id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
5,937 |
\left|{X^{\frac{1}{2}}\times h}\right| = \left|{h\times X^{\frac12}}\right|
|
-20,149 |
\frac{1}{5 \cdot q + 40} \cdot (q \cdot 30 + 40) = \frac{5}{5} \cdot \dfrac{6 \cdot q + 8}{q + 8}
|
9,173 |
a^D a^z = a^{z + D}
|
9,141 |
(-1) + (1 + y) \cdot (1 + y) = y^2 + 2\cdot y
|
-21,895 |
-4/12 + 2/6 = -4/(12) + 2\cdot 2/(6\cdot 2) = -\dfrac{1}{12}4 + 4/12 = -(4 + 4)/12 = 0/12
|
-15,323 |
\frac{t^{15}}{\frac{1}{n^{10}} \frac{1}{t^2}} = \frac{(t^3)^5}{\frac{1}{n^{10} t t}}
|
31,835 |
\delta_1^{n + 2} = \delta_1^n*(\delta_1 + 1) = \delta_1^{n + 1} + \delta_1^n
|
-4,365 |
\frac{1}{t^2}7 = \frac{7}{t^2}
|
21,588 |
(z + 1)^4 (z + 1) = (z^4 + 1) (z + 1) = z^5 + z^4 + z + 1
|
12,872 |
(-r + 1)*(r + 1) = 1 - r * r
|
-18,974 |
1/3 = \frac{\varphi_t}{9 \cdot \pi} \cdot 9 \cdot \pi = \varphi_t
|
30,320 |
\frac{\partial}{\partial z} z^k = k \cdot z^{k + \left(-1\right)}
|
-10,704 |
-\frac{1}{2 + p} \times \dfrac44 = -\frac{4}{8 + 4 \times p}
|
28,283 |
\frac16 \cdot (6 - i) = -i/6 + 1
|
6,956 |
x \cdot (x^2)^{1006} = x^{2013}
|
22,915 |
\cos(2\cdot x) = \cos^2\left(x\right) - \sin^2(x) = \cos^2(x) - 1 - \cos^2(x) = 2\cdot \cos^2(x) + \left(-1\right)
|
-7,059 |
5/10*\frac{1}{11}*2 = 1/11
|
20,781 |
\frac{1}{1 + x^2}x^2 = x\frac{x}{1 + x^2}
|
16,840 |
(-p^2 + p^3)/2 = (p + (-1))/2*p^2
|
17,597 |
a\cdot b = 168 \Rightarrow 168/b = a
|
-30,554 |
108/36 = \dfrac{1}{12} \cdot 36 = 12/4 = 3
|
10,169 |
4^{-\frac{2}{3}} = 2^{2/3}/4
|
23,700 |
a^{90} = a^{64} \cdot a^8 \cdot a^2 \cdot a^{16}
|
-10,768 |
\frac{10}{12 + 3 \cdot s} \cdot \frac55 = \frac{50}{15 \cdot s + 60}
|
4,896 |
-1/8 + t^2/4 = \dfrac{t^2}{4} - 2/16
|
32,851 |
l*h = l*h
|
-10,588 |
-\frac{1}{b^3\cdot 20}\cdot (b\cdot 2 + 3)\cdot 15/15 = -\tfrac{1}{300\cdot b^3}\cdot \left(45 + 30\cdot b\right)
|
-26,452 |
\left(z*7\right)^2 = 49*z * z
|
-2,760 |
9^{1 / 2}\cdot 3^{1 / 2} + 3^{\dfrac{1}{2}}\cdot 16^{\frac{1}{2}} = 3^{1 / 2}\cdot 3 + 4\cdot 3^{\frac{1}{2}}
|
26,121 |
\frac{1}{\tan{2 \times x}} \times (\sec{2 \times x} + (-1)) = \frac{1}{\sin{2 \times x}} \times (1 - \cos{2 \times x}) = \tan{x}
|
23,091 |
(1 + n^3 - n) (n^2 + n + 1) = (n^2 + n + 1) (n^3 - n^2 + n^2 - n + 1)
|
-18,265 |
\dfrac{1}{-8\cdot p + p^2}\cdot (16 + p^2 - p\cdot 10) = \frac{1}{(8\cdot (-1) + p)\cdot p}\cdot (p + 8\cdot (-1))\cdot (p + 2\cdot (-1))
|
5,982 |
\cos(2\cdot y) = \cos^2(y) - \sin^2(y) = 1 - 2\cdot \sin^2\left(y\right) = 2\cdot \cos^2\left(y\right) + (-1)
|
27,464 |
2*a*b = b*(a + a)
|
-2,665 |
\sqrt{3}\cdot \left(2 + 5\right) = 7\sqrt{3}
|
25,787 |
(a^2 + a \cdot x + x \cdot x) \cdot (a - x) = a^3 - x^3
|
-20,869 |
\frac{1}{\left(-1\right)\cdot 60\cdot y}\cdot (10\cdot y + 100\cdot (-1)) = \dfrac{10}{10}\cdot \frac{1}{y\cdot (-6)}\cdot \left(y + 10\cdot (-1)\right)
|
33,466 |
\frac{1}{(k + (-1))!} + \frac{1}{(k + 2\cdot (-1))!} = \tfrac{k^2}{k!}
|
-10,659 |
-\frac{1}{12 \times r^3} \times \left(24 \times (-1) + r \times 16\right) = -\frac{1}{r^3 \times 3} \times \left(4 \times r + 6 \times \left(-1\right)\right) \times 4/4
|
-5,848 |
\frac{-x*40 + 2*(x + 2*(-1)) - (10*(-1) + x)*15}{10*\left(10*(-1) + x\right)*(x + 2*\left(-1\right))} = -\frac{x*40}{(2*(-1) + x)*(x + 10*\left(-1\right))*10} + \frac{2*(2*(-1) + x)}{10*(x + 2*(-1))*(x + 10*(-1))} - \frac{15}{(x + 2*(-1))*(10*(-1) + x)*10}*\left(10*(-1) + x\right)
|
9,158 |
4t^2 a^4 - 4t^3 a^2 + 1 = 0\Longrightarrow a^2 = \tfrac{1}{t \cdot 2}\left(t^2 \pm \left((-1) + t^4\right)^{1/2}\right)
|
3,997 |
(B + Y) \left(Y - B\right) = Y Y - B^2
|
23,309 |
10 = \dfrac12\times (7 + 13)
|
21,471 |
x^2 = k*U*3/m \Rightarrow x = \sqrt{3*k*U/m}
|
27,157 |
a \cdot a - 2\cdot a\cdot g + 2\cdot g^2 = g^2 + (a - g)^2
|
7,959 |
-2*g + 1 = 1 - g - g
|
-675 |
(e^{\dfrac{\pi*i}{12}*19})^{15} = e^{15*19*\pi*i/12}
|
-18,074 |
12 = 31 + 19 (-1)
|
5,714 |
z = y\cdot i \Rightarrow y = \tfrac{1}{i}\cdot z
|
14,263 |
6 = 2 \cdot m \cdot n \Rightarrow 3 = m \cdot n
|
-5,615 |
\frac{5}{x\cdot 5 + 40\cdot \left(-1\right)} = \frac{5}{(8\cdot (-1) + x)\cdot 5}
|
-3,491 |
\frac{1}{100}*9 = 0.09
|
28,823 |
r/2 + r = 3\cdot r/2
|
19,000 |
(a + 2\cdot b\cdot \cos(v))^2 = a^2 + 4\cdot a\cdot b\cdot \cos(v) + 4\cdot b^2\cdot \cos^2\left(v\right) = \left(a + b\cdot \cos(v)\right)\cdot 4\cdot b\cdot \cos(v) + a^2
|
-6,701 |
2/10 + \dfrac{8}{100} = \frac{8}{100} + \frac{20}{100}
|
34,844 |
16\cdot x \cdot x - 8\cdot x + 1 = (4\cdot x)^2 - 2\cdot 4\cdot x + 1^2 = (4\cdot x + (-1))^2
|
18,527 |
\frac{1}{y}-\frac{1}{x}=\frac{x-y}{xy}
|
16,284 |
4 = \binom{4}{3} \binom{0 + 4 + (-1)}{0}
|
35,468 |
\frac11f + c/1 = (f + c)/1 = (f + c)/1
|
-21,018 |
\tfrac{1}{2p + 6(-1)}(21 - 7p) = -7/2 \dfrac{p + 3\left(-1\right)}{p + 3(-1)}
|
18,225 |
((-1)^2)^{\frac{1}{2}} = 1
|
-2,971 |
\sqrt{5}\cdot 4 + 3\cdot \sqrt{5} - \sqrt{5}\cdot 5 = \sqrt{16}\cdot \sqrt{5} + \sqrt{9}\cdot \sqrt{5} - \sqrt{25}\cdot \sqrt{5}
|
15,323 |
xe^y \approx dy = e^x - e^y \approx dx\Longrightarrow e^y - e^x \approx dx + xe^y \approx dy = 0
|
-15,788 |
7/10 - 6 \cdot 9/10 = -47/10
|
-20,250 |
-2/1 (-\dfrac{5}{-5}) = \frac{10}{-5}
|
12,741 |
2 - \frac{1}{2^n} = 1 + \frac{1}{2} + 1/4 + \ldots + \frac{1}{2^n}
|
9,633 |
(5^l + (-1))*5 + 4 = (-1) + 5^{l + 1}
|
18,124 |
0 = s^3 + s^2 - 3\cdot s + 1 = (s + (-1))\cdot (s \cdot s + 2\cdot s + (-1))
|
-3,257 |
(3 + 2(-1))\cdot 2^{1/2} = 2^{1/2}
|
-20,861 |
\frac{s \cdot (-45)}{5 \cdot s + 30} = 5/5 \cdot \frac{(-9) \cdot s}{s + 6}
|
3,181 |
n^9 - n^3 = ((-1) + n^3)\cdot (n^3 + 1)\cdot n^3
|
13,732 |
i^3 = 1/5 rightarrow i = \frac{1}{5^{\frac13}}
|
4,650 |
\dfrac12*(3*5 + 5^2) + 4*(-1) = 16
|
-3,903 |
\frac{5}{n n n} = \frac{5}{n^3}
|
14,194 |
(YB)^T = Y^T B^T = B^T Y^T
|
31,916 |
\frac{1}{2 + 4x} - \frac12 = \frac{(-1) x}{1 + 2x}
|
-3,791 |
45/20\times \frac{y^5}{y^3} = \dfrac{45\times y^5}{y^3\times 20}
|
16,850 |
\sin\left(\pi + 3 \cdot q + 4 \cdot (-1)\right) = \sin\left(-q \cdot 3 + 4\right)
|
15,867 |
6^3-5^3=216-125=91
|
7,475 |
b \cdot b + 1 - b = \frac{1}{1 + b}\cdot (1 + b^3)
|
23,907 |
3/2 = \tfrac{3 + 0*(-1)}{2 + 0*(-1)}
|
19,914 |
x!\cdot \frac{m!}{x!\cdot \left(-x + m\right)!} = \frac{m!}{(-x + m)!}
|
11,658 |
2^m \cdot 3 + 2 \cdot (-1) = (3 \cdot 2^{\left(-1\right) + m} + (-1)) \cdot 2
|
-22,355 |
(q + 10*(-1))*(3*(-1) + q) = 30 + q^2 - 13*q
|
10,605 |
{14 \choose 6} = {6\left(-1\right) + 20 \choose 6}
|
-3,987 |
\frac{1}{a \cdot a} \cdot 6 = \frac{1}{a \cdot a} \cdot 6
|
16,292 |
2*\pi*\frac{1}{(-\frac{1}{2}*i + 2*i)*2}*i = \frac{\pi*2}{3}
|
-2,511 |
7^{\dfrac{1}{2}} = 7^{\frac{1}{2}}*(3 + 2\left(-1\right))
|
-22,361 |
q^2 + q*9 + 8 = (q + 1)*(q + 8)
|
50,623 |
200=20\cdot10
|
-12,837 |
11 \cdot \left(-1\right) + 19 = 8
|
7,808 |
0 = 0 \cdot g = g = g
|
10,685 |
1100 = -50*\dfrac12*50 + 3600 - 1/2*50*50
|
22,467 |
3\cdot 7^2 = 147
|
3,924 |
\left(17 \cdot \sqrt{5} + 38\right)^{\frac13} = \sqrt{5} + 2
|
13,343 |
\frac{x}{3} = \dfrac{1}{3}*\left(-2*x + 3*x\right)
|
36,661 |
3^{10^n} = 9^{\frac{1}{2} \cdot 10^n} = (10 + (-1))^{10^n/2}
|
26,980 |
24*6 = \frac{24}{2}*6*2
|
9,226 |
\frac{1}{60}*8 = \dfrac{1}{15}*2
|
-24,757 |
\dfrac{1}{4}\cdot (-\sqrt{6} - \sqrt{2}) = \cos{\pi\cdot 13/12}
|
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