id
int64
-30,985
55.9k
text
stringlengths
5
437k
-20,327
\frac{1}{8(-1) + z*2}(8 - 20 z) = \tfrac{1}{4\left(-1\right) + z}(-10 z + 4) \frac22
11,487
\left(\sqrt{2} + \sqrt{3}\right)^3 = \sqrt{3}\cdot 9 + 11\cdot \sqrt{2}
-18,371
\dfrac{s^2 + s\cdot 7}{49 + s^2 + 14\cdot s} = \frac{1}{(7 + s)\cdot (7 + s)}\cdot s\cdot (s + 7)
3,619
\frac{\left(n + 1\right)^{n + 1}}{n + 1} = (n + 1)^n
30,849
k + 2 \cdot (-1) = -(\left(-1\right) + 3) + k
17,500
(n + 1)^2 = n \cdot n + 2\cdot n + 1 \geq n + 1 + 2\cdot n + 1
-26,637
(5 + z)\cdot (5\cdot (-1) + z) = z^2 - 5^2
29,966
\frac{20!}{3! \cdot 17!} = 1140
-30,914
55 - m \cdot 3 = 55 - 3 \cdot m
1,332
F' \cdot x/F = \dfrac{\frac{1}{F^2} \cdot F' \cdot x}{x \cap F'/F} \cdot 1
19,655
\left(r + 2 \cdot (-1)\right)! \cdot r \cdot ((-1) + r) = r!
29,273
A^2 \cdot X^2 = (A \cdot X)^2
10,357
(y + 1)^x*(1 + y)^r = \left(y + 1\right)^{r + x}
15,560
(-x)^2 + (-d)^2 + (-e)^2 = x^2 + d^2 + e^2
-20,462
\dfrac{a + 9}{-a \cdot 2 + 2} \cdot 7/7 = \frac{a \cdot 7 + 63}{14 - a \cdot 14}
-16,750
3 = 3\cdot 3\cdot p + 3\cdot \left(-7\right) = 9\cdot p - 21 = 9\cdot p + 21\cdot \left(-1\right)
-12,223
2/5 = \tfrac{r}{6 \cdot \pi} \cdot 6 \cdot \pi = r
-6,517
\dfrac{4}{y^2 + y \cdot 5 + 36 \cdot (-1)} = \dfrac{1}{(y + 9) \cdot (4 \cdot (-1) + y)} \cdot 4
33,531
\epsilon\cdot y\cdot \vartheta = \epsilon\cdot \vartheta\cdot y = \vartheta\cdot \epsilon\cdot y
-3,249
(4 + 3 + 2) \cdot \sqrt{7} = 9 \cdot \sqrt{7}
20,173
2\cdot (1 + x) = 2\cdot x + 2
-24,779
\cos\left(\frac{5}{12}\cdot \pi\right) = (-2^{1/2} + 6^{1/2})/4
-2,651
\sqrt{7} \cdot 6 = \left(1 + 5\right) \cdot \sqrt{7}
-10,629
5/5 \cdot \frac{3}{3r + 12 (-1)} = \frac{15}{15 r + 60 (-1)}
-5,029
5.32 \times 10 = 5.32 \times 10/1000 = 5.32/100
24,711
1680-800=880
26,887
\left|{E_1 E_2}\right| = \left|{E_2 E_1}\right| = \left|{E_1}\right| \left|{E_2}\right|
18,502
\frac18\cdot \pi = \arctan(2^{1 / 2} + \left(-1\right))
10,703
\frac12 + 1/(2\cdot 3) + ... + \frac{1}{n\cdot (n + 1)} = 1 - \dfrac{1}{1 + n}
31,527
pg r^2\cdot \left(h_b - h_t\right) = (h_b - h_t) pgr^2
-30,550
-\dfrac{1}{-49}343 = -\frac{49}{-7} = -\dfrac{7}{-1} = 7
7,846
\sqrt{13}/2 = \sqrt{\frac{1}{1 - \frac{5}{13}} \cdot 2}
30,542
\left((-1) + \sqrt{5}\right)^2 = (\sqrt{5})^2 - \sqrt{5}\cdot 2 + 1
17,391
\frac{27}{36} = \tfrac34
10,160
(1 + i)! \cdot \left(2 + i\right) + \left(-1\right) = (2 + i)! + (-1)
13,263
(2^q + 1)\cdot (2^q + (-1)) = 4^q + (-1)
21,062
\left(\nu + 2\right)*\left(\nu + 1\right) = \nu * \nu + 3*\nu + 2
28,353
25 \cdot b^2 - 12 \cdot b + 2 = 2 \cdot (-b \cdot 3 + 1)^2 + 7 \cdot b^2
21,469
120 = 125 + 5*\left(-1\right)
34,587
2439 = 6561\cdot (-1) + 9000
6,977
b \cdot f' \cdot g \cdot 2 - x \cdot b^2 = b \implies b \cdot x = g \cdot f' \cdot 2 + (-1)
16,105
12 + 4 \cdot c = 4 \cdot (c + 3)
7,246
\cdots = 177\% \cdot 176
12,407
-\frac{11}{20} + 1 = 9/20
20,247
f_1^2 = f_1\cdot f_1
44,027
1 = -2 + 3
25,814
3\cdot 6^2+4\cdot 6 + 1 = 108+24+1=133
19,005
J/x = \frac1x(x + \psi J) = \tfrac{\psi J}{x \cap \psi J}
-1,216
-\frac{1}{2} \cdot 3 \cdot (-\frac12) = \frac{1}{1/3 \cdot (-2)} \cdot ((-1) \cdot \frac{1}{2})
10,014
(x_1 - x_2)\cdot 12 = 8\cdot (z_1 - z_2)\Longrightarrow 3\cdot (x_1 - x_2) = 2\cdot (-z_2 + z_1)
25,952
\left(0 + j\right)/2 = \frac{j}{2}
-14,234
\frac{1}{5 + 3} \cdot 56 = \frac{56}{8} = \frac18 \cdot 56 = 7
36,551
1820 = {12 + 4 + (-1) \choose 12} {4 \choose 1}
-2,346
\frac{8}{14} - \frac{7}{14} = \frac{1}{14}
7,839
\frac{1}{1 + 0\cdot (-1)}\cdot (1 + 0) = 1
-9,869
0.125 = \dfrac{1}{100}*12.5 = \frac{1}{8}
-1,297
\dfrac{\frac{1}{5}*7}{4} = 1/(\dfrac{1}{7}*5*4)
25,548
a\cdot h^2\cdot a = \frac{1}{a\cdot h\cdot a} = h\cdot a\cdot h
41,422
105 = |3|*5*7
16,949
1 + 3 + 3^2 + \cdots + 3^{n + (-1)} = ((-1) + 3^n)/2
19,568
\left(x^2 = 3 + x \Leftrightarrow 0 = x^2 - x + 3 (-1)\right) \Rightarrow x = (1 \pm \sqrt{13})/2
46,023
\left(1 + 1\right) \cdot (1 + 1)^2 = 1 + 1 + 3 + 3
16,579
\operatorname{E}[Xq] = \operatorname{E}[X] \operatorname{E}[q]
-4,725
-\frac{3}{x + 2(-1)} + \frac{1}{5 + x}5 = \frac{2x + 25 (-1)}{x^2 + x*3 + 10 (-1)}
-4,631
\frac{1}{x^2 - x*9 + 20}*(-4*x + 19) = -\frac{1}{x + 4*\left(-1\right)}*3 - \frac{1}{5*(-1) + x}
24,986
(\dfrac{3}{4})^X = \dfrac{1}{4^X} \cdot 3^X
21,989
-d = d\Longrightarrow 0 = d
30,380
z_2 z_1 = \dfrac{1}{z_2 z_1} = 1/(z_1 z_2)
-25,797
\frac{1}{48}\cdot 5 = 5\cdot 1/8/6
-9,658
-\frac{1}{10} \cdot \frac{1}{20} \cdot 7 = \frac{(-1) \cdot 7}{10 \cdot 20} = -7/200
6,643
-z\cdot V\cdot x\cdot 3 + x^3 + V^3 + z^3 = ((-x + z)^2 + (-V + x)^2 + (V - z) \cdot (V - z))\cdot (z + x + V)/2
-4,460
-\frac{1}{z + 4} - \frac{1}{z + 5 \times \left(-1\right)} = \frac{1 - 2 \times z}{20 \times (-1) + z^2 - z}
3,299
1-\frac 14=\frac 34
3,081
(n + 1)\cdot (n^2 + n\cdot 3 + 2) = (n + 1)^2\cdot \left(n + 2\right)
-7,646
\frac{i \cdot 19 + 4}{-5 - 2 \cdot i} \cdot \dfrac{2 \cdot i - 5}{2 \cdot i - 5} = \tfrac{19 \cdot i + 4}{-2 \cdot i - 5}
8,991
5 \cdot (x \cdot x + 3 \cdot \left(-1\right)) = 5 \cdot x^2 + 15 \cdot (-1)
-10,693
\frac{20}{100 z + 100} = \dfrac{5}{25 + z \cdot 25} \cdot 4/4
-20,484
\frac{6\cdot (-1) + s}{6\cdot (-1) + s}\cdot (-\frac{7}{3}) = \frac{1}{3\cdot s + 18\cdot \left(-1\right)}\cdot \left(-s\cdot 7 + 42\right)
-3,921
\frac{84*p^2}{42*p^5} = \frac{84}{42}*\frac{1}{p^5}*p * p
2,136
M^4 - F^4 = (M^2 - F^2) (M \cdot M + F^2)
20,387
2\cdot l = 2^{l - t} - 2^t = 2^t\cdot \left(2^{l - 2\cdot t} + (-1)\right)
-1,067
12/45 = 12\cdot \dfrac13/(45\cdot 1/3) = \tfrac{4}{15}
-4,633
-\frac{1}{x + 5}\cdot 2 + \frac{4}{2 + x} = \dfrac{1}{x^2 + 7\cdot x + 10}\cdot (2\cdot x + 16)
-6,744
90/100 + 6/100 = 9/10 + 6/100
30,579
\left(y + 1\right)^k = (y + 2 + (-1))^k
17,684
\dfrac{1}{7/5 + (-1)}\cdot ((-1) + 1/5) = -2
20,425
a + x + c = 0 \Rightarrow c = x + a
-26,662
(7\cdot x^2)^2 - 2^2 = 4\cdot (-1) + x^4\cdot 49
-10,588
-\frac{1}{300 \cdot f^3} \cdot (45 + 30 \cdot f) = -\frac{1}{20 \cdot f^3} \cdot (3 + f \cdot 2) \cdot \frac{15}{15}
2,257
(x + 4) \left(x + 2\right) = 8 + x^2 + 6x
22,267
\sin{4\cdot \pi/3} = -\sin{\dfrac13\cdot \pi}
26,928
\operatorname{asin}\left(\sin(2)\right) = \operatorname{asin}(\sin(2 \cdot (-1) + \pi))
31,346
y^2*z^2 = (z + y)^2 + 2*(z + y) + 1 rightarrow y^2*z^2 = (z + y + 1)^2
28,522
-(5(-1) + y^2 - 4y) = -y^2 + 5 + 4y
-20,517
-\frac{45}{27\cdot (-1) + y\cdot 9} = \frac{1}{9}\cdot 9\cdot \left(-\tfrac{1}{y + 3\cdot (-1)}\cdot 5\right)
33,259
1/\left(\sqrt{2}\right) + \frac{1}{\sqrt{2} + 2} = 1
18,061
1/36 + \frac{1}{18} + \frac{1}{12} = (1 + 2 + 3)/36 = \frac{1}{36}6 = 1/6
35,174
\frac{A}{2 \cdot 2} \cdot (E \cdot 2) \cdot (E \cdot 2) = E^2 \cdot A
20,667
20/91 = \tfrac{{5 \choose 2}}{{15 \choose 3}}\cdot {10 \choose 1}
9,632
3^h = \frac12 \Rightarrow 3^{h + (-1)} = \dfrac{1}{4} = \dfrac14