id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-20,704 | \frac{-72\cdot x + 81}{9 - x\cdot 8} = \dfrac{9 - x\cdot 8}{9 - x\cdot 8}\cdot 9/1 |
2,494 | c \cdot (x + \tfrac{f}{c}) = c \cdot x + f |
35,754 | x^2 - 2\times i = x^2 - (1 + i) \times (1 + i) = (x + (-1) - i)\times \left(x + 1 + i\right) |
5,176 | 3 = (1 + 2(1 + 3(1 + 4(1 + 5(1 + (1 + 7)^{1/2}*6)^{1/2} \ldots)^{1/2})^{1/2})^{1/2})^{1/2} |
4,132 | x^3 = -x^2 - 2x = -x + 2 |
17,431 | (1 - 1)\cdot \xi = 0\cdot \xi |
-7,955 | \frac{1}{2 - 4i}(2 - i \cdot 4) \frac{1}{i \cdot 4 + 2}\left(-i \cdot 24 + 8\right) = \frac{1}{2 + 4i}(8 - 24 i) |
39,439 | \dfrac{1}{G^2 * G} = \frac{1}{G^3} |
5,999 | 4\left(-1\right) + y^4 - 3y^2 = (y^2 + 4\left(-1\right)) (1 + y * y) |
10,493 | \dfrac{1}{3 \cdot 9} + \frac{1/3}{36} \cdot 2 = 1/18 |
-14,102 | 3 - 7\cdot 4 + 9/3 = 3 - 7\cdot 4 + 3 = 3 + 28\cdot (-1) + 3 = -25 + 3 = -22 |
27,745 | \left(1 + x\right)^4 = x^4 + x^3*4 + x^2*6 + x*4 + 1 |
25,744 | g \cdot g + h\cdot g + h^2 = \frac12\cdot ((g + h)^2 + g^2 + h^2) |
19,129 | \sin{z}\cdot 3\cdot \sin(\cos{z}) = 3\cdot \sin(\cos{z})\cdot \sin{z} |
-718 | \frac{187}{12}\cdot \pi - 14\cdot \pi = 19/12\cdot \pi |
-2,000 | \frac16 \cdot \pi = \pi \cdot \frac{5}{4} - \tfrac{1}{12} \cdot 13 \cdot \pi |
5,604 | \int \tfrac{x + 1}{2\cdot \sqrt{1 + x}}\,dx = \int \frac{1 + x}{(x + 1)^{1/2}\cdot 2}\,dx |
1,015 | ( -z(t)*x\left(t\right), -z(t)*y\left(t\right), 1 - z^2(t)) = \left( \frac{\mathrm{d}}{\mathrm{d}t} x(t), \frac{\mathrm{d}}{\mathrm{d}t} y\left(t\right), \frac{\mathrm{d}}{\mathrm{d}t} z\left(t\right)\right) |
9,013 | 92852^4 - 3428^4 = 3818 \times (13083^4 - 9957^4) |
2,053 | -\sin^{-1}\left(e\right) = \sin^{-1}(-e) |
21,852 | \alpha |A|^2 + \beta |A^2| = \alpha |A|^2 + \beta |A|^2 = (\alpha + \beta) |A|^2 |
-20,625 | 4/4\cdot \frac{(-7)\cdot p}{7 - p\cdot 5} = \dfrac{1}{-20\cdot p + 28}\cdot (p\cdot (-28)) |
27,222 | 2j = 2^1 + 2^2 + \ldots + 2^{n + 1} = j - 2^0 + 2^{n + 1} |
3,052 | F_t=F_t^+ |
8,208 | \cos\left(\arcsin(t)\right) = \left(\cos^2(\arcsin\left(t\right))\right)^{1/2} = (1 - \sin^2(\arcsin(t)))^{1/2} = (1 - t^2)^{1/2} |
-20,048 | \frac{1}{x\cdot 9 + 9\cdot (-1)}\cdot \left(-x\cdot 5 + 5\right) = -\frac59\cdot \frac{1}{x + (-1)}\cdot (x + (-1)) |
17,903 | 89 + 1\cdot 23 + 4\cdot \left(-1\right) + 5 + 6\cdot (-1) + 7\cdot (-1) = 100 |
42,484 | 4181 = 19\cdot (-1) + 4200 |
13,950 | \left(k + 1\right)^2 - k^2 = 1 + 2 \cdot k |
-7,786 | \dfrac{1}{32} \cdot (16 - 144 \cdot i - 16 \cdot i + 144 \cdot (-1)) = \tfrac{1}{32} \cdot (-128 - 160 \cdot i) = -4 - 5 \cdot i |
21,633 | 1/10 = 2\cdot \dfrac{1}{5}/4 |
-18,947 | \frac{41}{45} = C_t/(25 π)*25 π = C_t |
-11,706 | 16^{-\frac12} = (\frac{1}{16})^{1/2} = 1/4 |
5,042 | \left(z^4 + 1\right) \cdot ((-1) + z^4) = (-1) + z^8 |
1,928 | |x^2 - y^2| = |x + y| |x - y| \leq \left(|x| + |y|\right) |x - y| |
34,707 | \alpha^{1/2} = \left(-(-1) \cdot \alpha\right)^{1/2} = i \cdot (-\alpha)^{1/2} |
-1,492 | \dfrac{45}{12} = \frac{45 \cdot 1/3}{12 \cdot 1/3} = \dfrac{15}{4} |
30,368 | -1 = \left(p + (-1)\right) \cdot (1 + p + p^2 + \dots) = p + (-1) + \left(p + (-1)\right) \cdot p + \left(p + (-1)\right) \cdot p^2 + \dots |
21 | 3 \cdot \left(-1\right) + 37 + 31 \cdot \left(-1\right) + 21 + 19 \cdot \left(-1\right) + 17 \cdot \left(-1\right) + 13 + 11 + 7 \cdot (-1) + 5 = 10 |
9,041 | xh/x = xh/x |
16,415 | -\frac18 \cdot \pi + \pi/2 = \dfrac{\pi}{8} \cdot 3 |
-18,957 | \tfrac{14}{15} = \dfrac{A_t}{25 \times \pi} \times 25 \times \pi = A_t |
3,037 | \frac{\sin{z^5}}{z^5} z^4 = \sin{z^5}/z |
18,321 | \left(a + b\right)^2 = b^2 + a^2 + ba \cdot 2 |
-22,930 | \frac{1}{45} \cdot 40 = \tfrac{40}{5 \cdot 9} \cdot 1 |
19,436 | ( a'^2\cdot 4 + b'^2\cdot 8 + 10, 20) = ( 5 + 2\cdot a'^2 + b' \cdot b'\cdot 4, 10)\cdot 2 |
-3,426 | \sqrt{3} \cdot ((-1) + 4) = \sqrt{3} \cdot 3 |
-5,774 | \frac{1}{4\cdot y + 24}\cdot 5 = \frac{5}{\left(y + 6\right)\cdot 4} |
17,040 | e^{Q*Y/Q} = \frac{e^Y*Q}{Q} |
17,377 | 0=32A+12B+4=4A+3B+2 |
26,089 | z_l*z_\mu = z_\mu*z_l |
-22,264 | t \times t + 14\times t + 48 = (t + 6)\times (8 + t) |
23,529 | 24 x = (2 + (-1))\cdot 2^{l + (-1)} \Rightarrow 2^{l + \left(-1\right) + 3(-1)}/3 = x |
9,297 | f_1 = f_1 = f_1 \cdot (51781 \cdot f_2 + 4655 \cdot e) = 51781 \cdot f_1 \cdot f_2 + 4655 \cdot f_1 \cdot e |
18,412 | -5^{1/2}/2 + \frac{1}{2} = \frac{1}{2}*(-5^{1/2} + 1) |
-8,878 | -2^5 = (-2) \times (-2) \times \left(-2\right) \times (-2) \times (-2) |
24,269 | a \cdot a - b^2 = (a + b) (a - b) |
21,559 | 1 = \frac{1}{13^4}\cdot 13^4 |
-11,855 | 7.427 \cdot 0.1 = 7.427/10 |
29,690 | (\left(-1\right) + 12) \cdot (\left(-1\right) + 12) = 121 |
6,248 | (a - b)*(b^2 + a^2 + b*a) = -b^3 + a^3 |
-16,062 | 8*7*6*5 = \dfrac{8!}{(8 + 4 (-1))!} = 1680 |
29,030 | \csc(x) = \frac{1}{\sin(x)} = \frac{1}{\sqrt{1 - \cos^2(x)}} |
23,685 | (z + i y) (z + i y) (z - i y)^2 = \left((z + i y) (z - i y)\right)^2 = (z^2 + y^2)^2 |
-4,058 | \frac{1}{p^3}\cdot 4 = \dfrac{4}{p^3} |
23,500 | 3^{k + 1} = 3\cdot 3^k > 3\cdot k^2 = k^2 + k^2 + k \cdot k \geq k \cdot k + 2\cdot k + 1 |
45,172 | 21 = 3*10 + (-9) |
6,241 | \dfrac13 = \frac{1}{10 + 5}\cdot 5 = 5/10 = \frac{1}{2} |
-12,251 | 31/36 = \frac{q}{18 \cdot \pi} \cdot 18 \cdot \pi = q |
-11,327 | (y + f)^2 = (y + f)*(y + f) = y * y + 2*f*y + f^2 |
17,393 | 5^2 = x^2 + y^2 \Rightarrow y = \sqrt{25 - x^2} |
6,400 | x \cdot Y + X \cdot x = (X + Y) \cdot x |
40,619 | 294 = \left(6 + 15\right)*14 |
-18,564 | \frac{50}{20} = \frac{1}{2}5 |
21,895 | 2 \cdot b + 1 = 4 \cdot b \implies 1/2 = b |
-27,067 | \sum_{l=1}^\infty \tfrac{\left(0 + 2\right)^l}{(l + 1) (-2)^l} = \sum_{l=1}^\infty 1*\frac{2^l}{(l + 1) \left(-2\right)^l} = \sum_{l=1}^\infty \frac{(-1)^l*2^l}{\left(l + 1\right)*2^l}1 = \sum_{l=1}^\infty \frac{(-1)^l}{l + 1} |
24,927 | 9 + 247^2 \cdot 247 + 273 (-1) = 5y^2 \Rightarrow y^2 = 3013797 |
12,754 | 71.4 = y \cdot 1.1 + y\Longrightarrow y = 34 |
-1,261 | -\frac{2}{9}\cdot 8/9 = \frac{\frac{1}{9}\cdot (-2)}{9\cdot 1/8} |
53,274 | 11\cdot 19 = 209 |
258 | \binom{n + r + \left(-1\right)}{r} = \binom{r + n + (-1)}{r} |
-24,134 | 6\cdot (6 + 8) = 6\cdot 14 = 84 |
-11,501 | -5 + 25 (-1) - i*20 = -30 - 20 i |
-22,762 | \frac{60}{108} = \frac{5\cdot 12}{9\cdot 12} |
35,779 | (k + 1)\cdot 2 = 2k + 2 |
19,981 | \left(-A_t^2 + (X_t + A_t)^2 - X_t^2\right)/2 = A_t X_t |
1,709 | y^2 + y + 1 = y^2 - 2 y + 1 = (y + (-1))^2 = (y + 2)^2 |
-16,407 | 6*\sqrt{9*11} = \sqrt{99}*6 |
-6,392 | \tfrac{1}{(k + 9) \cdot (6 + k)} \cdot k = \frac{1}{54 + k \cdot k + k \cdot 15} \cdot k |
13,883 | -z^6 - z^{180} + z^{90} + z^{48} = -\left(z^6\right)^{30} + (z^6)^{15} + (z^6)^8 - z^6 |
12,987 | x^{nm} \Lambda_n^\sigma \Lambda_m^i = \Lambda_m^i \Lambda_n^\sigma x^{nm} |
29,414 | 5^{c_1} \cdot 5^{c_2} = 5^{c_1 + c_2} |
-30,567 | \frac{1}{t + 3\cdot (-1)}\cdot (t^2 + 5\cdot t + 24\cdot (-1)) = \frac{(t + 8)\cdot \left(t + 3\cdot (-1)\right)}{t + 3\cdot (-1)} = t + 8 |
-3,853 | \frac14*5 = 5/4 |
-18,417 | \frac{(l + 2) (2\left(-1\right) + l)}{(l + 5(-1)) (2(-1) + l)} = \frac{1}{l^2 - 7l + 10}\left(4(-1) + l * l\right) |
32,239 | 502 = \frac{1}{4}*\left(2009 + (-1)\right) |
9,125 | d^2\times y = d^2\times y |
30,720 | {14 \choose 3}*{16 \choose 2} = 43680 |
-26,135 | (-\frac{1}{e^{14}} + e^7) \cdot 7 = 7 \cdot e^7 - \frac{7}{e^{14}} |
738 | (n + (-1))! = ((-1) + n) (n + 2(-1)) \left(n + 3(-1)\right) ...\cdot 2\cdot 3 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.