id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
38,355 |
5 \cdot 7^2 \cdot 17 = 4165
|
38,390 |
e^0 = \left(e^0\right)^{1 / 2}
|
1,682 |
\frac{1}{1 - x + 2 + 2\cdot (-1)}\cdot (x + 2\cdot (-1)) = \dfrac{x + 2\cdot (-1)}{-1 - x + 2\cdot (-1)} = -\frac{1}{1 + x + 2\cdot (-1)}\cdot (x + 2\cdot (-1))
|
7,739 |
5 = z\cdot 6 + \nu \Rightarrow \nu = 5 - 6\cdot z
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-9,461 |
-x*35 + 20 (-1) = -2*2*5 - x*5*7
|
27,068 |
(-1) + A^{12} = ((-1) + A^6) \cdot (A^6 + 1)
|
4,165 |
\left(1 + 2\right)^\varphi = 3^\varphi
|
-20,705 |
\frac{1}{x\cdot 2 + 6\cdot (-1)}\cdot ((-1)\cdot 4\cdot x) = \frac{1}{3\cdot (-1) + x}\cdot ((-2)\cdot x)\cdot 2/2
|
35,241 |
\overline{w \times x} = \overline{w} \times \overline{x}
|
-4,367 |
\frac{q^3 \cdot 56}{q^2 \cdot 42} = \frac{1}{42}56 \dfrac{1}{q^2}q \cdot q \cdot q
|
3,632 |
m + \left(-1\right) = \frac{1}{m} \cdot (m + (-1)) \cdot m
|
23,650 |
48/52 \cdot 4/51 = \dfrac{192}{2652} = \dfrac{16}{221}
|
19,566 |
-3\cdot x\cdot d\cdot (-2/3) = 2\cdot d\cdot x
|
35,189 |
1/(ab) = 1/\left(ab\right)
|
4,467 |
\frac{z}{n} = w\Longrightarrow n\cdot w = z
|
10,311 |
|\left(-1\right) \cdot \left(-1\right) + x| = |1 + x|
|
14,834 |
{n \choose k} = \frac{1}{\left(n - k\right)! \cdot k!} \cdot n!
|
-30,430 |
0 = p^2 * p + p = (p^2 + 1) p
|
9,063 |
9 = 3^{1 / 2} \times 3 \times 3^{1 / 2}
|
-10,446 |
10 = -32 - 80r + 20 = -80r - 12
|
31,806 |
(\varphi + 1)! = \varphi! \cdot \left(1 + \varphi\right)
|
-205 |
\binom{7}{4} = \dfrac{7!}{4! (7 + 4\left(-1\right))!}
|
31,168 |
\sin{π\cdot \frac32} = -1
|
21,418 |
\dfrac 1{\frac 1{3^4}}=1/(1/3^4)=1/3^{-4}=3^4
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27,144 |
\frac{1}{4^2} (2^2 - 1^2) = 3/16
|
11,771 |
\tan{\dfrac{\pi\times 5}{6}} = -1/(\sqrt{3})
|
18,675 |
-f^2 + c^2 = \left(c - f\right)*(c + f)
|
-10,948 |
85 \div 5 = 17
|
1,150 |
\frac{1}{6 + \sqrt{34}} \cdot (6 - \sqrt{34}) = 35 - \sqrt{34} \cdot 6
|
-20,203 |
\frac{1}{60\cdot \left(-1\right) + p\cdot 40}\cdot (-36\cdot p + 54) = -\frac{1}{10}\cdot 9\cdot \frac{1}{4\cdot p + 6\cdot (-1)}\cdot (p\cdot 4 + 6\cdot (-1))
|
-23,000 |
26/39 = \frac{13\cdot 2}{3\cdot 13}
|
-10,527 |
-\dfrac{16}{4z + 20} = -\frac{1}{10 + z*2}8*\frac{1}{2}2
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40,056 |
(1 - 0.6)^3 = 0.4 * 0.4^2 = 0.064
|
-4,157 |
\frac{1}{35} 63 \frac{1}{y^5} y^2 y = \frac{y^3}{35 y^5} 63
|
11,628 |
\frac12\cdot (-\cos(2\cdot x) + 1) = \sin^2(x)
|
19,711 |
\sin^2{x} - 4 \cdot \cos^2{x} = \left(\sin{x} + \cos{x} \cdot 2\right) \cdot \left(\sin{x} - 2 \cdot \cos{x}\right)
|
11,147 |
1 + x * x + x = \frac{1}{4}((x*2 + 1)^2 + 3)
|
15,160 |
19/50 = \frac{1}{50}\cdot 3 + \frac{4}{50} + \frac{4}{50} + \frac{4}{50} + \tfrac{1}{50}\cdot 4
|
13,190 |
B \cdot C^2 = 16 + 9 + 6 \cdot (-1) = 19 \Rightarrow B \cdot C = \sqrt{19}
|
-5,779 |
\frac{l \cdot 3}{(l + 6) \cdot (l + 5)} \cdot 1 = \frac{3 \cdot l}{l^2 + 11 \cdot l + 30}
|
37,505 |
2 = 7 + 5\times (-1)
|
34,302 |
17/\left(\sqrt{17}\right) = \sqrt{17}
|
-22,243 |
q^2 + 10q + 21 = (q + 7)(q + 3)
|
33,579 |
3^x + 3^{x + 2} = 3^x + 3^x\cdot 3^2 = 3^x + 9\cdot 3^x = 10\cdot 3^x
|
-19,112 |
\dfrac{3}{4} = A_s/\left(64\cdot \pi\right)\cdot 64\cdot \pi = A_s
|
39,471 |
z^3 + (-4 + i) z^2 + (-i*5 + 1) z + 6*(1 + i) = (z * z - z*5 + 6) (1 + z + i)
|
7,767 |
\sin\left(\pi/2\cdot 2\right) = 0
|
33,125 |
(2 + i)*(2 - i) = 2^2 - i * i = 4 - -1 = 5
|
15,333 |
z \cdot q \cdot k = k \cdot z \cdot q
|
20,964 |
16 = -3 \cdot 2^{1 + z} + 2^{z \cdot 2} \implies 2^z = -2
|
-1,588 |
7/4 \pi + \pi\cdot 5/4 = 3\pi
|
5,627 |
-60^2 + 65 * 65 = 25^2
|
-4,808 |
63.0 \cdot 10 \cdot 10^2 = 63 \cdot 10^{5 - 2}
|
432 |
\dfrac{4}{3^5} = \dfrac{1}{3^5}*(3 + 1)
|
1,004 |
\frac{1}{1 - x \cdot x} = \dfrac{1}{2 \cdot (-x + 1)} + \dfrac{1}{(1 + x) \cdot 2}
|
37,643 |
(2^{290})^{14}\cdot 2^{182} = 2^{4242}
|
15,890 |
(x\cdot z\cdot \frac{1}{x\cdot z})^2\cdot x\cdot z\cdot 1/(x\cdot z)\cdot x\cdot 1/(x\cdot z)\cdot z = (x\cdot z\cdot 1/(x\cdot z))^4
|
7,085 |
\left(z + x + y\right) (-zx + x^2 + y^2 + z * z - yx - yz) = x^3 + y * y * y + z^3 - 3yz x
|
29,120 |
4/81 = \frac{16}{4}\times 1/81
|
23,913 |
\left(L - J = M - x \Rightarrow -x + J = -M + L\right) \Rightarrow -J + x = M - L
|
-15,884 |
5/10 \cdot 10 - 8 \cdot \frac{1}{10} \cdot 5 = \dfrac{10}{10}
|
22,545 |
3 \cdot 8/9 \cdot \frac{1}{9} \cdot 8/9 = \dfrac{64}{243} = 0.2634
|
2,348 |
(\dfrac{1}{X} + X)^2 + 2*(-1) = \dfrac{1}{X^2} + X^2
|
20,308 |
1/3 = 5/(5*3)
|
-27,710 |
\frac{\mathrm{d}}{\mathrm{d}z} (-12\times \cos(z)) = 12\times \sin(z)
|
-5,501 |
\dfrac{2}{(q + 7)\cdot 2} = \dfrac{1}{2\cdot q + 14}\cdot 2
|
32,658 |
3\cdot 2 = 3\cdot 4 = 0
|
24,655 |
8 + x = 7 + 4 \Rightarrow 3 = x
|
13,093 |
d/dy (\frac{3}{y}) = 3 \cdot (-\dfrac{1}{y^2}) = -\frac{3}{y^2} = -\frac{3}{y \cdot y}
|
37,476 |
\lim_{n\to\infty}\frac{n}{n+1} = \lim_{n\to\infty}\frac{1}{\quad\frac{n+1}{n}\quad} = \lim_{n\to\infty}\frac{1}{\frac{n}{n}+\frac{1}{n}} = \lim_{n\to\infty}\frac{1}{1+\frac{1}{n}}
|
6,176 |
\cosh(\overline{z}) = \overline{\cosh\left(z\right)}
|
-22,769 |
\frac{10}{10 \cdot 3} \cdot 7 = \frac{70}{30}
|
5,486 |
\cos(x) = \sin(\dfrac{1}{2}\cdot \pi - x)
|
28,041 |
\operatorname{atan}(-1/\left(\sqrt{3}\right)) = -\frac16 \cdot \pi
|
30,368 |
-1 = (q + (-1))\cdot (1 + q + q^2 + \ldots) = q + (-1) + (q + (-1))\cdot q + (q + (-1))\cdot q^2 + \ldots
|
12,734 |
\left(-1\right) + y \cdot y = \left(1 + y\right) \cdot (y + (-1))
|
8,908 |
1/(1/a) = \dfrac{1}{\frac{1}{a}} = \frac1a \cdot a/(1/a)
|
-18,406 |
\dfrac{z}{(z + 8*\left(-1\right))*\left(8*(-1) + z\right)}*\left(z + 8*(-1)\right) = \tfrac{-z*8 + z^2}{64 + z^2 - z*16}
|
3,278 |
1/2 \cdot \frac18/2 = 1/32
|
23,203 |
E[C^2 - 2CE[C] + E[C]^2] = E[C^2] - 2E[C]^2 + E[C] \cdot E[C] = E[C \cdot C] - E[C] \cdot E[C]
|
10,253 |
\dfrac{p_M - \frac{1}{p_M}}{p_M + (-1)} = 1 + \frac{1 - 1/(p_M)}{p_M + (-1)} \geq 1 + \frac{1}{2\cdot (p_M + (-1))}
|
2,708 |
1 + 2 + 2^2 + ... + 2^{j + (-1)} = \frac{1 - 2^j}{1 + 2\cdot (-1)} = 2^j + (-1)
|
16,243 |
z \cdot \frac{-z^k + 1}{-z + 1} = z + z^2 + ... \cdot z^k
|
-12,112 |
\frac{14}{45} = s/(12 \pi)*12 \pi = s
|
316 |
0 = s \cdot s\cdot a\cdot 2 - 3\cdot s\cdot a^2 \Rightarrow a = \tfrac{s}{3}\cdot 2
|
28,373 |
158 = 4^0*2 + 4^3*2 + 4^2 + 3*4^1
|
4,621 |
(2 + \sqrt{4})\cdot (2 - \sqrt{4}) = 0
|
-1,064 |
8/1 \cdot 3/4 = 1/4 \cdot 3/(1/8)
|
-10,536 |
-\dfrac{1}{r*16}*14 = -7/(8*r)*\frac{2}{2}
|
12,881 |
\sin(π\cdot k + W) = \sin\left(π\cdot k\right)\cdot \cos\left(W\right) + \cos(π\cdot k)\cdot \sin(W) = (-1)^k\cdot \sin(W)
|
21,443 |
m = \left\{m, \dots, 2, 1\right\}
|
40,314 |
-\dfrac{1}{7}10 = -10/7
|
-22,226 |
d^2 - 4\cdot d + 3 = (d + (-1))\cdot (3\cdot (-1) + d)
|
-20,745 |
(5 - 10 m)/(-8) \cdot 9/9 = \frac{1}{-72}(45 - 90 m)
|
7,206 |
\sin\left(w + z\right) = \sin(z + w)
|
-22,242 |
(r + 9 \cdot \left(-1\right)) \cdot \left(r + 3\right) = r^2 - r \cdot 6 + 27 \cdot (-1)
|
18,339 |
\dfrac{1}{Jg} = \tfrac{1}{Jg}
|
-30,245 |
y^2 - y\cdot 2 + 1 = ((-1) + y) (y + (-1))
|
18,303 |
4! - 3! \cdot 5 + 5 \cdot 2! - 5 \cdot 1! + 1 + (-1) = -1
|
-23,248 |
\frac{6}{25} = \frac{1}{5}2*\frac35
|
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