
|
t \cdot U = t \cdot Y = k rightarrow t \cdot U \cdot Y = k
|
39,097
|
(f - c)^2 = -(d - g)^2 rightarrow 0 = \left(-g + d\right)^2 + \left(-c + f\right)^2
|
-19,501
|
\frac{4 \cdot 1/3}{7 \cdot 1/6} = 4/3 \cdot 6/7
|
1,684
|
M + M^2 + M^3 + M^4 + \dotsm = \frac{M}{1 - M}
|
24,321
|
\frac{\pi}{12} = -\frac{\pi}{6} + \frac{\pi}{4}
|
28,627
|
d \cdot 0 = 0 = 0 \cdot d
|
14,160
|
h + h = (h + h)^2 = h^2 + h \cdot h + h^2 + h^2 = h + h + h + h \Rightarrow 0 = h + h
|
18,217
|
2a + 6a = 8a = 2^3 a
|
20,754
|
\left(x + \sqrt{2}\right) \cdot \left(x - \sqrt{2}\right) = 2 \cdot (-1) + x \cdot x
|
-20,008
|
\dfrac{1}{1}\cdot 1 = \frac{-4\cdot a + 2}{2 - 4\cdot a}
|
22,910
|
(-1) + x^3 - x^2 + x = \left(1 + x^2\right)\times \left((-1) + x\right)
|
-23,242
|
\tfrac{5}{18} = \tfrac{5}{8} \cdot 4/9
|
2,370
|
y^{2 \cdot (-1) + 4/3} = y^{-\frac{2}{3}}
|
20,920
|
y\frac{dy}{dx}=\frac{d}{dx}\left(\frac{y^2}{2}\right)
|
32,736
|
c^{m + n} = c^n*c^m
|
-4,364
|
x\dfrac134 = x*4/3
|
-3,275
|
\sqrt{16\cdot 7} - \sqrt{7} + \sqrt{4\cdot 7} = \sqrt{28} + \sqrt{112} - \sqrt{7}
|
6,940
|
d_1 \cdot d_2 = 0 = d_2 \cdot d_1
|
-27,459
|
5 + \frac{15}{4} + \frac{1}{16} 45 = 185/16
|
-26,549
|
y^2 \cdot 3 + 30 y + 75 = 3 \left(25 + y^2 + y \cdot 10\right)
|
29,462
|
2\alpha + \beta = \left(\beta/2 + \alpha\right) \cdot 2
|
22,018
|
(-h + a)*(h + a) = -h^2 + a^2
|
-2,255
|
-7/11 + \dfrac{10}{11} = 3/11
|
30,092
|
\left(\frac{\partial}{\partial x} (x\cdot u) = e^x \Rightarrow x\cdot u = \int e^x\,dx = e^x + b\right) \Rightarrow (e^x + b)/x = u
|
-3,578
|
\dfrac{p^5}{p} = pp p p p/p = p^4
|
-18,265
|
\frac{(2*\left(-1\right) + s)*(s + 8*(-1))}{s*\left(s + 8*\left(-1\right)\right)} = \frac{16 + s^2 - s*10}{-s*8 + s^2}
|
-5,492
|
\frac{3}{\left(t + 4 \cdot \left(-1\right)\right) \cdot 2} = \frac{3}{8 \cdot (-1) + 2 \cdot t}
|
14,138
|
\frac{1}{2^n \cdot n \cdot 2} \cdot 2^{2 \cdot n} = \tfrac{2^n}{n \cdot 2}
|
-29,412
|
-\dfrac{6}{7} \times \left(-\dfrac{5}{4}\right) = \dfrac{-6 \times (-5)}{7 \times 4} = \dfrac{30}{28} = \dfrac{15}{14}
|
8,016
|
\binom{2}{1} \binom{4}{1} \binom{4}{1} \binom{10}{1} + 8 = 328
|
29,520
|
c \cdot x \cdot B = c \cdot x \cdot B
|
-24,779
|
\frac14 (-\sqrt{2} + \sqrt{6}) = \cos{\pi\cdot 5/12}
|
7,149
|
x_i = x_i*0*0
|
1,284
|
3 = 3^{\tfrac12} \cdot 3^{1/2}
|
-6,754
|
72 = 6 \cdot 4 \cdot 3
|
2,963
|
1^3 + 2^3 + 3^3\cdot \dots + m^3 = (1 + 2 + 3\cdot \dots + m)^2
|
24,361
|
x c = 1 \Rightarrow c x = 1
|
10,695
|
(-p + 1)/p = \tan^2(w) rightarrow \cos^2(w) = p
|
-18,053
|
38 + 3\times (-1) = 35
|
2,757
|
|h + x*i| = \left(h^2 + x^2\right)^{1 / 2} = |h - x*i|
|
41,241
|
\tan(x+y)=\frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)}=1 \implies x+y=\frac{\pi}{4}
|
-21,130
|
\frac{3}{4}\cdot \frac{2}{2} = \frac{1}{8}\cdot 6
|
9,041
|
d/b \cdot b = d \cdot b/b
|
25,488
|
\left(b_X + (-1)\right) \cdot (1 + b_X) = (-1) + b_X \cdot b_X
|
11,525
|
y^2 + 10\cdot y + 15 = y^2 + 10\cdot y + 25 + 10\cdot (-1) = (y + 5)^2 - \left(\sqrt{10}\right)^2
|
25,068
|
1/2 = 0 + \frac14 + \frac18 + \dotsm
|
-6,382
|
\dfrac{2}{40\cdot (-1) + x \cdot x - 3\cdot x} = \tfrac{2}{(x + 8\cdot (-1))\cdot (x + 5)}
|
12,418
|
n*x - x*m = (n - m)*x
|
-1,858
|
\pi/3 + \frac143 \pi = \pi \dfrac{13}{12}
|
31,433
|
\tfrac16\times (1 + 2 + 3 + 4 + 5 + 5) = \frac{10}{3} = 3.333
|
159
|
\cos(y) \cos(z) - \sin(y) \sin(z) = \cos(z + y)
|
2,268
|
e * e*e * e * e*0 = 0
|
27,322
|
\frac{y}{\sqrt{y^2 + 1}} = \sin\left(\tan^{-1}(y)\right)
|
33,936
|
\frac{dz}{dt} = \frac{dz^1 + 1}{dt^1 + 1}/(\frac{dz}{dt})
|
31,051
|
3000 = 5^3*2 * 2 * 2*3
|
-6,177
|
\frac{1}{2 \cdot \left(s + 5 \cdot (-1)\right)} \cdot 2 = \dfrac{2}{s \cdot 2 + 10 \cdot \left(-1\right)}
|
-4,049
|
y^2*\dfrac32 = \dfrac{y^2*3}{2}
|
-20,264
|
\frac{1}{-20\cdot p + 30}\cdot (p\cdot 24 + 36\cdot \left(-1\right)) = -\frac15\cdot 6\cdot \frac{-p\cdot 4 + 6}{6 - 4\cdot p}
|
11,185
|
-k_2 + k_1 \cdot (\left(-1\right) + k_2) = -k_2 + k_2 \cdot k_1 - k_1
|
13,895
|
z_2^2 + z_1^2 + z_2 \cdot z_1 \cdot 2 = (z_1 + z_2) \cdot (z_1 + z_2)
|
17,594
|
\frac{1}{12} = \frac1y\cdot 7 \Rightarrow y = 84
|
-23,161
|
-\frac19*16*2/3 = -\frac{1}{27}*32
|
32,456
|
(p^2)^2 = p^4
|
9,212
|
\frac{1}{x + 1} = \frac{1}{x^2 + (-1)}*((-1) + x)
|
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