id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
13,482
|
-3 \cdot m \cdot n = n^2 + -(m + n) \cdot (n + m) + m^2 - n \cdot m
|
17,729
|
q^2 \cdot t \cdot t^2 \cdot {4 \choose 2} = q^2 \cdot t \cdot t \cdot t \cdot 6
|
8,016
|
{10 \choose 1} \cdot {2 \choose 1} \cdot {4 \choose 1} \cdot {4 \choose 1} + 8 = 328
|
-18,924
|
7/12 = Y_s/(36 \pi)*36 \pi = Y_s
|
32,740
|
\tfrac{1}{3^{\frac{1}{2}} + (-1)} = \frac{1}{2}*(1 + 3^{\frac{1}{2}})
|
-6,024
|
\dfrac{q}{40\cdot (-1) + q^2 + 6\cdot q}\cdot 3 = \frac{q\cdot 3}{(10 + q)\cdot (q + 4\cdot (-1))}
|
10,607
|
z = \dfrac{1}{z^2 - z}\cdot \left(z^3 - z^2\right)
|
11,435
|
(g_2 - g_1)^2 = -2*g_1*g_2 + g_2^2 + g_1^2
|
-2,221
|
\frac{1}{19} \cdot 3 = \frac{10}{19} - \frac{1}{19} \cdot 7
|
8,808
|
det\left(x^q*x\right) = det\left(x*x^q\right)
|
-16,263
|
216^{\frac{1}{3}} = 216^{\frac13} = 6
|
-4,754
|
\frac{22 + x*2}{x^2 - 2*x + 15*(-1)} = \dfrac{4}{x + 5*(-1)} - \frac{1}{3 + x}*2
|
24,163
|
t + 3 x = 4 x + t - x
|
27,653
|
3 = \frac{(2 + 1)!}{2! \cdot 1!}
|
2,958
|
\tfrac{1}{1/5 \sqrt{5}}3 = \frac{1}{\sqrt{5}}15
|
22,827
|
4 y + y + 3 (-1) = 13 (-1) + 10 + 5 y
|
-22,047
|
\frac{35}{10} = \frac72
|
22,419
|
E\left[W + A\right] = E\left[W\right] + E\left[A\right]
|
-3,566
|
\frac{66}{x \cdot 88} \cdot x^3 = \frac1x \cdot x \cdot x^2 \cdot \frac{1}{88} \cdot 66
|
31,214
|
x + a\times x^2 = a + a^2\times x + x\Longrightarrow 0 = -a + a\times x^2 - x\times a^2
|
2,656
|
\left(\left(-\sqrt{5} + 1\right)/2\right)^2 = (3 - \sqrt{5})/2
|
4,502
|
\dfrac45 = (h + b)/(h\cdot b) = \frac1h + 1/b
|
-20,812
|
\frac{1}{-x\cdot 14 + 56\cdot (-1)}\cdot 70 = \frac{1}{8\cdot (-1) - 2\cdot x}\cdot 10\cdot 7/7
|
9,610
|
(c + bi) (c - bi) = c^2 - b^2 i^2 = c * c + b^2
|
23,184
|
5/6\cdot Y + \frac{8}{9}\cdot 3\cdot Y = \frac{5}{6}\cdot Y + 16/6\cdot Y = \frac{7}{2\cdot Y}
|
-10,468
|
\frac{10}{10} \cdot (-\dfrac{1}{5 \cdot l + 5} \cdot 6) = -\frac{1}{l \cdot 50 + 50} \cdot 60
|
13,457
|
\left(2 \cdot x + 1\right)^{1 / 2} = x - (x^2 - 2 \cdot x + 1)/7 = \dfrac{1}{7} \cdot \left(-x \cdot x + 9 \cdot x + 1\right)
|
9,533
|
4 = z + x + y rightarrow 4 - y = x + z
|
10,802
|
-\frac{1}{4} + 1 = \tfrac34
|
33,887
|
2^{20} + (-1) = 5^2\times 3\times 11\times 31\times 41
|
24,005
|
e = z*x \Rightarrow x = z = e
|
-2,471
|
\sqrt{3} \cdot \left(4 \cdot \left(-1\right) + 5\right) = \sqrt{3}
|
19,067
|
1/4 + 1/4 \cdot 2 + \frac{1}{4} \cdot 3 + 1/4 \cdot 4 = 2.5
|
9,062
|
13 = x + 2 + 3 \Rightarrow x = 8
|
11,212
|
\binom{-1}{r} = \frac{1}{r!} ((-1) \left(-2 ... \left(-1 - r + 1\right)\right)) = (-1)^r
|
9,519
|
(dg)^3 = g \cdot g \cdot g d^3
|
20,465
|
540 = {4 \choose 2}*{2 \choose 2}*3!*{1 \choose 1}*{5 \choose 1}*{3 \choose 2}
|
24,614
|
\left\{Z, B\right\} \Rightarrow B \cap Z = Z
|
-592
|
\frac{3}{2}*\pi = \pi*\frac12*63 - 30*\pi
|
5,512
|
\frac{1}{-\sqrt{2}\cdot 6 + 11} = \frac{1}{(-\sqrt{2} + 3)^2}
|
-2,063
|
-\frac{\pi}{4} = \pi \cdot \frac{5}{12} - 2/3 \cdot \pi
|
21,592
|
4 \cdot (1 + x_1 + x_2) = x_2 \cdot x_1 \cdot 2 \Rightarrow 8 = (x_1 + 2 \cdot (-1)) \cdot \left(2 \cdot (-1) + x_2\right)
|
38,794
|
\binom{4 + 8}{4} = \binom{12}{4}
|
17,018
|
a^2 + \dfrac{1}{a^2} + 1 = (a + \frac1a)^2 + \left(-1\right) = \left(a + \frac1a + 1\right) (a + \dfrac1a + (-1))
|
-7,991
|
\frac{1}{2} \cdot (-7 + 3 \cdot i + 7 \cdot i + 3) = \left(-4 + 10 \cdot i\right)/2 = -2 + 5 \cdot i
|
-17,720
|
10 = 2\cdot (-1) + 12
|
36,800
|
\frac12(-(h^2 + g_2 \cdot g_2 + g_1^2) + \left(h + g_2 + g_1\right)^2) = hg_1 + hg_2 + g_1 g_2
|
-20,842
|
\frac99\cdot \left(3\cdot (-1) + z\right)/(-5) = \frac{1}{-45}\cdot (z\cdot 9 + 27\cdot (-1))
|
10,045
|
-b\times y_k + 1 = (-y_k + 1/b)/(1/b)
|
9,977
|
\frac22\pi r = r\pi
|
5,556
|
84 = \binom{6 + 4 + \left(-1\right)}{\left(-1\right) + 4}
|
-7,943
|
(d - b) (d + b) = d^2 - b^2
|
24,897
|
gc_2 c_1 = gc_2 c_1
|
12,302
|
m\cdot 4 + (-1) = (-1) + 2\cdot 2\cdot m
|
1,118
|
c + g_2 + g_1 + 3 + s + 4 = 13 \Rightarrow s + c + g_2 + g_1 = 6
|
-5,106
|
10^{4 + 2 \cdot (-1)} \cdot 0.75 = 0.75 \cdot 10^2
|
3,838
|
\tfrac{2}{a\cdot 2 + 1} - \frac{1}{a \cdot a\cdot 2}\cdot \left((-1) + a\cdot 2\right) = \dfrac{1}{(2\cdot a + 1)\cdot 2\cdot a^2}
|
7,686
|
((-1) + 5^l)\times (5^{l\times 2} + 5^l + 1) = 5^{3\times l} + (-1)
|
11,210
|
x + G\cdot 2 - G = x + G
|
3,493
|
\sin(X)*\cos(B) = \frac12*(\sin(X - B) + \sin(B + X))
|
-19,460
|
\frac15*7/(8*\frac19) = \tfrac18*9*\dfrac75
|
7,936
|
z^2 \cdot z + 27 \cdot (-1) = (z^2 + 3 \cdot z + 9) \cdot (z + 3 \cdot (-1))
|
-5,367
|
10^4\times 0.24 = 0.24\times 10^{-1 - -5}
|
-2,411
|
\sqrt{6} + 3 \times \sqrt{6} = \sqrt{6} \times \sqrt{9} + \sqrt{6}
|
28,494
|
\sin(2x) = \sin x \cos x + \cos x \sin x = 2 \sin x \cos x
|
18,432
|
1/\left(g_1*g_2\right) = \frac{1}{g_1*g_2}
|
10,726
|
8 = \frac{4\cdot 90}{15\cdot 3}
|
1,513
|
\cos^2{r} = \sin{2 \cdot y} \Rightarrow \sin{2 \cdot y} + 1 = (\cos{y} + \sin{y})^2 = \cos^2{r} + 1
|
27,917
|
x \cdot x_i \cdot C = x \cdot x_i \cdot C
|
31,352
|
a \times \cos^2{h} = -\cos{h} + d\Longrightarrow a \times \cos^2{h} + \cos{h} - d = 0
|
18,284
|
\int\limits_0^1 -2\pi W\,\mathrm{d}W = -2\pi \int\limits_0^1 W\,\mathrm{d}W = -2\pi W^2/2
|
-19,105
|
1/5 = A_s/(36 \pi)*36 \pi = A_s
|
22,034
|
2^{1 + f} = 2^f*2
|
7,510
|
xzy*2 = x^2 + y * y + z * z \Rightarrow x = y = z = 0
|
315
|
0 = y + 4 \Rightarrow -4 = y
|
-4,825
|
\frac{1}{10}*6.9 = 6.9/10*10^2 = 6.9*10^1
|
20,105
|
K \geq 10 rightarrow |2K^2 + 20 K| \leq |2K^2| + |20 K| \leq |2K^2| + |20 K^2| = 22 |K|^2
|
-4,570
|
\frac{1}{6 + x^2 + 5x}\left(3x + 7\right) = \frac{2}{x + 3} + \dfrac{1}{2 + x}
|
5,525
|
9 \times \left(-1\right) + 10 = 1
|
8,225
|
\frac{1}{\left(-1\right) X_m} ((-1) F_m) = F_m/(X_m)
|
-10,741
|
5/5 \times \frac{10}{4 + 5 \times t} = \frac{50}{25 \times t + 20}
|
-28,886
|
21 = \left(m + 2(-1)\right) (m + 2) = m^2 + 4(-1)
|
27,021
|
\sqrt{\pi}/2 = \int_0^\infty e^{x \cdot x}\,dx > \int\limits_0^1 e^{x^2}\,dx
|
-12,773
|
8 = 14 + 6*(-1)
|
-2,449
|
5 \cdot \sqrt{10} = \sqrt{10} \cdot (3 + 2)
|
25,429
|
64 = x\cdot 2 + 4\cdot x + 6\cdot x\Longrightarrow x = \frac{64}{12} = 32/6 = \frac{16}{3}
|
24,222
|
y^2 + (y^2)^2 = 4 \times y^2 \implies -3 \times y^2 + y^4 = 0
|
35,015
|
-b \cdot b + a \cdot a = \left(-b + a\right) \cdot (b + a)
|
14,634
|
\frac{f}{b \cdot x} = \frac1b \cdot f/x
|
9,715
|
-y \cdot 8 + 16 + y^2 \leq 12 - y^2 \cdot 2 \Rightarrow 0 \geq 3y \cdot y - 8y + 4
|
-26,624
|
(9\cdot t - x\cdot 8)^2 = t^2\cdot 81 - t\cdot x\cdot 144 + 64\cdot x^2
|
-30,914
|
55 - 3*l = 55 - l*3
|
-9,229
|
-t \cdot 2 \cdot 2 \cdot 2 \cdot 3 = -24 \cdot t
|
7,555
|
10002 = \sqrt{\left(100 \cdot 2\right)^2 + (98 \cdot 100 + 2) \cdot (2 + 100 \cdot 102)}
|
3,235
|
11 = (-1 + \sqrt{3}*2)*(\sqrt{3}*2 + 1)
|
6,515
|
-\frac{2}{y^5} = \frac{y}{-y^6 \cdot \frac{1}{2}}
|
13,989
|
1 + {n \choose 1} + {n \choose 2} = 22 \Rightarrow 21 = {n \choose 2} + {n \choose 1}
|
19,842
|
-\dfrac{1}{z_2} + 8 + 1/3 = z_1\Longrightarrow \left[z_2, z_1\right] = [3,8]
|
1,620
|
n*m = 1 rightarrow m = n = 1
|
12,638
|
\frac{\partial}{\partial x} (w_1*w_2) = \frac{\partial}{\partial x} w_1*w_2 + \frac{\partial}{\partial x} w_2*w_1
|
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