id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
-20,000
|
9/8 \cdot \frac{-7 \cdot z + 5 \cdot (-1)}{-7 \cdot z + 5 \cdot (-1)} = \dfrac{-63 \cdot z + 45 \cdot (-1)}{-56 \cdot z + 40 \cdot \left(-1\right)}
|
21,381
|
a - x - c = a - x - c
|
22,380
|
\|-z_1 + V\| = \|V - z + z - z_1\|
|
-19,461
|
\frac{\tfrac12 \times 7}{9 \times 1/8} = 7/2 \times \frac89
|
11,927
|
-xy + x * x + y^2 = ((x - y) * (x - y) + x^2 + y^2)/2
|
35,440
|
\frac{1}{100}\cdot 20 = 1/5
|
696
|
(w^2 + 27 \cdot x^2) \cdot 4 = (2 \cdot x)^2 \cdot 27 + (w \cdot 2) \cdot (w \cdot 2)
|
6,723
|
\left(k + 1\right)\cdot (k + 1)\cdot (1 + k) = (k + 1) \cdot (k + 1) \cdot (k + 1)
|
18,333
|
\frac{1}{z\cdot z} = \frac{1}{z \cdot z}
|
40,849
|
|b| = |z - b - z| \leq |z - b| + |z|
|
11,413
|
2^{\dfrac{1}{2}}\cdot 11 + 9\cdot 3^{1 / 2} = (3^{1 / 2} + 2^{\frac{1}{2}}) \cdot (3^{1 / 2} + 2^{\frac{1}{2}}) \cdot (3^{1 / 2} + 2^{\frac{1}{2}})
|
12,399
|
z^4 + 5*z + 1 = \left(z^2 + 1\right)*(z^2 + (-1)) + 5*z + 5*(-1) = (z + (-1))*(z^3 + z^2 + z + 6)
|
-28,531
|
-y^2 - 4\cdot y + 21 = 21 - y^2 + 4\cdot y = 21 + 4 - y^2 + 4\cdot y + 4 = 25 - \left(y + 2\right)^2 = 5^2 - (y + 2)^2
|
2,583
|
x = z = \dfrac{1}{x} + 1/z
|
19,053
|
-27 = (-4) \cdot 12 + (-3) - 2 \cdot (-6) - (-2) \cdot 6
|
-19,649
|
7\times 6/\left(9\right) = \frac{42}{9}
|
7,071
|
15 + 5*100*a + 10*b*5 = a*100 + b*10 + 1 + 100*a + 10*b + 2 + ... + a*100 + b*10 + 5
|
-23,912
|
\frac{60}{4 + 8} = 60/12 = \frac{1}{12}*60 = 5
|
29,140
|
A\cdot Z = A\cdot Z
|
13,341
|
d \cdot h \cdot d \cdot b/d = b \cdot h \cdot d
|
12,817
|
(\left(-1\right) + y_2)^2 = \left((-1) + y_1\right)^2 \Rightarrow |\left(-1\right) + y_2| = |\left(-1\right) + y_1|
|
19,074
|
z\cdot e = e\cdot z
|
34,269
|
-y = \left(-4 \cdot y\right)^2 + y^2 = 17 \cdot y \cdot y
|
7,967
|
2 = x^{x^{x^x*\dotsm}} rightarrow x^2 = 2
|
29,894
|
2 \cdot r \cdot r \cdot \pi \cdot 2 = 4 \cdot \pi \cdot r^2
|
28,581
|
\frac{1}{n + 1} \cdot \left(n + (-1)\right) = \dfrac{1}{n + 1} \cdot (n + 1 + 2 \cdot (-1)) = 1 - \tfrac{1}{n + 1} \cdot 2
|
11,811
|
1 + x = \dfrac{(-1) + x^2}{(-1) + x}
|
-26,736
|
\sum_{l=1}^∞ \frac{1}{(l + 1)*\left(-2\right)^l}*(0 + 2)^l = \sum_{l=1}^∞ 1*\dfrac{2^l}{(l + 1)*(-2)^l} = \sum_{l=1}^∞ \frac{(-1)^l*2^l}{(l + 1)*2^l} = \sum_{l=1}^∞ \dfrac{(-1)^l}{l + 1}
|
4,081
|
x^3 + 24 \cdot (-1) = x \implies x^3 - x + 24 \cdot (-1) = (x + 3 \cdot (-1)) \cdot (x \cdot x + 3 \cdot x + 8) = 0
|
-4,753
|
y \cdot y + y \cdot 8 + 15 = (y + 3) \cdot (5 + y)
|
5,556
|
{6 + 4 + (-1) \choose \left(-1\right) + 4} = 84
|
-4,554
|
3*(-1) + x^2 - 2*x = \left(x + 1\right)*(3*\left(-1\right) + x)
|
36,311
|
a^n\times a^m = a^{m + n}
|
-29,004
|
\dfrac{1}{2} \cdot (-27 - 44) = -35.5
|
-2,210
|
-1/17 + \frac{1}{17} \cdot 5 = 4/17
|
8,050
|
136*(-1) + 504 = 368
|
-17,093
|
-3 = -3*2*t - -9 = -6*t + 9 = -6*t + 9
|
-711
|
e^{\pi \cdot i/4 \cdot 19} = (e^{\dfrac{\pi}{4} \cdot i})^{19}
|
16,386
|
-(\sqrt{17} + 1)/4 = -\sqrt{17}/4 - \frac14
|
156
|
2^{1.4} = 2^{\frac{1}{5}7} = (2^7)^{\tfrac15} = 128^{1/5} > 99^{1/5}
|
33,640
|
1 - \left(\frac56\right) * \left(\frac56\right) * \left(\frac56\right) (5/6 + \frac164) = 1 - \frac{125}{144} = \frac{19}{144}
|
-8,088
|
\frac12\cdot (-3 - 7\cdot i + 3\cdot i + 7\cdot (-1)) = \frac12\cdot (-10 - 4\cdot i) = -5 - 2\cdot i
|
8,064
|
\dfrac{\pi}{5}\cdot 2 + \frac{\pi}{10} = \pi/2
|
16,284
|
4 = {4 \choose 3}\cdot {0 + 4 + (-1) \choose 0}
|
479
|
-x^2 + 2 - x^2 = 2 - 2*x^2
|
5,057
|
i/2 = \frac{1}{2} + i - \frac{1}{2}\cdot (i + 1)
|
-20,396
|
\frac{t\cdot 5 + 4}{16\cdot (-1) - t\cdot 20} = -\tfrac{1}{4}\cdot \frac{-5\cdot t + 4\cdot \left(-1\right)}{-t\cdot 5 + 4\cdot (-1)}
|
12,506
|
-g^2 + f^2 = (f - g) \cdot \left(g + f\right)
|
-11,080
|
(x + 4\cdot (-1))^2 + f = (x + 4\cdot \left(-1\right))\cdot \left(x + 4\cdot (-1)\right) + f = x^2 - 8\cdot x + 16 + f
|
19,390
|
-k + b^2 \cdot k - b \cdot b + 1 = 0\Longrightarrow 0 = (b^2 + (-1)) \cdot \left(\left(-1\right) + k\right)
|
3,952
|
99 = 11\cdot 9 = (3^2 + 2\cdot 1^2)\cdot 3^2 = \left(3^2 + 2\cdot 1 \cdot 1\right)\cdot \left(1^2 + 2\cdot 2^2\right)
|
-2,841
|
6^{\frac{1}{2}}*9^{1 / 2} + 6^{1 / 2} = 6^{\frac{1}{2}} + 3*6^{\dfrac{1}{2}}
|
26,334
|
52 = 39 \left(-1\right) + 91
|
-598
|
\left(e^{i\pi/12}\right)^{15} = e^{15 i\pi/12}
|
38,738
|
\infty +2=\infty
|
9,714
|
t \cdot t + 6\cdot t + 10 = 1 + \left(t + 3\right)^2
|
25,040
|
l! = l\cdot \left(l + \left(-1\right)\right)!
|
38,535
|
\frac{1}{\sin{x}} = \csc{x}
|
11,578
|
\sqrt{k} + q\cdot b = q\cdot b + q\cdot b + \sqrt{k} - q\cdot b = 2\cdot b\cdot q + \tfrac{(\sqrt{k} - q\cdot b)\cdot (\sqrt{k} + q\cdot b)}{\sqrt{k} + q\cdot b} = 2\cdot b\cdot q + \frac{1}{(\sqrt{k} + b\cdot q)\cdot 1/\left(2\cdot q\right)}
|
294
|
\frac{2 \cdot y}{y + 2 \cdot \left(-1\right)} = \dfrac{1}{y + 2 \cdot \left(-1\right)} \cdot (2 \cdot y + 4 \cdot (-1) + 4) = 2 + \frac{4}{y + 2 \cdot \left(-1\right)}
|
41,578
|
\cos{0} + i \sin{0} = 1
|
36,494
|
\tan^2(\theta) = \sec^2\left(\theta\right) + (-1)
|
-157
|
-18 + 3 (-1) = -21
|
-28,763
|
\frac{y + 5\cdot (-1)}{-2\cdot y + 2} = -1/2 - \frac{1}{2 - y\cdot 2}\cdot 4
|
7,502
|
8/9 = 8\cdot \dfrac{1}{27}/(\frac{1}{3})
|
21,463
|
x_k = kx_k/k
|
9,884
|
\frac{4\cdot n + (-1)}{4\cdot n + 1} = \tfrac{1}{4\cdot n + 1}\cdot (4\cdot n + 1 + 2\cdot (-1)) = 1 - \frac{2}{4\cdot n + 1}
|
-20,400
|
-\dfrac{7}{10\cdot (-1) + n}\cdot \frac{9}{9} = -\frac{1}{9\cdot n + 90\cdot (-1)}\cdot 63
|
9,135
|
x^2 + 2\cdot x + 4 = x^2 + 2\cdot x + 1 + 3 = \left(x + 1\right)^2 + 3
|
16,082
|
32 \cdot (1 + 1/2 + \tfrac14 + \dots) = 10000 + 1000 + 100 + 10 + 1
|
9,401
|
(c \cdot b + 1) \cdot (c \cdot b + \left(-1\right)) = b^2 \cdot c^2 + (-1)
|
31,239
|
\mathbb{E}(\frac{1}{x^2}) = \dfrac{1}{x x}
|
-16,056
|
9\cdot 8\cdot 7\cdot 6 = \frac{9!}{(9 + 4\cdot (-1))!} = 3024
|
27,288
|
(N_k + 1) \cdot (N_x + (-1)) = N_k \cdot N_x + N_x - N_k + (-1) \gt N_k \cdot N_x
|
25,852
|
\frac{1}{8 + z \cdot 5} \cdot 2 = \frac{2 \cdot 1/z}{\frac{1}{z} \cdot 8 + 5}
|
-10,289
|
(10 \cdot (-1) + k \cdot 5)/k \cdot \frac44 = \frac{1}{4 \cdot k} \cdot \left(20 \cdot k + 40 \cdot (-1)\right)
|
-4,278
|
\frac{a^4}{a \cdot a \cdot a} \cdot 44/132 = \frac{44}{132 \cdot a^3} \cdot a^4
|
-20,187
|
\dfrac88 \cdot \frac{4 - 2 \cdot t}{3 + t} = \frac{32 - 16 \cdot t}{24 + 8 \cdot t}
|
3,918
|
-2 = 8 + \left(-10\right)
|
-10,279
|
-\dfrac{5}{3\cdot x + 12\cdot (-1)}\cdot \frac{5}{5} = -\frac{25}{x\cdot 15 + 60\cdot (-1)}
|
-18,483
|
4\cdot x + 2 = 10\cdot (3\cdot x + 7\cdot (-1)) = 30\cdot x + 70\cdot (-1)
|
36,262
|
\frac{1}{4} \sqrt{33} + 3/4 = \left(\sqrt{33} + 3\right)/4
|
3,906
|
\dfrac{1}{(t^2 + g^2)^2} \cdot t = \frac{\dfrac{1}{t \cdot t + g^2}}{t^2 + g^2} \cdot t
|
10,294
|
(-1/2)^{1 + k} = \frac{(-1)^{k + 1}}{2^{1 + k}}
|
33,608
|
(6^2 + (-1))/12 = \frac{35}{12}
|
6,964
|
2/n + 1 = \frac{1}{n} \cdot (2 + n)
|
19,551
|
-l \cdot 2 + x = 1 \Rightarrow l = \frac{1}{2} \cdot ((-1) + x)
|
2,117
|
-((-1) + x) + l + 1 = 2 + l - x
|
-2,175
|
-\pi/6 = -\pi\cdot \frac{1}{12}\cdot 23 + 7/4\cdot \pi
|
44,162
|
\frac{1}{x^2+4x+3}=\frac{1}{(x+1)(x+3)}=\frac{1}{2}\left(\frac{1}{x+1}-\frac{1}{x+3}\right)=\frac{1}{2}\left(\frac{1}{(x-2)+3}-\frac{1}{(x-2)+5}\right)
|
32,723
|
(-h + f) \cdot (h + f) = -h^2 + f^2
|
-7,002
|
\frac16\cdot 3\cdot \frac{1}{8}\cdot 5\cdot \frac{4}{7} = \frac{5}{28}
|
23,805
|
1 + 3 + \cdots + 2\times m + (-1) = m\times (2\times m + \left(-1\right) + 1)/2 = m^2
|
689
|
\dfrac{1}{c_1^2}\cdot c_2 \cdot c_2 = 3 \Rightarrow \frac{1}{c_1}\cdot c_2 = \frac{c_1\cdot 3}{c_2}
|
15,418
|
\tfrac{-v + 1}{(-v + 1)^{3/2}} = \tfrac{1}{\left(-v + 1\right)^{1/2}}
|
12,636
|
(a + b)^2 = a * a + 2*b*a + b * b
|
10,851
|
k^{1 / 2} = k^{1/2} = k^{1 - \frac{1}{2}} = \tfrac{1}{k^{1/2}}*k
|
31,286
|
\left\{..., 2, 3, 1\right\} = \mathbb{N}
|
-6,806
|
4 \times 8 \times 8 = 256
|
-15,819
|
-6\cdot 9/10 + 9/10 = -\frac{1}{10}\cdot 45
|
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