id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
8,087 |
-t = -s \times Q \Rightarrow Q \times s = t
|
47,681 |
\left(32 = \tfrac{1}{4\cdot x^2}\cdot (\lambda \cdot \lambda + 1 + \lambda\cdot 2) + \frac{1}{x \cdot x\cdot 4}\cdot \lambda^2 + \frac{\lambda^2}{x \cdot x\cdot 4} \Rightarrow \lambda^2\cdot 3 + 2\cdot \lambda + 1 = x^2\cdot 128\right) \Rightarrow 3\cdot \lambda^2 + 2\cdot \lambda - x^2\cdot 128 + 1 = 0
|
-178 |
\binom{10}{6} = \frac{10!}{(6\cdot (-1) + 10)!\cdot 6!}
|
7,354 |
z \cdot z \cdot z + (-1) = (z + (-1)) (z^2 + z + 1) = 0\Longrightarrow 1 = z^3
|
3,981 |
\left(-1\right) + (l + 2)! = (-1) + (l + 1)! \cdot (l + 2)
|
5,935 |
x^3*y^3 = (x*y)^3
|
4,331 |
20\cdot y + 3\cdot y^2 = (y\cdot 2 + 10)^2 - (y + 10)^2
|
13,411 |
\dfrac{8!}{(8 + 2\cdot (-1))!} = 8\cdot 7
|
-20,137 |
-9/\left(-9\right) \frac91 = -\dfrac{1}{-9}81
|
20,078 |
|e^{i*t} + \left(-1\right)|^2 = |\cos{t} + \left(-1\right) + i*\sin{t}|^2 = (\cos{t} + (-1))^2 + \sin^2{t}
|
37,447 |
36 + 14 \cdot (-1) = 22
|
20,608 |
(1 + k) \cdot ((-1) + k) = k^2 + (-1)
|
-19,053 |
17/24 = A_q/\left(36\times \pi\right)\times 36\times \pi = A_q
|
29,571 |
\left(4 + 5(-1)\right)^2 \cdot (4 + 10) = 4 + 10 \gt 0
|
232 |
n = 5\cdot k + 2\Longrightarrow n = 5\cdot \left(2\cdot (-1) + k\right) + 4\cdot 3
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35,227 |
(\tfrac12 + 3/4) ((-1) + 2)/2 = \frac58
|
22,019 |
-1/2 = \sin(\frac76\cdot \pi)
|
13,150 |
(y + (-1)) \cdot (y + (-1)) \cdot (y^2 + 7) = (y + (-1)) \cdot \left(y + (-1)\right) \cdot \left(y^2 + 7\right) = (y + (-1)) \cdot (y^3 - y^2 + 7 \cdot y + 7 \cdot (-1))
|
-859 |
\frac{4208}{10000} = 0 + 4/10 + \frac{1}{100}*2 + \tfrac{0}{1000} + \frac{1}{10000}*8
|
-9,493 |
45 - a*10 = 3*3*5 - 2*5*a
|
31,105 |
\frac{1}{1 + a^2} = \frac{\mathrm{d}}{\mathrm{d}a} \tan^{-1}(a)
|
23,398 |
\left(1 + i*\sqrt{3}\right)^{6*n} = (2*e^{\frac{π*i}{3}*1})^{6*n} = 2^{6*n}
|
-6,305 |
\frac{1}{z^2 - 3*z + 54*(-1)} = \dfrac{1}{(6 + z)*(9*\left(-1\right) + z)}
|
-25,229 |
-\dfrac{1}{1^7}\cdot 6 = -\frac{1}{1}\cdot 6 = -6
|
11,978 |
\frac{27}{9} = \frac{27/9}{9/9} = \frac{3}{1} = 3
|
-12,801 |
21 = 31 + 10\cdot \left(-1\right)
|
11,932 |
g \cdot d = \|g\| \cdot \|d\| \cdot \left(\cos(x) + i \cdot \sin(x)\right) = \|g\| \cdot \|d\| \cdot e^{i \cdot x}
|
-20,641 |
\frac{24\cdot (-1) - 9\cdot t}{-t\cdot 6 + 15\cdot (-1)} = \frac{8\cdot (-1) - t\cdot 3}{5\cdot (-1) - 2\cdot t}\cdot \frac{3}{3}
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16,367 |
2 \cdot (3/2 + 1) = 5
|
6,313 |
t\cdot e - \left(t + (-1)\right)\cdot (e + (-1)) = \left(-1\right) + t + e
|
-7,930 |
(72 + 8*i - 90*i + 10)/41 = \left(82 - 82*i\right)/41 = 2 - 2*i
|
-7,015 |
3/9*\frac{2}{8} = \frac{1}{12}
|
-27,503 |
60\cdot w = 2\cdot 5\cdot w\cdot 3\cdot 2
|
19,968 |
(q^2 - q) \left(q^2 + (-1)\right) = q^4 - q^3 - q^2 + q
|
10,293 |
\frac{1587}{12167} = \frac{1}{x\cdot y\cdot z}\cdot (x\cdot y + y\cdot z + x\cdot z) = 1/x + 1/y + \frac1z
|
-29,472 |
\frac{136}{-10 + 7*\left(-1\right)} = 136/(-17) = -8
|
-3,657 |
\dfrac{k^4}{k^3} = kk k k/(kk k) = k
|
17,369 |
\tfrac{1}{\frac{1}{3^4}} = \frac{1}{1/81}
|
7,163 |
\frac{\mathrm{d}}{\mathrm{d}x} \tan{x} = \dfrac{1}{\cos^2{x}} = 1 + \tan^2{x}
|
1,767 |
y\cdot A\cdot z = y\cdot z\cdot A
|
27,609 |
\left(z^2 + x^2\right) \cdot (x^2 - z^2) = x^4 - z^4
|
-20,052 |
-5/8 \cdot \dfrac{3 \cdot m + 10}{m \cdot 3 + 10} = \dfrac{1}{80 + 24 \cdot m} \cdot \left(50 \cdot (-1) - m \cdot 15\right)
|
15,199 |
-\dfrac{1}{5*(\frac{4}{5} + (-1))} = -\frac{1}{5*(-1/5)} = 1
|
29,410 |
3 + 1/2 = \frac{1}{2} 7
|
22,347 |
\left(y^{75} + 1 + y^{25} + y^{50}\right)\cdot \left(-y^{25} + 1\right) = -y^{100} + 1
|
-20,931 |
7/7 \frac{(-1) + k}{k + 4 (-1)} = \frac{k*7 + 7 \left(-1\right)}{k*7 + 28 \left(-1\right)}
|
25,065 |
\left(i = a + \sqrt{-2} \cdot b \Rightarrow a^2 + 2 \cdot \sqrt{-2} \cdot a \cdot b - b^2 \cdot 2 = -1\right) \Rightarrow \sqrt{-2} = \frac{1}{a \cdot b \cdot 2} \cdot (2 \cdot b^2 + (-1) - a^2)
|
31,375 |
0 = \frac{4}{d^3} + \frac2d - \frac{1}{d^2}c = \frac{1}{d^3}(4 + 2d^2 - cd)
|
-20,510 |
\dfrac{2k + 8(-1)}{k*2 + 14} = \frac{4(-1) + k}{k + 7}*\frac{1}{2}2
|
8,961 |
BA + DB - DA = BA + BD - DA
|
-3,932 |
\dfrac{\dfrac{1}{11}}{r}\cdot 3 = 3/(11\cdot r)
|
28,720 |
\sqrt{2} \approx 1 + 1/2 - \frac18 + \dfrac{1}{16} = \frac{1}{16}23 \approx 1.4375
|
6,470 |
\tan(z*3) = \tan\left(z*3\right)
|
45,386 |
5 = \frac{1}{1}5
|
31,490 |
\frac{\mathrm{d}}{\mathrm{d}z} (-\csc\left(z\right)) = \csc\left(z\right) \cdot \cot(z)
|
1,959 |
|x| = |y| = |(x \cdot x + y^2)^{1/2}|
|
-19,070 |
1/20 = \dfrac{X_x}{25 \cdot \pi} \cdot 25 \cdot \pi = X_x
|
3,840 |
1 - a\times y^2 = (\frac{1}{a} - y^2)/\left(1/a\right)
|
7,558 |
(x + 100\cdot a + 10\cdot g)^2 = x^2 + a^2\cdot 10000 + 2000\cdot a\cdot g + 200\cdot a\cdot x + g^2\cdot 100 + g\cdot x\cdot 20
|
7,805 |
\frac14 \cdot 3 \cdot \int \frac{1}{Y^{\frac13}}\,\mathrm{d}Y = \frac34 \cdot \int Y^{-1/3}\,\mathrm{d}Y
|
39,279 |
|z|^n = \|z^n\| = \|z^n + 1 + \left(-1\right)\| \leq \|z^n + 1\| + 1
|
-12,014 |
7/8 = \frac{q}{6\cdot \pi}\cdot 6\cdot \pi = q
|
43,802 |
3^2 \cdot 3 = 27 \gt 20
|
25 |
(n + (-1))! \times (n + (-1) + 1) = (n + (-1))! \times n = n!
|
31,597 |
(f + a) * (f + a) = f^2 + a^2 + 2*a*f
|
11,455 |
37 = -2^2*3 + 7^2
|
14,693 |
f^{n + m} = f^n*f^m
|
11,787 |
(n + 1)^3/3 \geq 3(n + 1) + 3(-1) = \dfrac13(n + 1)^3 \geq 3n
|
-2,323 |
3/17 = -2/17 + \frac{1}{17}\cdot 5
|
-20,672 |
\dfrac{1}{-2} \cdot (-3 \cdot t + 8 \cdot (-1)) \cdot 3/3 = (24 \cdot (-1) - t \cdot 9)/(-6)
|
-20,963 |
\left(18\cdot (-1) - 54\cdot x\right)/\left(-90\right) = \dfrac{9}{9}\cdot \frac{1}{-10}\cdot (-x\cdot 6 + 2\cdot \left(-1\right))
|
9,806 |
\dfrac{25*24*99}{100*99} = 6
|
-2,037 |
-\pi \frac{5}{12} = \frac{\pi}{4} - 2/3 \pi
|
25,847 |
\frac{625}{3} = 5^2 \cdot 5/3 \cdot 5
|
25,953 |
k^2 + p^2 = k*k + p*p
|
21,475 |
2 = \left(1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60\right)/120
|
15,519 |
2^{15} + (-1) = (2^3)^5 + (-1) = (2 \cdot 2^2 + \left(-1\right))\cdot ((2^3)^4 + (2^3)^2 + 2^3 + 1)
|
5,962 |
\left(4 + 3\right)\cdot 5 = 35
|
-10,551 |
-\frac{1}{4*r + 4*(-1)}*5*\frac{1}{5}*5 = -\tfrac{25}{20*\left(-1\right) + 20*r}
|
3,336 |
\operatorname{P}(t) = t^4 - 2 \cdot t^3 - 6 \cdot t^2 - 2 \cdot t + 1 = \left(t + 1\right) \cdot (t^3 - 3 \cdot t^2 - 3 \cdot t + 1) = (t + 1)^2 \cdot (t^2 - 4 \cdot t + 1)
|
2,373 |
1 + \frac{1}{2^2} - \frac{1}{4^2} - \frac{1}{5^2} = \dfrac{459}{400}
|
-22,042 |
\dfrac{16}{10} = \dfrac{8}{5}
|
-2,979 |
\sqrt{7} = (2 \cdot (-1) + 4 + \left(-1\right)) \cdot \sqrt{7}
|
24,875 |
3 = y rightarrow y \in \left]3,4\right]
|
45,604 |
5 \cdot 13 = 65
|
-22,329 |
(z + 6) (z + 1) = z \cdot z + 7z + 6
|
-7,120 |
2/11 = \frac{1}{10}\cdot 4\cdot \frac{1}{11}\cdot 5
|
29,316 |
l \cdot t - m \cdot x = t \cdot l - m \cdot t + m \cdot t - m \cdot x
|
36,276 |
l = [1,2] = 1/l
|
36,422 |
\frac{11}{14} 630 = 495
|
5,417 |
625 \sqrt{5} = 5^4 \cdot 5^{\frac12} = 5^{9/2}
|
-9,011 |
78.7\% = \dfrac{78.7}{100}
|
15,145 |
(2 \cdot \left(-1\right) + k)! = (3 \cdot (-1) + k) \cdot (k + 4 \cdot (-1))! \cdot (2 \cdot (-1) + k)
|
16,974 |
\sqrt{1 + \tfrac14 + 1} = 3/2
|
4,257 |
c \cdot c\cdot f = c^2\cdot f
|
-30,976 |
120 = 60*2
|
12,188 |
l\cdot 2 - 2i \geq 1 + l \implies i \leq \frac{1}{2}(l + (-1))
|
10,776 |
(5 - 2\cdot 6^{1/2})\cdot \left(5 + 6^{1/2}\cdot 2\right) = 1
|
22,463 |
\frac{1}{100}\times (100 + 50) = 150/100 = 1.5
|
1,547 |
\dfrac{1}{2^{\dfrac{1}{2}}} \cdot z^{1 / 2} = \dfrac{z}{(z \cdot 2)^{\frac{1}{2}}}
|
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