id
int64
-30,985
55.9k
text
stringlengths
5
437k
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