id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
27,094 |
y^4 = y^4 + (-1) + 1 = (y^2 + 1) \left(y^2 + (-1)\right) + 1
|
21,705 |
\frac16 \cdot 91 = \left(1 + 4 + 9 + 16 + 25 + 36\right)/6
|
-20,389 |
\dfrac{1}{5}\cdot 5\cdot \dfrac{1}{-x + 5\cdot \left(-1\right)}\cdot x = \frac{5\cdot x}{25\cdot (-1) - x\cdot 5}
|
24,824 |
2^2 \cdot 2 \cdot 7 = 56
|
19,148 |
-2\cdot e^{(i\cdot (-1)\cdot \pi)/3} = -2\cdot e^{(\pi\cdot (-1)\cdot i)/3}
|
13,316 |
\frac{l^3 + 3 \cdot (-1)}{l^2 + 7 \cdot \left(-1\right)} = \frac{1}{l^2 + 7 \cdot (-1)} \cdot (l \cdot 7 + 3 \cdot (-1)) + l
|
-13,319 |
10 + 3 = 10 + 3 = 13
|
-7,605 |
\frac{1}{17} \cdot (-14 + 5 \cdot i - 56 \cdot i + 20 \cdot \left(-1\right)) = \frac{1}{17} \cdot \left(-34 - 51 \cdot i\right) = -2 - 3 \cdot i
|
5,908 |
-n^2 + (8 + n) * (8 + n) = 16*(n + 4)
|
17,671 |
y^4 - 2 \cdot y \cdot y + 8 \cdot (-1) = (y^2 + (-1)) \cdot (y^2 + (-1)) + 9 \cdot (-1) = \left(y^2 + (-1) + 3 \cdot \left(-1\right)\right) \cdot (y^2 + (-1) + 3) = (y + 2 \cdot (-1)) \cdot (y + 2) \cdot \left(y^2 + 2\right)
|
-12,748 |
\dfrac{21}{28} = \frac{1}{4}\cdot 3
|
36,575 |
146 = 162 + 16\cdot (-1)
|
1,140 |
((-1) + l)^2 + l \cdot 4 = (l + 1)^2
|
22,927 |
8 + 5\cdot (-1) = 3 = 3
|
15,156 |
\left(3 + x \cdot 7 = -37 \implies -40 = x \cdot 7\right) \implies x = -40/7
|
31,755 |
|x^2 - 4x - -3| = |x + 3\left(-1\right)| |x + \left(-1\right)| \leq 3|x + (-1)|
|
10,101 |
z^{\frac{k}{l}} = (z^k)^{1/l} = \left(z^{\frac{1}{l}}\right)^k
|
-15,855 |
\frac{46}{10} = 8 \cdot \frac{8}{10} - 9 \cdot 2/10
|
-24,875 |
\frac{1}{18} = s/6*6 = s
|
-602 |
(e^{\pi \cdot i \cdot 17/12})^{20} = e^{20 \cdot \pi \cdot i \cdot 17/12}
|
13,381 |
(n + 1)\cdot (n + 2) = 2 + n^2 + 3\cdot n
|
17,997 |
6 (-1) + 7 = 1
|
-16,522 |
8 \cdot 25^{1/2} \cdot 11^{1/2} = 8 \cdot 5 \cdot 11^{1/2} = 40 \cdot 11^{1/2}
|
8,082 |
4zx = (x + z)^2 - (x - z)^2
|
15,639 |
(x + (-1))*(1 + x)*(1 + x^2) = \left(-1\right) + x^4
|
5,647 |
2 + x^4 - 4 \times x^2 = 2 \times (-1) + (2 \times (-1) + x^2)^2
|
-30,813 |
4(6 + z^2) = z^2\cdot 4 + 24
|
19,122 |
\sqrt{( x^2, z \cdot z \cdot z)} = \sqrt{x^2\cdot z^3} = \sqrt{x^2}\cdot \sqrt{z \cdot z \cdot z} = x\cdot z = [x,z]
|
39,283 |
18 = 3\times (12 + 6\times (-1))
|
12,468 |
\frac{720}{24}=30
|
36,502 |
1/2 + 1/3 + \tfrac{1}{9} + \frac{1}{18} = 1
|
3,566 |
24/(\sqrt{6}) = 12 \cdot 1/(\sqrt{3}) \cdot 2/(\sqrt{2})
|
37,907 |
350 = {7 \choose 3}\cdot {5 \choose 3}
|
-4,280 |
d/3 = \frac13 \cdot d
|
-20,371 |
\tfrac{2x}{14 x} = \frac{1}{x*2}*x*2/7
|
9,250 |
\frac{1}{z \cdot \frac1y} = \frac{y}{z}
|
-20,701 |
\frac{-7 k + 56}{k + 8 \left(-1\right)} = -7/1 \frac{k + 8 (-1)}{k + 8 (-1)}
|
-2,679 |
12^{\frac{1}{2}} + 75^{\frac{1}{2}} = (25\cdot 3)^{\dfrac{1}{2}} + (4\cdot 3)^{\frac{1}{2}}
|
-10,598 |
\tfrac{3 \cdot \left(-1\right) + 3 \cdot n}{n + 2 \cdot \left(-1\right)} \cdot \frac{4}{4} = \frac{12 \cdot \left(-1\right) + 12 \cdot n}{8 \cdot (-1) + 4 \cdot n}
|
675 |
-I\cdot x + I + Y = -I\cdot ((-1) + x) + Y
|
15,824 |
26^{1 / 2} + y \geq 0 \Rightarrow y \geq -26^{\frac{1}{2}}
|
7,050 |
x*g*\gamma_n = x*\gamma_n*g
|
22,080 |
4 \cdot 43 = 172
|
15,048 |
4 = \frac12\left(5 + 3\right)
|
28,857 |
A A A = A^3
|
5,315 |
\frac{11!}{5!\cdot 5!\cdot 1!} = 11!/(5!\cdot 5!) = 2772
|
-2,198 |
\tfrac{5}{19} = \dfrac{7}{19} - 2/19
|
-15,530 |
\frac{1}{\frac{1}{\frac{1}{x^3} \cdot t}} \cdot (t^3)^3 = \dfrac{t^9}{x^2 \cdot x \cdot \tfrac1t}
|
-27,664 |
\sin(\theta \cdot 2) = \cos(\theta) \cdot \sin(\theta) \cdot 2
|
-22,338 |
(x + 1) (x + 9 \left(-1\right)) = 9 (-1) + x^2 - 8 x
|
11,347 |
a_2 + a_3 + ... + a_k + a_{k + 1} = a_2 + a_3 + ... + a_k + a_{k + 1}
|
-1,697 |
\frac94 \pi = \pi \frac56 + \pi \frac{17}{12}
|
13,502 |
\dfrac{z}{z^3} = \dfrac{1}{z * z}
|
6,863 |
1 - \frac{1}{y + 1} \cdot y = \frac{1}{1 + y}
|
27,328 |
(-2) \cdot 4 = -(2 \cdot 2 + (-1)) \cdot (2 \cdot 2 + (-1)) + (2 \cdot 2 + 3 \cdot (-1))^2
|
24,071 |
0 = -g/2\cdot T^2 + T\cdot \sin(\theta)\cdot V\Longrightarrow 2\cdot \sin(\theta)\cdot V/g = T
|
35,783 |
s_{11}\cdot s_{21} = s_{22}\cdot s_{12}\Longrightarrow s_{21}\cdot s_{12}\cdot s_{11} = s_{12} \cdot s_{12}\cdot s_{22}
|
-10,908 |
12 = \frac{60}{5}
|
24,697 |
x - i = x - i*2 + i
|
-22,298 |
7\cdot (-1) + r^2 - r\cdot 6 = (1 + r)\cdot (r + 7\cdot \left(-1\right))
|
-18,778 |
2 = \dfrac{1}{7} \cdot 14
|
3,566 |
24/(\sqrt{6}) = 2\cdot \frac{1}{\sqrt{3}}/(\sqrt{2})\cdot 12
|
-20,692 |
10*a/\left(a*10\right)*\frac57 = \dfrac{a*50}{a*70}
|
2,021 |
(-1)^y = (e^{i\times \pi})^y = \cos{\pi\times y} + i\times \sin{\pi\times y}
|
-19,474 |
\dfrac{1}{\frac18\cdot 5\cdot 9} = 1/5\cdot 8/9
|
20,870 |
f*e = -e*f = e*f
|
25,763 |
\left(-2\right)*(-3)*(-4)*\left(-5\right) = 120
|
51,802 |
\frac{p}{p - i\cdot c} = \dfrac{1}{p^2 + c^2}\cdot (p^2 + i\cdot c\cdot p) = \frac{p^2}{p^2 + c^2} + i\cdot \frac{c\cdot p}{p \cdot p + c^2}\cdot 1
|
23,894 |
(x + 1)^{\dfrac{1}{2}} = \left(x + 1\right)^{1/2}
|
17 |
(z + x + y)^3 - (-x + y + z)^3 - (z + x - y)^3 - \left(-z + x + y\right)^3 = y \cdot z \cdot x \cdot 24
|
25,450 |
((-1) + r) \cdot \left(r + 1\right) \cdot \left(r \cdot r + 1\right) \cdot \left(r^4 + 1\right) = r^8 + (-1)
|
51,973 |
18 = 9*2
|
36,379 |
\sqrt{6}*\sqrt{10} = \sqrt{15}*2
|
16,619 |
2^k r*2^{k/2}*2^{-k} = 2^{k/2} r
|
25,780 |
\frac{1}{1 - x} = \frac{1}{1 - x + 3\cdot (-1) + 3\cdot (-1)} = \frac{1}{-2 - x + 3\cdot (-1)} = \frac{1}{1 + \frac12\cdot (x + 3)}\cdot (\left(-1\right)\cdot 1/2)
|
1,072 |
\frac{(a - x\cdot i)^{-1}\cdot (a - i\cdot x)}{x\cdot i + a} = (a + x\cdot i)^{-1}
|
-18,643 |
-\frac{9}{30} = -\frac{1}{10}\cdot 3
|
24,923 |
649352163073816339512038979194880 = \frac{1}{5!^6*(-5*6 + 48)!}*48!
|
34,447 |
4^{2\cdot r + 2} + 4 = 16\cdot \left(4^{2\cdot r} + 4\right) + 60\cdot (-1)
|
37,668 |
\tfrac{1}{m\cdot n} = \frac{1}{m\cdot n}
|
9,789 |
(x + 1)*(x * x + 1)*(1 + x^4)*\dotsm*(1 + x^{2^k}) = \frac{-x^{2^{k + 1}} + 1}{-x + 1}
|
11,391 |
(99999 + 10002*\left(-1\right))/3 + 1 = \frac13*\left(10002*(-1) + 99999\right) + 1
|
3,805 |
\sqrt{1 + x} = (x + 1)^{\frac{1}{2}}
|
20,367 |
1 < e^{\frac1x} < 3^{\frac1x} = (1 + 2)^{1/x} \lt 1 + \frac1x*2
|
20,234 |
v \cdot v = m^2 \Rightarrow v = m
|
37,392 |
1 - y^4 = \left(1 - y\right) \cdot (1 + y + y^2 + y^3)
|
13,677 |
0 = \tfrac{1}{2 \cdot x^2 + 7 \cdot x + 5} \cdot \left(13 + x \cdot 4\right) \Rightarrow 0 = 13 + 4 \cdot x
|
15,454 |
(7 \cdot 7 \cdot 7)^{1/3} = 7
|
33,163 |
2r\pi\cdot 2R\pi = \pi \cdot \pi Rr\cdot 4
|
19,590 |
\mathbb{E}[\sum_{i=1}^l T_i] = \mathbb{E}[\sum_{i=1}^l T_i]
|
-20,236 |
\frac{1}{-x\cdot 20 + 40\cdot (-1)}\cdot (12 + x\cdot 6) = -3/10\cdot \frac{-2\cdot x + 4\cdot (-1)}{4\cdot (-1) - 2\cdot x}
|
6,584 |
\left(z \cdot z - a \cdot z + (-1)\right) \cdot \left(z^2 + a \cdot z + \left(-1\right)\right) = \left(z^2 + (-1)\right)^2 - a^2 \cdot z^2 = z^4 - (2 + a^2) \cdot z \cdot z + 1
|
-20,117 |
\frac{2\cdot (-1) + 8\cdot s}{s\cdot 8 + 2\cdot (-1)}\cdot (-7/9) = \tfrac{-s\cdot 56 + 14}{18\cdot (-1) + s\cdot 72}
|
14,661 |
\sin^2(t) = x\Longrightarrow \cos(2t) = 1 - 2\sin^2\left(t\right) = 1 - 2x
|
-1,197 |
\frac{1}{(-1) \cdot 7 \cdot 1/8} \cdot (\left(-8\right) \cdot \frac15) = -\frac{8}{7} \cdot (-\dfrac15 \cdot 8)
|
13,859 |
{10 \choose 1}*{5 \choose 3} + {5 \choose 2}*{10 \choose 2}*{2 \choose 1} + {3 \choose 1}*{5 \choose 1}*{10 \choose 3} + {4 \choose 1}*{5 \choose 0}*{10 \choose 4} = 3640
|
13,477 |
n + n = n + n = \left(1 + 1\right) n = 2 n
|
7,458 |
\sin\left(-x + \tfrac12\cdot \pi\right) = \cos{x}
|
50,311 |
\sum_{n=1}^\infty \frac{4^n \cdot 1/n}{6^n \cdot \frac1n} = \sum_{n=1}^\infty \frac{4^n}{6^n} = \sum_{n=1}^\infty (\dfrac13 \cdot 2)^n
|
-20,200 |
\dfrac{9}{8} \times \dfrac{z + 9}{z + 9} = \dfrac{9z + 81}{8z + 72}
|
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