id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
29,728 |
9^9 \frac{1}{e^9}/9! = 9^8 \dfrac{1}{e^9}/8!
|
17,809 |
\nu_x^1 = \nu_x
|
-20,697 |
\frac{4 + r}{r \cdot 9 + 4(-1)} \frac{5}{5} = \dfrac{5r + 20}{45 r + 20 \left(-1\right)}
|
48,010 |
\left(x^{1/2}\right)^2 = x
|
21,571 |
a = a \cdot b = b \implies b = a
|
3,457 |
(4 + x)\cdot \left(1 + x\right) = (-1) + x^2 + x\cdot 5 + 5
|
31,753 |
z\cdot R\cdot x = x\cdot R\cdot z
|
-4,055 |
9\cdot a^2/5 = 9/5\cdot a^2
|
-1,987 |
\pi \dfrac{7}{12} + 5/12 \pi = \pi
|
23,392 |
\alpha - \beta = \frac{1}{\alpha + \beta} (-\beta \beta + \alpha^2)
|
-26,658 |
3 + 2\cdot x \cdot x + 7\cdot x = (2\cdot x + 1)\cdot (x + 3)
|
12,625 |
x^2 + g * g + gx*2 = \left(x + g\right)^2
|
-15,309 |
\frac{1}{1/m \frac{1}{p^5}}m^3 = \frac{m^3\cdot \frac{1}{1/m}}{\frac{1}{p^5}} = m^{3 - -1} p^5 = m^4 p^5
|
11,068 |
15 = (60\cdot (-1) + 90)\cdot \frac{1}{2}
|
34,521 |
a^{x + l} = a^l a^x
|
6,322 |
\frac{1/3*2}{3}*1 = \dfrac29
|
1,452 |
(-y + x) * (-y + x) = y^2 + x^2 - 2*x*y
|
23,880 |
(L - c)*(b - d) = L*b + c*d - L*d - b*c = L*b + c*d - L*d + b*c
|
12,380 |
2\cdot x = \pi \Rightarrow x = \pi/2
|
21,503 |
\chi \gt -R + 1 \Rightarrow -\chi + 1 \lt R
|
1,768 |
[a, b] = \left[f,d\right] rightarrow a = b,f = d
|
26,907 |
6/6 + 6/5 + \frac{6}{4} + 6/3 + \frac{6}{2} + \frac{6}{1} = 14.7
|
15,252 |
\lim_{m \to \infty}(-b_m + c_m) = 0 \implies 1 = \lim_{m \to \infty} c_m/(b_m)
|
-25,510 |
\frac{d}{dt} (\frac{4}{2 + t}) = -\frac{4}{(t + 2)^2}
|
-1,650 |
\frac{11}{12}\cdot π + 4/3\cdot π = \frac14\cdot 9\cdot π
|
-16,552 |
5 \cdot (9 \cdot 5)^{\frac{1}{2}} = 5 \cdot 45^{\frac{1}{2}}
|
24,236 |
X \backslash C + y = X \cap \overline{C + y} = X \cap \overline{C} + y
|
5,479 |
\tfrac{1}{2!} 4!*3!/2! = 3!*3! = 36
|
-11,540 |
4 + 6\times i = 4 + 0\times (-1) + i\times 6
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51,267 |
\frac{14}{95^{\frac{1}{2}} + 9 \cdot (-1)} = \left(95^{1 / 2} + 9\right)/1 = 18 + \frac{1}{1} \cdot (95^{\tfrac{1}{2}} + 9 \cdot (-1))
|
21,873 |
\left(0 = 1 + 1 + 2n - n \cdot 6 + 10 \left(-1\right) \implies 8(-1) - 4n = 0\right) \implies n = -2
|
-26,554 |
-(3 \times y)^2 + 10^2 = (10 + 3 \times y) \times (-y \times 3 + 10)
|
11,029 |
-b + ba - a = a\cdot \left(b + (-1)\right) + b\cdot (-1)
|
-9,160 |
-a\cdot 2\cdot 3\cdot 3 a - 2\cdot 13 a = -18 a \cdot a - 26 a
|
6,642 |
(b + f)\cdot 2 = f + b + f + b
|
5,060 |
\dfrac{1}{-1} \cdot \sqrt{|-1| \cdot 2 - (-1)^2} = -1
|
1,008 |
(k + 1) \cdot \pi/3 = \pi/3 + \tfrac{\pi}{3} \cdot k
|
31,802 |
\frac{1}{12}\cdot \left(1 + \sqrt{6}\right) = \sqrt{6}/12 + \frac{1}{12}
|
20,856 |
A \cdot A^T \cdot A^T \cdot A \cdot A^T \cdot A = A \cdot A \cdot A^T \cdot A \cdot A^T \cdot A^T
|
-20,533 |
\tfrac{5 + 7 \cdot z}{7 \cdot z + 5} \cdot 4/1 = \frac{20 + 28 \cdot z}{7 \cdot z + 5}
|
8,087 |
-s\cdot t = -x \implies x = s\cdot t
|
6,723 |
(1 + \alpha)^3 = (1 + \alpha) (\alpha + 1) (1 + \alpha)
|
-24,017 |
10 + 6*16/2 = 10 + 6*8 = 10 + 6*8 = 10 + 48 = 58
|
29,948 |
1 = \frac{1}{-\tfrac{2}{3 + (-1)} + 3} \cdot 2
|
-22,307 |
2 + r \cdot r + r\cdot 3 = (r + 1)\cdot (2 + r)
|
27,255 |
h\cdot e\cdot h = e = h\cdot e\cdot h
|
10,430 |
19 + q^4 - q^2\cdot 20 = (19\cdot (-1) + q \cdot q)\cdot \left(q^2 + (-1)\right)
|
-5,713 |
\frac{3}{10 + 5 \cdot m} = \frac{1}{5 \cdot (m + 2)} \cdot 3
|
-22,835 |
\frac{108}{120} = \frac{9\cdot 12}{10\cdot 12}
|
23,394 |
\left(1 + 6 + 3\right)^n = 10^n
|
527 |
1 = \frac{1}{2} \cdot \left(v - u + 2\right) + u + v + 4 \cdot (-1) \Rightarrow v \cdot 3 + u = 8
|
13,055 |
l\cdot 2\cdot 2 = 4\cdot l
|
28,142 |
-z^3 + z = \frac{1}{X^2}\cdot L\cdot M rightarrow (1 - z^2)\cdot z = \tfrac{L}{X \cdot X}\cdot M
|
30,520 |
\frac{x}{\sqrt{\frac{xy}{n}}}=x\sqrt{\frac{n}{xy}}=\sqrt{\frac{nx}y}
|
-17,708 |
80 = 18*\left(-1\right) + 98
|
34,849 |
3952*253 - 255*3921 = 1
|
30,900 |
(z_2 - z_1)\cdot (z_2^2 + z_2\cdot z_1 + z_1^2) = z_2^3 - z_1^3
|
47,341 |
39 = 14 + 1\cdot 25
|
884 |
1 = \left|{\dfrac{A}{A}}\right| = \left|{A}\right|\cdot \left|{\tfrac{1}{A}}\right|
|
36,115 |
|v\cdot x| = |v|\cdot |x|
|
32,698 |
1431 = 1 + 2\times 26^2 + 3\times 26
|
22,814 |
-1/2\cdot x_4 + x_1 = 0 \Rightarrow x_1 = 1/2\cdot x_4
|
15,252 |
\lim_{n\to\infty}(a_n-b_n)=0\Rightarrow \lim_{n\to\infty}\frac{a_n}{b_n}=1
|
-18,069 |
4 = 73 (-1) + 77
|
-18,787 |
2 = \frac63
|
13,495 |
(x + 4\cdot (-1))/2\cdot 2 = x + 4\cdot (-1)
|
-12,038 |
\frac{2}{3} = s/(16\times \pi)\times 16\times \pi = s
|
24,855 |
\left(1423 \cdot D\right) \cdot \left(1423 \cdot D\right) = 1423^2 \cdot D = 12 \cdot 34 \cdot D = D
|
-26,622 |
(9\cdot (-1) + 4\cdot x^3)\cdot (x \cdot x \cdot x\cdot 4 + 9) = -9^2 + \left(4\cdot x^3\right) \cdot \left(4\cdot x^3\right)
|
-18,779 |
\dfrac{8x}{4} = 2x
|
-20,323 |
(2 + x \cdot 2)/\left(-10\right) \cdot \frac{1}{4} \cdot 4 = \dfrac{1}{-40} \cdot (x \cdot 8 + 8)
|
2,675 |
\tan{x} = \frac{1}{\cos{x}} \cdot \sin{x} = 1/\cot{x}
|
-23,374 |
\frac{1}{6} = \frac{1}{3*2}
|
-10,962 |
48 = \dfrac14 \cdot 192
|
3,971 |
(4^3 - 4^2 + 4*(-1) + 1)*4^{2013} = 4^{2016} - 4^{2015} - 4^{2014} + 4^{2013}
|
33,438 |
\pi \cdot \frac13 \cdot 2 = 2 \cdot \pi/3
|
23,846 |
\dfrac{1}{n + k}*n = \frac{1}{n + k}*(n + k - k) = 1 - \frac{k}{n + k}
|
-543 |
(e^{19 \pi i/12})^{10} = e^{10 \frac{1}{12}\pi*19 i}
|
44,882 |
\sum_{l=i}^n l = \sum_{l=0}^{n - i} (i + l) = \sum_{l=0}^{n - i} i + \sum_{l=0}^{n - i} l
|
-22,429 |
8^{\frac{7}{3}}=\left(8^{\frac{1}{3}}\right)^{7}=2^{7} = 2\cdot2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2 = 4\cdot2\cdot 2\cdot 2\cdot 2\cdot 2 = 8\cdot2\cdot 2\cdot 2\cdot 2 = 16\cdot2\cdot 2\cdot 2 = 32\cdot2\cdot 2 = 64\cdot2 = 128
|
4,760 |
4\cdot y + 4\cdot \left(-1\right) = 4\cdot \left(y + 2\cdot (-1)\right) + 8 + 4\cdot (-1) = 4\cdot \left(y + 2\cdot \left(-1\right)\right) + 4
|
14,422 |
\frac{3}{50} = \frac{8}{4 + 8} \cdot \frac{3}{5 + 3} \cdot (\left(-1\right) \cdot 0.4 + 1) \cdot 0.4
|
550 |
1 - 8/y^3 = 0 \implies y=2
|
29,596 |
\left(\left(-1\right) + y\right)^3 + y^3 + \left(1 + y\right)^3 = y*6 + 3 y^3
|
33,657 |
l^3 - l^2 + l^2 - l = l \cdot l^2 - l
|
8,301 |
0 = x^2 * x - 2*x^2 - 5*x + 6 = (x + \left(-1\right))*(x + 2)*\left(x + 3*(-1)\right)
|
-1,664 |
-2 \cdot \pi + \pi \cdot 13/6 = \frac{\pi}{6}
|
7,513 |
\dfrac{y}{1} = \left(1 - z\right)/3 = r rightarrow y = r\wedge z = 1 - r\cdot 3
|
39,382 |
12 \left(-1\right) + 22 = 10
|
-3,695 |
\frac{132\cdot q}{99\cdot q^2} = \frac{1}{q^2}\cdot q\cdot 132/99
|
23,692 |
n^{j \cdot 2} + (-1) = (\left(-1\right) + n^j) \cdot \left(n^j + 1\right)
|
25,363 |
\frac{1}{2}\cdot \sqrt{X\cdot 4} = \sqrt{X}
|
24,366 |
b^{s/q} = (b^{\frac{1}{q}})^s = (b^s)^{\dfrac{1}{q}}
|
48,475 |
F_2 = F_2
|
-28,894 |
20!=20\cdot19\cdot18\cdot...\cdot3\cdot2\cdot1
|
48,842 |
(-1)^{2/2} = (-1)^1 = -1
|
46,887 |
52 = \dfrac{1}{1/52}
|
21,528 |
b^{y + x} = b^x b^y
|
26,216 |
-z_2 * z_2 + z_1 * z_1 = (z_1 - z_2)*\left(z_2 + z_1\right)
|
-26,543 |
9 - 25 z^2 = \left(-z*5 + 3\right) (z*5 + 3)
|
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