id
int64
-30,985
55.9k
text
stringlengths
5
437k
9,924
(-z + 1)*(1 + z + z^2) = 1 - z^3
-7,873
\frac{1}{-3 - i}(2 - i\cdot 16) = \dfrac{2 - i\cdot 16}{-3 - i} \dfrac{-3 + i}{-3 + i}
28,637
\cos\left(x\cdot 2\cdot \pi\right) = \cos\left(\frac{1}{3}\cdot \pi\cdot 6\cdot x\right)
1,277
\frac{r^{n + 1} + (-1)}{(-1) + r} = 1 + r + \dotsm + r^n
-30,612
2 \cdot y^2 + 14 \cdot (-1) = 2 \cdot (y^2 + 7 \cdot (-1))
28,759
\sin{3 \cdot L} = 3 \cdot \sin{L} - \sin^3{L} \cdot 4
9,833
12^3 + 1^3 = 9^3 + 10 * 10^2
18,735
5(-1) - T^2*2 - 2T = -2T + 3(-1) - 2\left(T^2 + 1\right)
139
\tfrac{4}{27} = 2\cdot \frac13\cdot 1/3\cdot 2/3
6,109
\lambda^3*2/\lambda = \lambda * \lambda*2
9,824
(g\cdot h/g)^n = g\cdot h^n/g
10,865
3/7 = 3/7 + 0 + 0 + 0
24,590
\frac{1}{z + (-1)} = -\frac{1}{1 - z} = \frac{1}{z} + \frac{1}{z^2} + \frac{1}{z^3} + \ldots
59
\dfrac{1}{(l - i + 1) \cdot (l - i + 1)} \cdot (i + (-1)) = \frac{1}{\left(l - i + 1\right) \cdot \left(l - i + 1\right)} \cdot (-(l - i + 1) + l)
-30,563
3750/750 = \frac{1}{150}*750 = \tfrac{150}{30} = 5
8,230
K = (d\cdot K)^x = d^x\cdot K
37,580
\dfrac{{13 \choose 1}}{{52 \choose 3}} \cdot {39 \choose 2} = 38/50 \cdot 39/51 \cdot 13/52 + \dfrac{38}{50} \cdot 13/51 \cdot \frac{1}{52} \cdot 39 + \frac{39}{52} \cdot \frac{1}{51} \cdot 38 \cdot 13/50
16,544
n \cdot (-Q + l) = ln - nQ
-20,314
9/4\cdot \frac{1}{5\cdot r + 7}\cdot (7 + 5\cdot r) = \frac{63 + 45\cdot r}{28 + 20\cdot r}
27,965
{n \choose k} = \frac{1}{k!\cdot \left(n - k\right)!}\cdot n!
24,583
(1 + 1/2) (-1/2 + 1) = 1 - 1/4
12,421
q^2*\pi*2*Q*\pi = 2*q^2*Q*\pi^2
-2,185
\frac{6}{12} - 1/12 = \dfrac{5}{12}
18,627
x^2 = x^{1/2}\cdot x\cdot x^{1/2}
17,714
a^1 \cdot a^k = a \cdot a \cdot \dots \cdot a = a \cdot a \cdot \dots \cdot a = a^{1 + k}
-1,607
\pi \cdot \tfrac{1}{12} \cdot 7 = \frac{31}{12} \cdot \pi - 2 \cdot \pi
10,019
s^{(-1) + m}\cdot s = s^m
16,128
1 - y \cdot y \cdot y = (-y + 1)\cdot (y^2 + y + 1)
7,521
\frac{f}{b^2 + f f} = f^2\cdot \frac{1}{b b + f^2}/f
6,838
1/6 = \frac{2 / 3}{4}\times 1
11,851
\frac{1}{\left(1 - z\right) \cdot \left(1 - z\right)} = \frac{1}{1 - z} + \frac{z}{(-z + 1)^2}
34,006
q^2\cdot 2 + r^2 - 2\cdot q\cdot r = q^2 + (-q + r) \cdot (-q + r)
44,737
2048 = 13 \times 111 + 605
-20,200
\dfrac{9}{8} \cdot \frac{9 + x}{9 + x} = \frac{81 + x \cdot 9}{8 \cdot x + 72}
16,232
g = g + h + \left(-1\right) \gt g + h + 2 \cdot (-1)
5,356
x\Longrightarrow (x^2 - 3\cdot x + 1) \cdot (x^2 - 3\cdot x + 1) - 3\cdot (x^2 - 3\cdot x + 1) + 1 = x^2 - 3\cdot x + 1 = x
7,903
\frac{1}{\frac1c\cdot f} = c/f
-22,938
24/36 = 12\cdot 2/\left(12\cdot 3\right)
-1,991
\pi/2 - \frac{7}{12}\cdot \pi = -\frac{\pi}{12}
23,489
\frac{49 + 6\cdot \left(-1\right)}{4\cdot (-1) + 49} = \frac{1}{45}\cdot 43
-2,856
5 \sqrt{6} = \sqrt{6}*(4 + 1)
-4,479
\tfrac{1}{12 + z^2 + 7\cdot z}\cdot (24 + z\cdot 7) = \frac{3}{3 + z} + \frac{4}{4 + z}
-10,515
-\tfrac{6}{15 \times m} \times \frac{4}{4} = -\dfrac{24}{m \times 60}
5,992
a * a^2 + f^3 + c^3 = (a + f + c)*(a * a + f * f + c^2 - a*f - f*c - c*a) + 3*a*f*c = 3*a*f*c
28,819
1/27 = \frac{8}{216}
4,005
\sin(\frac{3}{9}\cdot \pi) = \sin(\pi/3)
-522
\frac{361}{12}\cdot \pi - 30\cdot \pi = \pi/12
-20,326
\dfrac{90}{-40} = -\dfrac94\cdot (-10/(-10))
25,001
-\frac3n + 1 = \frac1n \cdot \left(n + 3 \cdot (-1)\right)
25,921
m \cdot n + 3 \cdot (m + n) = 0\Longrightarrow \left(3 + n\right) \cdot (m + 3) = 9, m, n \leq 0
35,605
(g + g)\cdot g + g\cdot (g + g) = \left(g + g\right)\cdot (g + g)
14,579
(x + 1) \cdot (x + 3 \cdot (-1)) = (x + (-1) + 2) \cdot (x + (-1) + 2 \cdot \left(-1\right)) = (x + \left(-1\right))^2 + 4 \cdot (-1)
-4,764
\frac{6*y + 7*(-1)}{y^2 - y*3 + 2} = \frac{1}{(-1) + y} + \frac{5}{y + 2*(-1)}
-3,936
\dfrac{t^5}{t^2} = \dfrac{t \cdot t \cdot t \cdot t \cdot t}{t \cdot t} = t^3
23,360
3\cdot {x + 1 \choose 4} = {{x \choose 2} \choose 2}
-18,320
\frac{q^2 - 2q}{8 + q^2 - 6q} = \dfrac{(q + 2(-1)) q}{(2(-1) + q) (4(-1) + q)}
10,314
{13 \choose 4} = {9 + 5 + (-1) \choose 5 + \left(-1\right)}
23,959
\tan\left(2\cdot x + x\right) = \tan(3\cdot x)
-23,158
-8/9 \cdot (-\frac23) = 16/27
30,041
\frac{1}{2^6} \cdot (1^2 + 3^2 + 3 \cdot 3 + 1^2) = 20/64 = 5/16
24,514
(-z)^{1/2}\cdot (-z)^{1/2} = \left((-z)^{1/2}\right)^2 = -z
-15,773
\dfrac{6}{10} = 1 - 4/10
-15,571
\frac{1}{y^{25}\cdot (\dfrac{y}{k^5})^3} = \frac{1}{y^{25}\cdot \frac{1}{k^{15}}\cdot y^3}
16,365
m = k + 2*(m - t - k) = 2*m - 2*t - k\Longrightarrow k = -2*t + m
-15,934
10 \cdot \frac{5}{10} - 5 \cdot 5/10 = 25/10
28,461
26 = 5^2 + 1 \cdot 1 = 4^2 + 3^2 + 1^2 = 3 \cdot 3 + 3^2 + 2^2 + 2^2
21,546
\frac{1}{l_1 l_2 + 2(-1)}(l_1 l_2 + 2(-1) - ((-1) + l_1) \cdot 2) = \frac{(l_2 + 2(-1)) l_1}{l_1 l_2 + 2\left(-1\right)}
20,941
r^2 - 2\cdot r + 2 = (r + (-1))^2 + 1
12,174
\frac12 + 1/4 = \dfrac{3}{4}
30,225
\frac{3}{6}\times \dfrac47 = \frac{1}{7}\times 2
28,271
\cos^2(y) = (\cos(2y) + 1)/2
49,808
20\cdot 59 + 10\cdot 32 = 1500
34,196
\dfrac{1.8}{2} = 0.9
911
(n + \left(-1\right))^2 - 2 \cdot (n + (-1)) + (-1) = n \cdot n - 2 \cdot n + 1 - 2 \cdot n + 2 + (-1) = n^2 - 4 \cdot n + 2
44,647
1024169717 + 1024169712 (-1) = 5
5,976
\left(9 + 1\right) \cdot \log_e(9 + 1) + 9 \cdot (-1) = 10 \cdot \log_e(10) + 9 \cdot (-1) = 10 + 9 \cdot (-1) = 1
26,744
x = \dfrac{1 - t^2}{t^2 + 1}\Longrightarrow x x = \frac{\left(-t^2 + 1\right)^2}{(1 + t^2)^2}
-6,341
\dfrac{4}{(x + 3)\cdot \left(x + 10\cdot (-1)\right)} = \tfrac{1}{x \cdot x - 7\cdot x + 30\cdot (-1)}\cdot 4
1,793
k_1*h_1*h_2*k_2 = k_1*k_2*h_1*h_2
3,570
3^n - 3^{n + 2(-1)} = 3^{n + 2\left(-1\right)} (9 + (-1))
15,264
\frac{1}{9}*7 = 1 - \frac19*2
20,594
\left(x - V\right) (x + V) = x - V^2 = (x + V) \left(x - V\right)
-3,614
\frac{1}{q \cdot q \cdot 4} \cdot 16 \cdot q^5 = \dfrac{1}{q \cdot q} \cdot q^5 \cdot 16/4
29,500
\sqrt{3} + 2 = \dfrac{1 + \sqrt{3}}{\sqrt{3} + (-1)}
5,255
\frac{1}{4}*(3^5 + 3^9 + 2*3^3) = 4995
13,465
\left(t \cdot 2 + 1 = 0 rightarrow t \cdot 2 = -1\right) rightarrow -\dfrac{1}{2} = t
29,193
(2 \cdot c)^2 - (2 \cdot f) \cdot (2 \cdot f) \cdot m = (c^2 - m \cdot f^2) \cdot 4
27,892
\dfrac1x = c + x\cdot b \Rightarrow x^2\cdot b + c\cdot x + (-1) = 0
12,637
(6 + \left(-1\right)) \cdot 5^i + (-1) = 5^i \cdot 6 + 6 \cdot (-1) - 5^i + 5
-6,894
192 = 6\cdot 4\cdot 8
25,331
(\frac{16}{54})^{\frac13} = (\dfrac{8}{27})^{1/3} = 2/3
15,955
1/405 = \frac{4}{180}\times \frac19
33,795
16*25*34 = 13600
-9,341
x\cdot 11 + 77 \left(-1\right) = -7\cdot 11 + x\cdot 11
16,071
1/4 + \frac{1}{4}*2 = 3/4 \lt 1
19,484
-\cos(x) = \sin(-\pi/2 + x)
32,187
4\cdot 126 = 504
12,636
(d + b) \cdot (d + b) = d^2 + b \cdot d \cdot 2 + b^2
6,528
Y \cdot (1 + o^2 + (-1)) = Y + (o^2 + (-1)) \cdot Y
-1,728
\pi \frac32 + \frac{1}{2}3 \pi = \pi*3