id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
1,813 |
0\cdot V + V\cdot 0 = V\cdot 0
|
-8,154 |
28 = \frac72 8
|
-2,331 |
\frac{6}{20} = \dfrac{3}{10}
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-222 |
5!/(3!\times 2!) = \binom{5}{3}
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-22,299 |
(n + 10 \left(-1\right)) (n + 7(-1)) = 70 + n^2 - 17 n
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31,203 |
\left(5 - 0.5\right) \times (12 - 0.5) \times ((-1) \times 0.5 + 10) = 491.625
|
4,714 |
\left( f, f*2, ...\right) = f
|
-23,119 |
63/16\cdot \tfrac34 = 189/64
|
-11,966 |
\frac{1}{20} = x/(20\cdot π)\cdot 20\cdot π = x
|
3,562 |
z \cdot z \cdot z + 8 \cdot (-1) = (4 + z^2 + 2 \cdot z) \cdot (z + 2 \cdot \left(-1\right))
|
27,031 |
c^{1 + l} \coloneqq c \cdot c^l
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-4,408 |
\frac{x\cdot 4 + 18\cdot (-1)}{x^2 - x\cdot 6 + 8} = \frac{1}{x + 2\cdot \left(-1\right)}\cdot 5 - \dfrac{1}{4\cdot (-1) + x}
|
27,479 |
\frac{1/6*5}{6} = 5/36
|
-1,633 |
\tfrac{13}{12}\cdot π - 0\cdot π = \dfrac{13}{12}\cdot π
|
-20,715 |
3/3*(2 + 9*n)/(8*n) = \frac{1}{24*n}*\left(6 + n*27\right)
|
4,104 |
-1 = 4 \times \left(-1\right) + n\Longrightarrow n = 3
|
24,990 |
(t - 1/2)^{r/2}*2^{\dfrac12*r} = (t*2 + (-1))^{r/2}
|
16,409 |
\beta = 7 + \frac{1}{2 + \dfrac{1}{\beta}} = \frac{15 \cdot \beta + 7}{2 \cdot \beta + 1}
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26,426 |
1/2 + (-1) = -\frac{1}{2}
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22,485 |
100 = (1 + 2 \cdot (-1) + 3 + 4 \cdot \left(-1\right) + 5) \cdot 6 + 7 \cdot (-1) + 89
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-22,964 |
\dfrac{1}{120} \cdot 36 = \dfrac{12 \cdot 3}{10 \cdot 12}
|
18,085 |
(a + b)^3 = a^3 + 3\cdot a \cdot a\cdot b + 3\cdot a\cdot b^2 + b^3
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-19,000 |
\frac78 = A_q/(64 \pi)*64 \pi = A_q
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5,498 |
-\frac13*s + s = s*2/3
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30,573 |
-G \leq -E \Rightarrow E \leq G
|
19,502 |
\tan x={\sin x}/{\cos x}
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26,470 |
x = \sqrt{-24\cdot i + 7} rightarrow x^2 = 7 - i\cdot 24
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-22,300 |
q^2 - 15\cdot q + 50 = (5\cdot \left(-1\right) + q)\cdot (q + 10\cdot (-1))
|
18,792 |
E\left(QY\right) = E\left(Q\right) E\left(Y\right)
|
-9,491 |
-2\cdot 2\cdot 2\cdot 2\cdot y + 2\cdot 2\cdot 11 = -y\cdot 16 + 44
|
77 |
a^4 + 4 g^4 = (g^2*2 + a^2 - g a*2) (2 g^2 + a^2 + g a*2)
|
19,287 |
\frac{1}{d_1} d_1 d_1 d_2 = d_1 d_2
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-20,298 |
\frac{3}{9\cdot (-1) - k\cdot 10}\cdot 8/8 = \dfrac{1}{72\cdot (-1) - 80\cdot k}\cdot 24
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35,084 |
2\sin(\alpha) \cos(\alpha) = \sin(\alpha*2)
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10,863 |
8 \cdot \frac{\mathrm{d}}{\mathrm{d}x} \arctan(x) = \frac{8}{x^2 + 1}
|
37,784 |
2 \cdot m + (-1) + 2 = 2 \cdot m + 1 = 2 \cdot (m + 1) + (-1)
|
5,965 |
\sum_{n=1}^\infty (-3)^n\cdot n\cdot c = \sum_{n=1}^\infty n\cdot (2\cdot \left(-1\right) - 1)^n\cdot c
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32,650 |
1 - 2*\sin^2{x} = \cos{x*2}
|
3,190 |
3^{2 \cdot 2^2} + (-1) = \left(3^2 + 1\right)\cdot (3^4 + 1)\cdot (3^2 + \left(-1\right))
|
43,232 |
85079 = -2 \cdot 3 + 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17
|
-26,599 |
640 - 10*x * x = 10*\left(64 - x^2\right) = 10*(8 + x)*(8 - x)
|
-104 |
-28 = 5\cdot (-1) - 23
|
-16,459 |
8 \sqrt{75} = 8 \sqrt{25\cdot 3}
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-4,773 |
-\frac{1}{y + 2\cdot (-1)}\cdot 3 + \tfrac{5}{1 + y} = \frac{1}{2\cdot (-1) + y^2 - y}\cdot \left(13\cdot (-1) + y\cdot 2\right)
|
-10,584 |
\frac{4}{x\cdot 12}\cdot 5/5 = \frac{1}{60\cdot x}\cdot 20
|
17,468 |
a^g \cdot a^x = a^{x + g}
|
-16,439 |
3\sqrt{9\cdot 11} = \sqrt{99}\cdot 3
|
9,429 |
\left(z - \dfrac1z\right)^2 + 2 + 1 = z^2 + 1 + \frac{1}{z^2}
|
8,044 |
1/(\rho\cdot z) = 1/(z\cdot \rho)
|
2,019 |
z^{p^k} = e \Rightarrow (1/z)^{p^k} = \frac{1}{z^{p^k}} = 1/e = e
|
3,582 |
L\cdot 2 = L + L
|
32,847 |
(1 + x^2 - x*\sqrt{2})*(x^2 + \sqrt{2}*x + 1) = 1 + x^4
|
6,315 |
2^{k + 1} = (1 + 1)^{k + 1} = {k + 1 \choose 0} + {k + 1 \choose 1} + \dotsm + {k + 1 \choose k + 1}
|
14,878 |
\left((n,1) = \left(m, 1\right) \Rightarrow n = m\right) \Rightarrow m = n
|
9,265 |
(-20^{1/2} + 6)^{1/2} = (-5^{1/2}*2 + 6)^{1/2}
|
26,407 |
2*\cos^2{y} + \left(-1\right) = \cos{2*y}
|
32,260 |
(x \times z)^2 = x^2 \times z^2
|
1,241 |
1 = |v| \Rightarrow 2 \geq |i - v|
|
7,058 |
6x + 6 = 6(x + 1)
|
2,318 |
1 + \left((-1) + x\right)\cdot (y + 1) = y\cdot x + x - y
|
-29,013 |
0 = (0.01 - 0.01)/2
|
1,328 |
y^{1 + 2 + 2}*2*2 = y^2*2 y*2y^2
|
27,551 |
\overline{r_1}[x_1]+...+\overline{r_n}[x_n]=[r_1x_1+...+r_nx_n]\in M/NM
|
-1,375 |
1/5\cdot 7/\left(1/8 \left(-1\right)\right) = -\dfrac81\cdot 7/5
|
10,518 |
\dfrac{1}{-\frac1x + x/x} \cdot (6 \cdot x/x - \frac{1}{x} \cdot 9) = 3 \cdot \tfrac{1}{x + (-1)} \cdot \left(2 \cdot x + 3 \cdot (-1)\right)
|
36,024 |
\tfrac{1}{\nu} = \frac{1}{\nu}
|
6,329 |
1 - x^6 = (x^4 + 1 + x^2)*(1 - x * x)
|
160 |
2450448 = \frac{18!}{10! \cdot 5! \cdot 3!}
|
11,463 |
-\frac{1}{d + k + 1} + \frac{1}{d + k} = \dfrac{1}{(k + d) \cdot (d + k + 1)}
|
22,003 |
\frac{2}{31} = \frac{30}{31}/30 + \tfrac{1}{31}
|
38,416 |
1 + 11 \cdot 9 = 10 \cdot 10
|
-10,279 |
-\dfrac{1}{12 (-1) + y\cdot 3}5\cdot 5/5 = -\frac{1}{y\cdot 15 + 60 (-1)}25
|
6,500 |
1/2 \cdot 2 + \dfrac{1}{2} = 3/2 \neq 5/3
|
-5,039 |
0.73 \cdot 10^5 = 0.73 \cdot 10^{0 \cdot \left(-1\right) + 5}
|
31,873 |
\cos{y} + \sin{y} = X \cdot \sin(y + y_0) = X \cdot \sin{y} \cdot \cos{y_0} + X \cdot \cos{y} \cdot \sin{y_0}
|
1,484 |
k^3 - (k + 2 \cdot (-1))^3 = k^3 - k^3 - 6 \cdot k \cdot k + 12 \cdot k + 8 \cdot (-1) = 6 \cdot k^2 - 12 \cdot k + 8
|
26,214 |
x \cdot \sum_{n=0}^m x^n = \sum_{n=1}^{m + 1} x^n = \sum_{n=0}^m x^n + x^{m + 1} + (-1)
|
-10,437 |
5/5*2/\left(16 t\right) = 10/(t*80)
|
8,605 |
\dfrac{1}{f_1 \cdot 1/\left(f_2\right)} = f_2/(f_1)
|
-20,972 |
(-63\cdot q + 14)/70 = \frac{7}{7}\cdot \frac{1}{10}\cdot (-9\cdot q + 2)
|
5,178 |
(\frac13 2) (\frac13 2)^2 = \frac{8}{27}
|
9,792 |
A \cdot n = 1 + 7/10 \cdot \left(A \cdot n - A\right) + 3/10 \cdot (A \cdot n + A) = A \cdot n + 1 - \frac25 \cdot A
|
27,768 |
4 = 2/x \Rightarrow x = \frac{1}{2}
|
35,422 |
-\pi + 2 \cdot \pi/3 = (\left(-1\right) \cdot \pi)/3
|
14,052 |
\frac{k}{2} + 1 = \dfrac{k}{2} + \frac22 = \frac12 \cdot (k + 2)
|
558 |
\left(U \cdot U \cdot U + 1 = 0 \implies (-1) + U^3 = -2\right) \implies -2 = ((-1) + U) \cdot (1 + U^2 + U)
|
-2,603 |
6*\sqrt{7} = \sqrt{7}*(3*(-1) + 5 + 4)
|
-22,349 |
8\cdot \left(-1\right) + l^2 + l\cdot 2 = (4 + l)\cdot (l + 2\cdot \left(-1\right))
|
18,562 |
f^5 = b^4 \Rightarrow (\frac{b}{f})^4 = f
|
34,314 |
-\tfrac{1}{2} + \sqrt{2} = \sqrt{2} - 1/2
|
-20,387 |
\frac{30\cdot x + 15}{70\cdot x + 35} = \frac{3}{7}\cdot \dfrac{10\cdot x + 5}{x\cdot 10 + 5}
|
18,585 |
\cos{1/z} z = z - 1/(z*2!) + \frac{1}{(z^{34})!} - \dotsm
|
21,460 |
z^4 + 1 = z^4 - 2 z z + 1 - -2 z^2 = \left(z^2 + \left(-1\right)\right)^2 - z^2 = (z^2 + (-1) + z) (z^2 + (-1) - z)
|
-18,332 |
\frac{x^2 + x\cdot 10}{x x + 13 x + 30} = \dfrac{(10 + x) x}{(x + 3) (10 + x)}
|
33,026 |
1 = \frac{1}{(-1)*0.5 + 1}*0.5
|
25,706 |
2\cdot x + (-1) = 2\cdot (-\dfrac{1}{2} + x)
|
19,112 |
\frac{\frac{1}{6!}\cdot 10!}{10^4} = 63/125
|
23,453 |
i^4 = i^{2 + 2} = i^2 i^2 = \left(-1\right) (-1) = 1
|
47,086 |
\tanh{i\times z} = \dfrac{\sinh{i\times z}}{\cosh{i\times z}} = \frac{\frac{1}{2}\times (e^{i\times z} - e^{-i\times z})}{\frac12\times \left(e^{i\times z} + e^{-i\times z}\right)} = i\times \sin{z}/\cos{z} = i\times \tan{z}
|
-20,565 |
\frac{1}{-a\cdot 15 + 30}\cdot (20\cdot a + 45) = \frac55\cdot \dfrac{9 + 4\cdot a}{-3\cdot a + 6}
|
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