id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-3,611 |
\frac{99\cdot y^5}{y^4\cdot 72} = \frac{y^5}{y^4}\cdot \frac{99}{72}
|
-23,410 |
\dfrac{4}{5} \cdot \dfrac{1}{7} = \dfrac{4}{35}
|
-23,381 |
\frac{3*\dfrac{1}{7}}{5} = 3/35
|
-25,046 |
\dfrac25 \cdot \tfrac{1}{6} = \frac{2}{30} = \frac{1}{15}
|
11,817 |
n \times (n + 1) = n + n^2
|
-6,007 |
\frac{4}{\left(z + 4\right) (10 + z)} = \frac{1}{z^2 + 14 z + 40}4
|
12,659 |
|x - y| = y - x = \tfrac{1}{x + y}*(y^2 - x^2) \lt \dfrac{1}{2*x}*\left(y^2 - x^2\right)
|
18,427 |
\sqrt{1 + b} = b \implies b^2 = 1 + b
|
5,528 |
n \cdot n \cdot n \cdot 2 = 2 \cdot n^3
|
19,537 |
-(x - 2z)^2 = -(x * x - 4xz + 4z^2) = -x^2 - 4z^2 + 4xz
|
46,448 |
(9 \cdot y + 8 \cdot y^2 + 1)/y = \frac9y \cdot y + \frac8y \cdot y^2 + 1/y = 9 + 8 \cdot y + \frac{1}{y}
|
35,917 |
\sqrt{f} \sqrt{f} = f
|
13,613 |
2.5 + \sin{z} = 1 \Rightarrow \sin{z} = -1.5
|
34,787 |
{(-1) + k \choose r + (-1)} = {(-1) + k \choose -r + k}
|
11,479 |
2/52*\frac{1}{52}*2 = \dfrac{1}{676}
|
14,493 |
(y - e^{2\pi/x}) \cdots e^{(x + (-1)) \pidot2/x} = 1 + y + \cdots + y^{x + (-1)}
|
-20,719 |
-\frac{9}{10}\cdot \frac{1}{3\cdot (-1) + z}\cdot (3\cdot (-1) + z) = \dfrac{1}{10\cdot z + 30\cdot (-1)}\cdot (-9\cdot z + 27)
|
30,993 |
d + a = 23 \Rightarrow d = 23 - a
|
11,949 |
76/7 = 38 \cdot 2/7
|
-5,176 |
0.69 \cdot 10^3 = 10^{7 + 4 \cdot (-1)} \cdot 0.69
|
34,195 |
(\frac{1}{\left(-1\right) + v} - \frac{1}{v + 1})/2 = \frac{1}{v^2 + (-1)}
|
11,252 |
\frac{\pi*2}{15} = \pi*2/3*2*1/5/2
|
4,967 |
7^{1 + x\cdot 2} = \left(7^2\right)^x\cdot 7
|
12,562 |
\dfrac{1}{(-x\cdot 6 + 1)^{\frac13}} = (1 - 6\cdot x)^{-1/3}
|
23,704 |
z^i = e^{i \cdot \log_e(z)} = \cos(\log_e(z)) + i \cdot \sin(\log_e(z))
|
40,329 |
-300000 = -80000 + 220000 \cdot \left(-1\right)
|
-6,672 |
\dfrac{4}{t \cdot t - t + 20 (-1)} = \frac{4}{(5(-1) + t) \left(t + 4\right)}
|
1,871 |
Q_x\cdot Q_x^{(-1) + m} = Q_x^m
|
10,152 |
y_v + 2\cdot \left(2 + (-1)\right)^2 = -1 \Rightarrow y_v = -1 + 2\cdot \left(-1\right) = -3
|
20,728 |
(b - d)^2 \geq 4(1 + b + d)^2 - 4\left(b + d\right)^2 = 4\cdot (1 + 2b + 2d) \gt 8(b + d)
|
42,647 |
3.14159265 \cdot 10^8 = 314159265
|
11,895 |
(A + B)^2 = B^2 + A \cdot A + A \cdot B \cdot 2
|
36,958 |
2^{l + 1} = 2.2^l > l * l + l * l
|
14,870 |
\frac{\mathrm{d}}{\mathrm{d}y} \cos\left(-y\right) = -\sin(-y)\cdot \frac{\mathrm{d}}{\mathrm{d}y} (-y) = \sin\left(-y\right) = -\sin\left(y\right)
|
-13,246 |
7 + \frac17\cdot 35 = 7 + 5 = 7 + 5 = 12
|
33,777 |
2 \cdot 2/3 \cdot 2 = 8/3
|
-7,700 |
(60 - 100 \cdot i + 15 \cdot i + 25)/17 = \frac{1}{17} \cdot \left(85 - 85 \cdot i\right) = 5 - 5 \cdot i
|
17,793 |
{2 + 3 + 2 \cdot (-1) \choose \left(-1\right) + 2} = 3
|
-15,907 |
6/10 \cdot 10 - 7 \cdot \frac{4}{10} = 32/10
|
16,964 |
\left(a + b\right)^2 = a^2 + b \cdot b + 2 \cdot a \cdot b
|
-1,963 |
\dfrac{\pi}{3} - 3/2*\pi = -\frac16*7*\pi
|
1,348 |
2^{n + (-1)}*2 - 2^{(-1) + n} = 2^{(-1) + n}
|
-3,536 |
\dfrac{7*5}{20*5} = \tfrac{35}{100}
|
-3,759 |
\tfrac{1}{99}\cdot 121\cdot \frac1x\cdot x^3 = \tfrac{121\cdot x^3}{99\cdot x}
|
25,924 |
4r = j_2^2 - j_1 \cdot j_1 \Rightarrow (j_2 + j_1) (-j_1 + j_2) = r \cdot 4
|
5,395 |
l*7 = 4*(-1) + k*10 + 3 rightarrow -7*l + k*10 = 1
|
5,103 |
\frac{1}{g} + \dfrac{1}{x} = 1/c \Rightarrow xg = cg + cx
|
32,725 |
7 - 4 - 1 = 7 - 4 + 1
|
11,516 |
\frac{1}{1}\sqrt{5} = \sqrt{5}
|
1,139 |
15 = 5*\left(-1\right) + 4*5
|
-20,001 |
\dfrac{9}{6\cdot (-1) + z\cdot 10}\cdot 9/9 = \frac{81}{54\cdot (-1) + z\cdot 90}
|
-27,374 |
49 = \left(-1\right) + 50
|
-3,427 |
32^{1/2} + 50^{1/2} + 2^{1/2} = 2^{1/2} + (16\cdot 2)^{1/2} + \left(25\cdot 2\right)^{1/2}
|
2,880 |
\left(-1\right) + 2 \cdot z = (z - 1/2) \cdot 2
|
11,888 |
n + (-1) = \binom{\left(-1\right) + n}{1}
|
32,277 |
\cos\left(y + \pi\right) = -\cos{y}
|
22,185 |
2n + 1 = 2n + 1 + n^2 - n^2
|
21,169 |
z z^2 - 3 z^2 - z + (-1) = (z + (-1))^3 - 3 z + 1 - z + \left(-1\right) = (z + (-1)) (z + (-1)) (z + (-1)) - 4 \left(z + (-1)\right) + 4 \left(-1\right)
|
37,654 |
\beta*2 + x*2 = x*2 + \beta*2
|
24,960 |
108973^l = (10 \cdot 10897 + 3)^l
|
6,901 |
\sin^2{x} = \left(e^{i \cdot x} - e^{-i \cdot x}\right)^2/(-4) = -(e^{2 \cdot i \cdot x} + 2 \cdot (-1) + e^{-2 \cdot i \cdot x})/4
|
-9,207 |
-4 \cdot y - y^2 \cdot 12 = -y \cdot y \cdot 2 \cdot 2 \cdot 3 - 2 \cdot 2 \cdot y
|
10,272 |
7 \cdot l + 4 = 7 \cdot (1 + l) + 3 \cdot (-1)
|
33,820 |
\tfrac{3 - x}{(x + 3\cdot (-1))^2} = -\dfrac{1}{(x + 3\cdot (-1))^2}\cdot (x + 3\cdot (-1)) = -\frac{1}{x + 3\cdot \left(-1\right)}
|
886 |
360 = 3!*\dfrac{1}{2!}*4!*{5 \choose 4}
|
30,181 |
(2\cdot x^2 + 1)^2 + \left(-1\right) = 4\cdot x^4 + 4\cdot x \cdot x = (2\cdot x^2)^2 + (2\cdot x)^2
|
31,749 |
(1 + 1) \left(x + d\right) = x + d + x + d = x + d + x + d
|
27,501 |
y\cdot a = x\cdot a \Rightarrow x = a\cdot x = a\cdot y = y
|
8,979 |
20538 = 3^2\cdot 2\cdot 7\cdot 163
|
32,913 |
y = y - By + By \Rightarrow \|y\| \leq \|By\| + \|-By + y\|
|
3,566 |
12 \frac{2}{\sqrt{2}}\frac{1}{\sqrt{3}} = \frac{24}{\sqrt{6}}
|
-4,558 |
\dfrac{2 \cdot x + 18}{x^2 + 6 \cdot x + 5} = -\frac{2}{5 + x} + \frac{1}{x + 1} \cdot 4
|
1,670 |
41650 \cdot (-1) + 1275 \cdot n = 425 \cdot (3 \cdot n + 98 \cdot (-1))
|
-22,224 |
y^2 + 9y + 20 = \left(y + 5\right) (4 + y)
|
5,012 |
\int (-u^{\dfrac12} + u^{\frac{1}{2}3})\,du = \int ((-1) + u) \sqrt{u}\,du
|
-23,124 |
\frac{1}{2}\cdot 3\cdot 2 = 3
|
-18,276 |
\frac{1}{z\cdot \left(9\cdot (-1) + z\right)}\cdot (z + 9\cdot (-1))\cdot (5\cdot (-1) + z) = \dfrac{z^2 - 14\cdot z + 45}{z^2 - z\cdot 9}
|
-10,398 |
-8 = 5z + 9\left(-1\right) + 10 (-1) = 5z + 19 (-1)
|
-2,915 |
\sqrt{11}*8 = \sqrt{11}*(1 + 4 + 3)
|
14,955 |
x k = k x
|
-4,455 |
\dfrac{-5 \cdot x + 8}{x^2 - 5 \cdot x + 4} = -\frac{4}{4 \cdot (-1) + x} - \frac{1}{(-1) + x}
|
34,782 |
2^{3^{1 + x}} + 1 = (2^{3^x})^3 + 1
|
-2,738 |
\left(2 + 4\right)\cdot \sqrt{10} = \sqrt{10}\cdot 6
|
1,222 |
1 = \frac{2}{0!*(2 + 0)!}*\dfrac{1}{(0 + 2)!*0!}*2
|
8,832 |
|\bar{z}^2/z| = \dfrac{1}{|z|} \times |\bar{z}|^2 = \frac{1}{|z|} \times |z|^2 = |z|
|
23,504 |
\arcsin\left(1\right) = \frac{\pi}{2}
|
20,143 |
(\left(-1\right) + n)^2 = n \cdot n - 2 \cdot n + 1
|
37,987 |
C^T\cdot z = C^T\cdot C\cdot x rightarrow \frac{z\cdot C^T}{C^T\cdot C} = x
|
-22,305 |
(s + 5)*\left(s + 9*(-1)\right) = s * s - 4*s + 45*(-1)
|
-14,669 |
348/4 = 87
|
-12,548 |
44 = 156 + 112\cdot (-1)
|
28,511 |
a^z*a^y = a^{z + y}
|
8,454 |
(d - x)\cdot (x^2 + d^2 + d\cdot x) = d^3 - x^3
|
-3,070 |
\sqrt{3}*(2 + 1 + 5) = 8*\sqrt{3}
|
44,149 |
2017 - 9 * 9 = 2017 + 81*(-1) = 1936 = 44^2
|
19,577 |
2071 = 19^3 - yx*57 \Rightarrow xy = 84
|
31,935 |
h/(g \frac{1}{f}) = \frac{f}{g} h
|
6,847 |
\cot(2*y) = \tfrac{1}{\tan(2*y)} = \frac{1}{2*\tan(y)}*(1 - \tan^2(y))
|
-1,425 |
-\tfrac{1}{15}20 = \frac{(-20) \cdot 1/5}{15 \cdot \frac{1}{5}} = -4/3
|
-4,811 |
10^{-2 + 2}\cdot 77.6 = 77.6\cdot 10^0
|
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