id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
24,072
|
0 = -3*\left(b - c\right) + b * b - c^2 \implies \left(b + c + 3*(-1)\right)*(b - c) = 0
|
25,510
|
n\cdot m - m - n = (m + (-1))\cdot n - m
|
-22,204
|
\left(\left(-1\right) + n\right) (n + 2\left(-1\right)) = n^2 - 3n + 2
|
11,652
|
(3l + (-1))^{\dfrac13} = x \Rightarrow 1 + x \cdot x \cdot x = 3l
|
14,834
|
\frac{n!}{(n - x)!*x!} = {n \choose x}
|
10,295
|
t\cdot 81 + 4 + 27\cdot 2 = 58 + 81\cdot t
|
33,753
|
\frac{1}{a + b \times 3^{1/2}} = \frac{1}{a + b \times 3^{1/2}} = \frac{\frac{1}{a - b \times 3^{1/2}}}{a + b \times 3^{1/2}} \times (a - b \times 3^{1/2})
|
37,920
|
\dfrac{1}{4} = \dfrac{1}{2 \cdot 2}
|
-6,216
|
\dfrac{1}{K\cdot 5 + 20}\cdot 2 = \dfrac{1}{5\cdot (K + 4)}\cdot 2
|
-1,637
|
-\pi*7/6 = -\pi \frac145 + \frac{1}{12}\pi
|
8,849
|
e^1 = e^{\frac{1}{n}*n} = (e^{1/n})^n
|
34,280
|
39580350810 = 9538864545210/241
|
-25,231
|
\frac{\mathrm{d}}{\mathrm{d}y} \sqrt{y^3} = 3/2\cdot y
|
21,876
|
58 = 50 + 1 - 2(-7) + 1^2 - 2*2 (-1) + 2(-7) + 2^2 + 2(-1)
|
34,008
|
2 \lt 1 \implies 1 > 4
|
31,754
|
4^{n + 1} = 4^n\cdot 4
|
-10,315
|
\frac55 \cdot \left(-\frac{8}{10 \cdot r}\right) = -\tfrac{1}{r \cdot 50} \cdot 40
|
36,093
|
x_j := x_j
|
-18,419
|
\dfrac{1}{\left(m + 7\right) (2 + m)}\left(m + 7\right) m = \tfrac{m*7 + m^2}{14 + m^2 + m*9}
|
-4,567
|
-\dfrac{1}{3\cdot (-1) + x}\cdot 5 + \frac{1}{2 + x} = \frac{1}{x^2 - x + 6\cdot (-1)}\cdot \left(-x\cdot 4 + 13\cdot \left(-1\right)\right)
|
6,054
|
0 + x \cdot x^2 + x^2 + x \cdot 2 = (x^2 + x + 2) (0 + x)
|
5,119
|
6 \times 12 + 30 \times (-1) rightarrow 42 = 30 \times \left(-1\right) + 72
|
-4,773
|
\frac{1}{x^2 - x + 2*\left(-1\right)}*(13*(-1) + 2*x) = -\dfrac{3}{2*(-1) + x} + \tfrac{5}{x + 1}
|
27,357
|
0 = 1 - 4*z^3\Longrightarrow z^3 = 1/4
|
13,004
|
-2zy + 3x^2 + 3y^2 + z^2\cdot 3 - xy\cdot 2 - 2xz = (x + y - z)^2 + \left(-x + y + z\right)^2 + \left(z + x - y\right)^2
|
19,015
|
\dfrac{1}{\left(l*3\right)!}l^2 * l = \dfrac{\frac{1}{(3l)!}}{27}(3l) * (3l) * (3l)
|
23,770
|
3^{n + 2 \cdot \left(-1\right)} = \frac13 \cdot 3^{n + (-1)} = \dfrac13 \cdot 3^{n + (-1)}
|
35,668
|
2\cdot \epsilon = \epsilon + \epsilon
|
4,443
|
2^t = 4 \cdot 2^{2(-1) + t}
|
-1,950
|
\pi \frac135 + 17/12 \pi = \pi \dfrac{1}{12}37
|
27,529
|
p^2 + (-1) = ((-1) + p)\cdot (1 + p)
|
1,926
|
l + 1 \leq 1 + l rightarrow 1 + l = l + 1
|
9,342
|
\left(2 - \sqrt{5}\right) \cdot \left(-\sqrt{5} + 2\right)^2 = 38 - \sqrt{5}\cdot 17
|
298
|
2/7 = \tfrac23\cdot 3/7
|
25,345
|
\left(1 + z\right)^2 = 1 + 2\cdot z + z^2 \gt 1 + 2\cdot z
|
29,934
|
\sqrt{3 * 3 + 2^2} = \sqrt{13}
|
-25,846
|
\frac{1}{y^l}\cdot y^k = y^{k - l}
|
6,522
|
\left(1 + x^2 + x\right)\cdot \left(x + (-1)\right) = (-1) + x^3
|
14,847
|
\frac{\partial}{\partial x} \left(x^2 \cdot y\right) = \frac{\mathrm{d}}{\mathrm{d}x} x \cdot x \cdot y + x^2 \cdot \frac{\mathrm{d}y}{\mathrm{d}x} = 2 \cdot x \cdot y + x \cdot x \cdot \frac{\mathrm{d}y}{\mathrm{d}x}
|
-25,483
|
-3*\sin\left(x\right) + x*8 = \frac{\mathrm{d}}{\mathrm{d}x} (x^2*4 + 3*\cos\left(x\right))
|
28,207
|
{x \choose s} = \frac{x!}{s!\cdot \left(-s + x\right)!}
|
19,118
|
{9 \choose 3} = \dfrac{9!}{3!*(9 + 3*(-1))!} = \frac{7}{3*2}*9*8 = 84
|
-8,040
|
\frac{1}{i - 1}(i \cdot 2 + 4) = \frac{2i + 4}{-1 + i} \frac{-1 - i}{-i - 1}
|
-13,005
|
20 = 4 + 9 + 7
|
-19,468
|
\tfrac{7}{5}*\frac{5}{2} = \dfrac{5*1/2}{5*\dfrac17}
|
12,560
|
x^3 + 3*x^2 + 5*x + 5 = (1 + x)^2 * (x + 1) + (1 + x)*2 + 2
|
29,947
|
\sin^{22}{y}/4 = (\sin{2y}/2) \cdot (\sin{2y}/2) = \sin^2{y} \cos^2{y}
|
12,760
|
\left(\sqrt{23} + 5\right) \cdot (24 - \sqrt{23} \cdot 5) = -\sqrt{23} + 5
|
27,071
|
(\frac12 + x)^2 = 1/4 + x^2 + x
|
35,156
|
2^{49} + 2^{99} = \frac12\cdot (-2^{50} + 4^{50}) + 2^{50}
|
-1,644
|
\pi\cdot \frac{5}{12} = \pi\cdot 29/12 - 2\cdot \pi
|
34,556
|
0 = x^4 - 5 \times x^3 + 20 \times x + 16 \times (-1) = (x + (-1)) \times \left(x^3 - 4 \times x^2 - 4 \times x + 16\right) = (x + \left(-1\right)) \times (x^2 + 4 \times (-1)) \times (x + 4 \times (-1))
|
19,366
|
1 \lt |x| \Rightarrow 1/|x| < 1
|
6,733
|
-4 = 2^2 \cdot 2 \cdot 1/(-4) \cdot 2
|
-20,355
|
\frac{9 \cdot x + 18 \cdot (-1)}{4 \cdot (-1) + x \cdot 2} = \frac92 \cdot \frac{2 \cdot \left(-1\right) + x}{x + 2 \cdot (-1)}
|
22,585
|
g^{b \cdot c} = (g^b)^c = (g^c)^b
|
-18,942
|
1/3 = \frac{1}{16*π}*Y_s*16*π = Y_s
|
20,769
|
3 \cdot g + B = (g + B) \cdot (g + B) \cdot (g + B) = (g + B)^3
|
39,718
|
-f_m = f_m - 2f_m
|
15,624
|
(u + y)^2 = y \cdot y + 2 \cdot u \cdot y + u^2
|
46,463
|
1111 = 555 + 555 + 1 = 10\times 111 + 1
|
4,755
|
\frac{1}{2 + \dfrac{2}{2 + ...}}\cdot 2 = \sqrt{3} + \left(-1\right)
|
2,966
|
180 - 180 - A - C = C + A
|
21,927
|
k^2 = \delta_{k + 1} - \delta_k = \frac{1}{k + 1 - k}\cdot (\delta_{k + 1} - \delta_k)
|
4,205
|
10 + \sqrt{3}\cdot 6 = \left(\sqrt{3} + 1\right) \cdot (\sqrt{3} + 1)^2
|
8,756
|
6 \lt -X + 3 \implies X < -3
|
-7,407
|
8/15 = \frac23\cdot 4/5
|
10,805
|
((-1) + l)*2 = 2*(-1) + 2*l
|
10,947
|
k^2 - k \cdot 2 + 1 = (k + (-1))^2
|
-16,410
|
\sqrt{4 \cdot 11} \cdot 12 = \sqrt{44} \cdot 12
|
-4,270
|
\frac{1}{a^5} \times a^2 \times a \times \dfrac{132}{144} = \frac{a^3}{a^5} \times \frac{11}{12 \times 12} \times 12
|
22,916
|
575757 = \frac{1}{(39 + 5*(-1))!*5!}*39!
|
4,401
|
5 = \frac12(40 \left(-1\right) + 50)
|
-20,427
|
\dfrac{1}{7k + 5}(5 + 7k) (-4/9) = \frac{-28 k + 20 (-1)}{45 + k*63}
|
24,217
|
1 - \tan(x) + \tan^2(x) - \tan^3(x) + ... = \frac{1}{1 + \tan(x\times 2)}\times \tan(x\times 2)
|
-20,793
|
\frac{(-1) + y}{y \cdot 8 + 8 \cdot \left(-1\right)} = (\left(-1\right) + y) \cdot \tfrac{1}{(-1) + y}/8
|
33,738
|
\operatorname{Var}(U \cdot Y_1) = \mathbb{E}((U \cdot Y_1)^2) - \mathbb{E}(U \cdot Y_1)^2 = \mathbb{E}(U^2) \cdot \mathbb{E}(Y_1^2) - \mathbb{E}(U)^2 \cdot \mathbb{E}(Y_1) \cdot \mathbb{E}(Y_1)
|
-472
|
(e^{\frac{i\pi}{12}5})^9 = e^{\frac{\pi i}{12}5*9}
|
10,195
|
\int_b^afdx=-\int_a^bfdx
|
32,919
|
1/L + 1/M + \dfrac1x = \tfrac{1}{L \cdot M \cdot x} \cdot (L \cdot M + x \cdot M + L \cdot x)
|
18,019
|
xz = 1\Longrightarrow xz = 2
|
1,786
|
\frac{\text{d}}{\text{d}x} e^{3x} = 3e^{3x}
|
8,565
|
44 \cdot 0.39/0.357 = 48.067 \cdot \cdots \approx 48
|
40,247
|
6 + \omega^{\omega^4} + \omega^4 + \omega^2*4 = \omega^4 + 3\omega^2 + 5 + \omega^{\omega^4} + \omega^2 + 1
|
3,849
|
(-z + x)^2 = z^2 + x^2 - x \cdot z \cdot 2
|
3,632
|
x + (-1) = x\cdot (x + (-1))/x
|
22,952
|
\sin{\frac{\pi}{3}} = \dfrac{\sqrt{3}}{2}
|
9,082
|
2^m + j = 2\cdot 2^{m + \left(-1\right)} + 2\cdot j/2 = 2\cdot (2^{m + (-1)} + j/2)
|
-3,112
|
\sqrt{13} \cdot 4 - \sqrt{13} = \sqrt{13} \cdot \sqrt{16} - \sqrt{13}
|
-13,919
|
\frac{1}{4 + 3 \cdot (-1)} \cdot 2 = 2/1 = \frac{1}{1} \cdot 2 = 2
|
20,419
|
x\cdot z = 1/(x\cdot z) = \dfrac{1}{z\cdot x} = z\cdot x^2
|
-14,340
|
3 \cdot 4 + 2 \cdot \dfrac{30}{6} = 3 \cdot 4 + 2 \cdot 5 = 12 + 2 \cdot 5 = 12 + 10 = 22
|
2,708
|
1 + 2 + 2^2 + \cdots + 2^{a + \left(-1\right)} = \dfrac{1}{1 + 2\cdot \left(-1\right)}\cdot (1 - 2^a) = 2^a + \left(-1\right)
|
36,727
|
\frac{1}{2! \cdot 6!} \cdot 8! = 28
|
-19,516
|
6/5\cdot 5/7 = \frac{1/7\cdot 5}{5\cdot \dfrac16}
|
12,236
|
(2\cdot x + 1)\cdot 3 = 3 + 6\cdot x
|
19,881
|
20 = \left\lfloor{12^{\frac{1}{3}}}\right\rfloor \cdot 1000^{\tfrac13} = 2 \cdot 10 = 20
|
6,417
|
\sin(s + x) = \sin(x)\cdot \cos(s) + \cos(x)\cdot \sin(s)
|
9,050
|
|C^A| + |C^A| \leq |C^A| \cdot |C^A| = |C^{A + A}| = |C^A|
|
-20,000
|
\frac{-x*63 + 45*(-1)}{-x*56 + 40*(-1)} = 9/8*\frac{-7*x + 5*(-1)}{-7*x + 5*(-1)}
|
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