id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
31,423
|
12!*2!*\binom{11}{2} = 14! - 13!*2! - 12!*2!*12 - 11!*2!*12*11
|
1,863
|
\left|{Z D + j}\right| = \left|{D Z + j}\right|
|
1,680
|
4 \cdot \cot(x) = \sqrt{3} \cdot (\cot^2(x) + 1) = \sqrt{3} \cdot \csc^2(x)
|
27,019
|
b^2 + 1 = xf\Longrightarrow x = \frac{1}{f}(b^2 + 1)
|
-21,030
|
\frac{1}{5 \cdot z + 20} \cdot \left(5 \cdot \left(-1\right) + 25 \cdot z\right) = \frac{1}{z + 4} \cdot ((-1) + 5 \cdot z) \cdot 5/5
|
2,575
|
1 + y^2 - 2\cdot y = \left((-1) + y\right)^2
|
14,126
|
(u\cdot u) \cdot (u\cdot u) = (u^2)^2 = u^4
|
11,396
|
\frac{2^1}{2}\cdot 5 = 20/4
|
30,571
|
3 \times (1/k - \frac{1}{k + \frac{1}{3}}) = \frac{1}{(k + 1/3) \times k}
|
32,470
|
r + (-r + 1)/4 = r \cdot \frac34 + 1/4
|
24,220
|
a^m h^n = a^m h^n
|
-11,953
|
2/5 = q/(20 π) \cdot 20 π = q
|
-19,703
|
8\cdot 4/\left(7\right) = \frac{32}{7}
|
-20,907
|
\frac33*\frac{x + 9*(-1)}{x*6 + 8} = \frac{3*x + 27*(-1)}{18*x + 24}
|
10,229
|
\sin(\frac{π*3}{2}) = -1
|
4,159
|
-((-1) + n) \cdot ((-1) + n) = (-1) - n \cdot n + 4\cdot n - 2\cdot n
|
-19,707
|
54/7 = \frac{54}{7} \cdot 1
|
28,472
|
|\alpha_1| = |\alpha_2| = r \implies |\alpha_1 \cdot \alpha_2| = r
|
26,184
|
3\cdot (\frac{1}{2}\cdot 3782 - 27\cdot 28/2) = 3\cdot (28 + 29 + \dots + 60 + 61)
|
23,405
|
H \cdot H = 0 \implies H = 0
|
-23,598
|
2/5 \cdot \frac17 \cdot 2 = \frac{1}{35} \cdot 4
|
-9,295
|
-3\cdot 2\cdot 3 + 3\cdot 3\cdot 3\cdot 3 t = 81 t + 18 \left(-1\right)
|
-5,615
|
\frac{1}{x \cdot 5 + 40 (-1)} 5 = \frac{5}{5 \left(8 (-1) + x\right)}
|
-10,410
|
\frac{2}{2}\cdot (-\frac{1}{5\cdot p + 5\cdot \left(-1\right)}) = -\frac{2}{10\cdot p + 10\cdot \left(-1\right)}
|
29,361
|
6z + 5y = 7z + 3y + 1 = 2\left(z + 6y + (-1)\right)
|
34,844
|
16 x^2 - 8x + 1 = (4x)^2 - 2 \cdot 4x + 1^2 = (4x + (-1))^2
|
31,809
|
\frac{G}{D} = \frac{G}{D}
|
-617
|
e^{\frac{\pi}{12} \cdot i \cdot 18} = (e^{\frac{i}{12} \cdot \pi})^{18}
|
414
|
\frac{1}{V\cdot (x + \frac{1}{V})} = \frac{1}{1 + V\cdot x}
|
-5,741
|
\frac{3 \times p}{(p + 9 \times (-1)) \times ((-1) + p)} = \frac{p \times 3}{9 + p \times p - 10 \times p} \times 1
|
35,157
|
\sin(\frac{\pi}{18} 5) > \sin(\dfrac{\pi}{4})
|
22,065
|
x^2 + x + 1 = \frac{x^3 + (-1)}{\left(-1\right) + x}
|
29,596
|
y^3\cdot 3 + 6\cdot y = (y + (-1))^3 + y^3 + (y + 1)^3
|
30,304
|
d/dx (2\cdot x^2 + 3\cdot x + 5) = 3 + 4\cdot x
|
-3,682
|
\dfrac89 \cdot y = \frac89 \cdot y
|
6,076
|
z^2 = 2\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{...\cdot 2}}}}}} = 2z
|
-26,595
|
-4\cdot y^2 + 81 = 9^2 - (y\cdot 2)^2
|
26,745
|
(2 \cdot n)^2 = 2 \cdot (m \cdot 2)^2 \Rightarrow n \cdot n = m^2 \cdot 2
|
-5,491
|
\frac{y*2}{2(-1) + y^2 - y} = \frac{2y}{(2(-1) + y) (1 + y)}
|
17,526
|
1/(f*b) = 1/(b*f) = b*f
|
-16,670
|
2 = 2\cdot 4\cdot x + 2\cdot \left(-2\right) = 8\cdot x - 4 = 8\cdot x + 4\cdot \left(-1\right)
|
-2,658
|
5 \cdot \sqrt{7} - \sqrt{7} \cdot 3 = \sqrt{25} \cdot \sqrt{7} - \sqrt{9} \cdot \sqrt{7}
|
19,276
|
2*π^2*r^2*R = π*R*2*r * r*π
|
-20,869
|
\frac{1}{(-6)*x}*\left(10*(-1) + x\right)*10/10 = (10*x + 100*(-1))/(x*(-60))
|
-25,585
|
\frac{\mathrm{d}}{\mathrm{d}t} \left(3 \cdot \cos(t)\right) = -3 \cdot \sin(t)
|
26,005
|
x \cdot r \cdot v + t \cdot x \cdot v = v \cdot x \cdot (t + r)
|
30,843
|
(3!)(2!)(2!)(2!)=48
|
22,494
|
2/4 \cdot \frac23 + 3 \cdot \frac14/3 = 7/12
|
29,102
|
644 + 1 + 322 + 161 + 160 = 1288
|
-20,979
|
\frac22 \cdot \tfrac12 \cdot (-z \cdot 7 + 5 \cdot (-1)) = (10 \cdot (-1) - 14 \cdot z)/4
|
39,461
|
19681 = 2\cdot \left(-1\right) + 3^9
|
46,739
|
\sum_{k=1}^n (x_k - m) = \sum_{k=1}^n x_k - \sum_{k=1}^n m = \sum_{k=1}^n x_k - m \cdot n
|
23,065
|
\sqrt{25\cdot l + 49} = 5\cdot \sqrt{l + 2 - \frac{1}{25}} \approx 5\cdot \sqrt{l + 2}
|
-26,622
|
\left(y^3 \times 4\right)^2 - 9^2 = (y^3 \times 4 + 9 \times (-1)) \times (y \times y \times y \times 4 + 9)
|
15,538
|
k = -5 \cdot k + 2 \cdot k \cdot 3
|
11,682
|
x y - y x_0 + y x_0 - x_0 y_0 = x y - x_0 y_0
|
13,678
|
5 = -202\cdot 37 + 7479
|
-6,430
|
\frac{1}{(t + 9) \cdot 3}5 = \dfrac{5}{t \cdot 3 + 27}
|
10,134
|
|x_0| = \sqrt{\frac{n\cdot 2}{n + 1}} \implies \frac{1}{2 - x_0 \cdot x_0}\cdot x_0 \cdot x_0 = n
|
-27,654
|
\frac{3}{2} + 5/2 + 2 \cdot \left(-1\right) = 4 + 2 \cdot (-1) = 2
|
-26,157
|
-1 + 25/(-1) - -5 + 25/\left(-5\right) = -26 + 10 = -16
|
33,030
|
0 = \tan^{-1}(\tfrac{0}{\sqrt{2}})
|
14,403
|
7^2*4 = 12^2 + 4^2 + 6^2
|
10,736
|
(f + 3) (\left(-1\right) + f) (1 + f)^2 = (f^2 + f \cdot 2 + 1) (3(-1) + f^2 + f \cdot 2)
|
12,756
|
x = k\dfrac{x}{k} = x/k + x/k
|
17,853
|
w - w + x - x = -(x + w) + x + w
|
22,815
|
(2 + 1) \left(4 + 1\right) (2 + 1) = 45
|
-1,246
|
\dfrac81 \cdot 3/2 = 3 \cdot 1/2/\left(1/8\right)
|
33,715
|
1/2 + 0 = \frac14\cdot 2 \lt \frac{1}{\pi}\cdot 2
|
-2,747
|
\sqrt{160} + \sqrt{40} = \sqrt{16\cdot 10} + \sqrt{4\cdot 10}
|
7,164
|
\frac{2}{3 - \frac{2}{-\frac{2}{3 + \left(-1\right)} + 3}} = 1
|
39,306
|
\frac{df}{d\theta} = \frac{df}{dy} \cdot \frac{dy}{d\theta} = \frac{df}{dy} \cdot \left(-(1 - y \cdot y)^{\frac{1}{2}}\right)
|
-26,544
|
100 - 9 \cdot x^2 = -\left(3 \cdot x\right)^2 + 10^2
|
2,495
|
\cos{e}\cdot \sin{c} + \cos{c}\cdot \sin{e} = \sin\left(c + e\right)
|
11,717
|
8 = d^2 - g^2 = (d + g) (d - g)
|
-10,323
|
\frac{1}{20 \cdot z} \cdot (z \cdot 2 + 8 \cdot (-1)) = 2/2 \cdot \frac{z + 4 \cdot (-1)}{z \cdot 10}
|
35,359
|
y^2 \cdot 7 + x \cdot x + x \cdot y \cdot 5 = \frac14 \cdot 3 \cdot y \cdot y + (x + 5 \cdot y/2) \cdot (x + 5 \cdot y/2)
|
-4,204
|
\frac{45 \cdot p^4}{60 \cdot p^5} \cdot 1 = \frac{p^4}{p^5} \cdot 45/60
|
-24,156
|
2 + 8\cdot 4 = 2 + 32 = 34
|
39,755
|
-\operatorname{arccot}(x) = \operatorname{arccot}\left(-x\right)
|
11,636
|
\frac{1}{8}*88 = 11
|
44,154
|
\lim_{x \to 0} \frac1x \cdot \left(\left(2 \cdot x\right)^{\dfrac{1}{2}} - 2^{1 / 2}\right) = 2^{1 / 2} \cdot \lim_{x \to 0} \frac{x^{\frac{1}{2}} + (-1)}{x + (-1) + 1} = 2^{\frac{1}{2}} \cdot \lim_{x \to 0} \dfrac{x^{1 / 2} + (-1)}{(x^{1 / 2} + (-1)) \cdot \left(x^{1 / 2} + 1\right) + 1} = 2^{1 / 2} \cdot \lim_{x \to 0} \frac{1}{x^{\frac{1}{2}} + 1 + \frac{1}{x^{1 / 2} + (-1)}}
|
6,969
|
1/16 (-150) + \dfrac{15}{16}\cdot 10 = 0
|
14,578
|
(a + 4\left(-1\right))^2 + b^2 = a^2 - 8a + 16 + b^2 = a^2 + b^2
|
-610
|
e^{π \cdot i \cdot 19/12 \cdot 8} = (e^{\frac{19}{12} \cdot π \cdot i})^8
|
2,846
|
t^2 - t\cdot 2 + 1 = ((-1) + t)\cdot (t + (-1))
|
47,241
|
1^2 = 1 \gt 0
|
-20,950
|
\frac{1}{-35\cdot p + 7\cdot (-1)}\cdot 35 = \frac{7}{7}\cdot \dfrac{5}{\left(-1\right) - 5\cdot p}
|
-2,127
|
-\frac{\pi}{2} = -\pi + \pi/2
|
46,800
|
10\times 4\times 2 = 80
|
34,261
|
-\pi/3 = \operatorname{asin}(\sin{4 \cdot \pi/3})
|
34,891
|
2^2\cdot10 = 40
|
3,579
|
0 = 24 + z*4 \implies z = -6
|
-11,081
|
(x + 10\times (-1))^2 + f = (x + 10\times \left(-1\right))\times \left(x + 10\times (-1)\right) + f = x^2 - 20\times x + 100 + f
|
19,384
|
a^j\cdot a^j = a^{j\cdot 2}
|
-7,741
|
\frac{i*26 + 2}{-3*i + 5} = \dfrac{i*26 + 2}{5 - i*3}*\frac{5 + i*3}{3*i + 5}
|
8,450
|
(a_n - a)*(a^2 + a_n^2 + a_n*a) = -a^3 + a_n^3
|
-1,265
|
\frac{1}{72} \cdot 15 = \frac{15 \cdot 1/3}{72 \cdot \frac{1}{3}} = \dfrac{5}{24}
|
22,318
|
(-1) + \left(d + (-1)\right)^3 + 2 \cdot (d + \left(-1\right)) = d^3 - 3 \cdot d \cdot d + 5 \cdot d + 4 \cdot (-1)
|
26,167
|
9\left(-1\right) + x^2*6 - 15 x = \left(x * x*2 - x*5 + 3(-1)\right)*3
|
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