id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-695 |
(e^{i*\pi*4/3})^{19} = e^{i*\pi*4/3*19}
|
-19,476 |
\frac{2 / 3}{1/7}\cdot 1 = 2/3\cdot \frac11\cdot 7
|
-4,332 |
\dfrac{y}{y^4} \cdot 28/70 = \frac{28 \cdot y}{70 \cdot y^4}
|
28,666 |
\sqrt{x} = x^{\frac12} = x^{3/6}
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14,784 |
3 = \frac22\cdot 3
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-596 |
\pi\cdot 92/3 - \pi\cdot 30 = \frac{2}{3}\cdot \pi
|
40,121 |
\frac{1}{6^5} \cdot 651 = 651/7776 = 217/2592
|
22,619 |
1 + x^2 - 2*x = 1 + x^2 - 2*x
|
3,232 |
1/(f*d) = 1/(d*f) = \frac{1}{f*d}
|
-60 |
5*\left(-1\right) - 17 = -22
|
38,324 |
\overline{u\times v} = |u\times v|^2/(u\times v) = |u|^2/u\times |v|^2/v
|
6,494 |
-\frac{1}{l + 1} + 1 = \frac{l}{l + 1}
|
6,799 |
\left(0 = 20\cdot (-1) + x^3 + 6\cdot x rightarrow 0 = (\left(1 + x\right) \cdot \left(1 + x\right) + 9)\cdot (x + 2\cdot (-1))\right) rightarrow x = 2
|
7,212 |
e^{|-z + x|} \cdot e^1 = e^{1 + |-z + x|}
|
-15,786 |
8\cdot 7/10 - 5\cdot 3/10 = \frac{41}{10}
|
20,111 |
nx\cdot 2 - n^2 = x^2 - \left(x - n\right)^2
|
-4,322 |
\frac{x}{x^3} = \frac{x}{x\cdot x\cdot x} = \dfrac{1}{x^2}
|
-2,202 |
2/12 = \frac16
|
-1,784 |
13/12 \cdot \pi - \pi/3 = \pi \cdot 3/4
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-5,700 |
\dfrac{2}{n^2 - n \cdot 16 + 63} = \frac{2}{(n + 9 \cdot (-1)) \cdot (n + 7 \cdot (-1))}
|
20,476 |
6 \cdot 15 \cdot 3^7 = 3^9 \cdot 2 \cdot 5
|
-4,521 |
\frac{1}{x^2 + x \cdot 5 + 4} \cdot (-9 \cdot x + 24 \cdot \left(-1\right)) = -\frac{5}{1 + x} - \frac{4}{x + 4}
|
-7,531 |
\dfrac{(-1+5i) \cdot (1+i)}{(1-i) \cdot (1+i)} = \dfrac{(-1+5i) \cdot (1+i)}{1^2 - (-1i)^2}
|
12,337 |
1/(a*b) = 1/(b*a) \neq 1/(a*b)
|
-10,676 |
\dfrac{1}{9\cdot a + 6\cdot \left(-1\right)}\cdot 6\cdot \frac{4}{4} = \dfrac{24}{36\cdot a + 24\cdot (-1)}
|
24,544 |
(-3)\cdot 2 = 2\cdot \left(-1\right) - 2 + 2\cdot (-1)
|
26,010 |
\frac{1}{4}3\cdot \frac{1}{3}2/2 = 1/4
|
26,490 |
(1 + m) m! = \left(m + 1\right)!
|
30,264 |
f + e \neq 0\Longrightarrow -e \neq f
|
22,975 |
2 = 1/x + x \implies x = 1
|
22,443 |
\sin\left(2\cdot z\right) = \sin(z)\cdot \cos(z)\cdot 2
|
7,621 |
a + (1 + l) \cdot z = y \Rightarrow \frac{-a + y}{1 + l} = z
|
16,317 |
2/3 + \frac76 = \frac{11}{6} = \frac{5}{3} + 1/6
|
7,771 |
1/(h_2 h_1) = \frac{1}{h_2 h_1}
|
-12,337 |
2\sqrt{5} = \sqrt{20}
|
-20,238 |
\frac16 6 \frac{1}{6 (-1) + k} (2 (-1) - k*5) = \tfrac{1}{36 (-1) + k*6} (-30 k + 12 (-1))
|
1,991 |
x\cdot v = v^W\cdot x = x^W\cdot v
|
2,012 |
\frac12*(4^2 + 4*\left(-1\right)) = 6
|
25,393 |
2k + 1 = (k + 1)^2 - k^2
|
2,154 |
10 = \frac{1}{4\cdot a^2}\cdot h^2\cdot a - \tfrac{1}{2\cdot a}\cdot h\cdot h + c = -h^2/(4\cdot a) + c
|
17,908 |
z^2 + z + 1 + 2*(-1) = z * z + z + \left(-1\right) \neq (z + \left(-1\right))*(z + 2)
|
10,825 |
x \cdot \left(1 - 0.95^6\right) = -x \cdot 0.95^6 + x
|
12,953 |
160 + x = 11\cdot (x + 10) \implies 110 + 11\cdot x = 160 + x
|
-10,598 |
\frac{1}{2(-1) + n}(n\cdot 3 + 3(-1)) \frac144 = \frac{1}{4n + 8(-1)}(12 n + 12 \left(-1\right))
|
4,685 |
\frac6y \leq -8\Longrightarrow y \geq -\frac68 = -3/4
|
12,328 |
\frac{10}{21} = 5/7\cdot \frac23
|
16,479 |
5555\cdot \cdots = 5/9
|
25,238 |
\tan\left(\frac{\pi}{4} + x\right) = \cot(\pi/4 - x)
|
16,604 |
0 = -\cos(2\cdot \pi) + 1
|
4,118 |
\frac{1/\left(\sqrt{2}\right)*\frac{2}{\sqrt{2}}}{2} = \frac12
|
-3,346 |
\left(4 \cdot 11\right)^{1/2} + (16 \cdot 11)^{1/2} = 44^{1/2} + 176^{1/2}
|
2,641 |
1/2 + \dfrac{5^{\frac{1}{2}}}{2} = \tfrac12 \cdot (5^{\frac{1}{2}} + 1)
|
34,741 |
n = \dfrac{n}{1}
|
39,650 |
E_{n}*\dots*E_{1}*E_{n+1}*B = I \Rightarrow I = B*E_{n+1}*E_{n}*\dots*E_{1}
|
24,317 |
a/(h_2) + c/(h_1) = \left(c\cdot h_2 + a\cdot h_1\right)/(h_1\cdot h_2) + 0
|
14,451 |
-2\cdot x^2 + 1 + x = (1 + 2\cdot x)\cdot (-x + 1)
|
5,316 |
n^2 = 9 \cdot k \cdot k + 12 \cdot k + 4 = 3 \cdot (3 \cdot k^2 + 4 \cdot k + 1) + 1\Longrightarrow n^2 + (-1) = 3 \cdot \left(1 + k \cdot k \cdot 3 + k \cdot 4\right)
|
28,937 |
-\sin(\beta) \times \cos(x) + \sin(x) \times \cos(\beta) = \sin\left(-\beta + x\right)
|
26,358 |
\sqrt{5} \cdot \frac{10}{5} \cdot \sqrt{30} = \sqrt{6} \cdot 10
|
-1,701 |
-2 \cdot \pi + \dfrac{17}{6} \cdot \pi = \dfrac{1}{6} \cdot 5 \cdot \pi
|
9,107 |
x + 4 + \dfrac{7}{4(-1) + x} = \frac{9\left(-1\right) + x^2}{x + 4(-1)}
|
-6,120 |
\frac{20\cdot (q + 7\cdot (-1))}{16\cdot (q + 10)\cdot (q + 7\cdot (-1))} + \frac{16\cdot (q + 10)}{(7\cdot (-1) + q)\cdot (q + 10)\cdot 16} - \frac{1}{16\cdot (10 + q)\cdot (q + 7\cdot \left(-1\right))}\cdot 48 = \frac{1}{(q + 7\cdot (-1))\cdot (10 + q)\cdot 16}\cdot \left(20\cdot (7\cdot \left(-1\right) + q) + 16\cdot (q + 10) + 48\cdot (-1)\right)
|
21,700 |
\cos{3 \cdot \theta} = -3 \cdot \cos{\theta} + \cos^3{\theta} \cdot 4
|
-22,029 |
\frac178 = 24/21
|
23,542 |
-r r r + (1 + r)^3 = 1 + 3 r^2 + 3 r
|
-20,179 |
\frac{1}{-z \cdot 3 + 9 \cdot \left(-1\right)} \cdot (-z \cdot 3 + 9 \cdot (-1)) \cdot (-7/4) = \frac{21 \cdot z + 63}{-z \cdot 12 + 36 \cdot (-1)}
|
-12,256 |
1/45 = \frac{p}{12 \cdot \pi} \cdot 12 \cdot \pi = p
|
52,812 |
10 + (-1) = 9 \neq 1
|
7,122 |
(p + t)^2 = p^2 + 2 \cdot p \cdot t + t^2
|
6,520 |
5/83 = \frac{\binom{13}{4}}{\binom{13}{4} + \binom{13}{3}\cdot 39}
|
7,767 |
\sin{2\cdot \dfrac{\pi}{2}} = 0
|
2,861 |
\frac{1}{44} = -\frac{1}{11} + \dfrac{1}{33} + \frac{1}{12}
|
31,153 |
-k^2*y^2 + z^2 = 1 \Rightarrow 1 = (k*y + z)*(z - k*y)
|
35,393 |
1 - (1 - \frac{1}{13})^5 = 122461/371293
|
-2,660 |
11^{1/2}\cdot 4 + 11^{1/2} = 11^{1/2}\cdot 16^{1/2} + 11^{1/2}
|
-20,140 |
\frac{z + 6}{3 \cdot (-1) + 9 \cdot z} \cdot 9/9 = \dfrac{9 \cdot z + 54}{z \cdot 81 + 27 \cdot (-1)}
|
19,461 |
\left(3^{1/2} + 7^{1/2}\right)^2 = 10 + 21^{1/2}\cdot 2
|
23,799 |
\left(1 = (-\sin{y} + 1)/2 \implies \sin{y} = -1\right) \implies y = \frac{\pi}{2} \cdot 3
|
42,706 |
\frac{3*z^2 + 3*z + 6*(-1)}{2*z^2 + 6*z + 4} = \dfrac{3*(z * z + z + 2*(-1))}{2*(z * z + 3*z + 2)} = \frac{3*(z + 2)*\left(z + (-1)\right)}{2*(z + 1)*(z + 2)}*1
|
11,415 |
0 + x + w + 0 = 0 + 0 + w + x \implies x + w = w + x
|
-21,010 |
\frac{7}{6}\cdot \frac{1}{p + 6\cdot (-1)}\cdot (p + 6\cdot (-1)) = \dfrac{7\cdot p + 42\cdot \left(-1\right)}{6\cdot p + 36\cdot \left(-1\right)}
|
30,240 |
4 \cdot 4 + 1^2 + 2^2 + 3^2 = (1 + 2 + 3 + 4) \cdot 3
|
18,900 |
(e^z - e^{-z})/2 = 2 \implies -e^{-z} + e^z = 4
|
-20,069 |
\frac33 \cdot \frac{5 \cdot z}{9 + 8 \cdot z} = \dfrac{z \cdot 15}{24 \cdot z + 27}
|
-27,176 |
\sum_{n=1}^\infty \frac{1}{n*4^n} 3 (3 + 1)^n = \sum_{n=1}^\infty \dfrac{3*4^n}{n*4^n} 1 = \sum_{n=1}^\infty 3/n = 3 \sum_{n=1}^\infty 1/n
|
24,735 |
8 \cdot s^3 - 12 \cdot s \cdot s + 6 \cdot s + (-1) = 16 \cdot s^3 - 48 \cdot s^2 + 48 \cdot s + 16 \cdot (-1) = 24 \cdot s \cdot s \cdot s - 108 \cdot s^2 + 162 \cdot s + 81 \cdot (-1)
|
34,484 |
x\times (-1) = -x
|
-7,361 |
5/15 \cdot \frac{6}{16} = \frac{1}{8}
|
18,197 |
\left((-1) + x^2\right)^3 = x^6 - 3*x^4 + 3*x^2 + \left(-1\right)
|
15,572 |
y^2 - 5 \cdot y + 6 = \left(2 \cdot (-1) + y\right) \cdot (y + 3 \cdot (-1))
|
-6,710 |
6/10 + 2/100 = 2/100 + 60/100
|
274 |
\dfrac{1}{2(\frac12 + (-1)) (2(-1) + \frac12) \ldots*(1 + 1/2 - n) n!} = {\frac{1}{2} \choose n}
|
23,910 |
y = e \cdot y = y \cdot e
|
-9,148 |
-x \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 + 2 \cdot 3 \cdot 3 \cdot 5 = 90 - 72 \cdot x
|
36,465 |
(-g) * (-g) = g^2
|
5,737 |
v v - v + 1 = \left(-\frac{1}{2} + v\right)^2 + \dfrac14 3
|
2,219 |
C_J \cdot x_J = C_J \cdot x_J
|
4,916 |
\sqrt{x + 3 \left(-1\right)} = \sqrt{-(3 - x)} = i \sqrt{3 - x}
|
5,662 |
((-3) \cdot z)/(\sqrt{z}) = -\sqrt{z} \cdot 3
|
1,737 |
8^{8^8} + 1 = (1 + 2^{2^{25}} - 2^{2^{24}}) \cdot (2^{2^{24}} + 1)
|
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