id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-4,408 | \dfrac{1}{x^2 - 6*x + 8}*(4*x + 18*(-1)) = -\frac{1}{x + 4*(-1)} + \frac{5}{2*(-1) + x} |
24,330 | a\cdot t = a\cdot t |
-26,593 | x^2 - 9^2 = \left(9 + x\right) (x + 9(-1)) |
-12,909 | 25 + 10*(-1) = 15 |
22,352 | b \cdot b + a^2 + 2\cdot a\cdot b = (a + b)^2 |
1,297 | y^2 + y \times 6 + 9 = (y + 3)^2 |
21,529 | m = g_m \cdot x_m = g_m \cdot x_m \implies \frac{1}{x_m} \cdot x_m = g_m/(g_m) |
3,633 | \cos(\arcsin{z}) = \sqrt{1 - \sin^2(\arcsin{z})} = \sqrt{1 - z \times z} |
13,695 | \frac{m^2}{1 + m^3} = \frac{1}{m + \frac{1}{m^2}} |
12,020 | 4^{p\cdot 2}\cdot 4^2 + 4 = 4^{2\cdot p + 2} + 4 |
-15,892 | -10 \cdot \frac{7}{10} + 3/10 \cdot 5 = -\frac{55}{10} |
-2,732 | \sqrt{25}\cdot \sqrt{7} + \sqrt{4}\cdot \sqrt{7} = 5\cdot \sqrt{7} + \sqrt{7}\cdot 2 |
29,273 | H^2 F^2 = (FH)^2 |
-2,460 | \sqrt{7} \cdot \left(4 + 2 \cdot (-1)\right) = 2 \cdot \sqrt{7} |
12,969 | y^2 + y\cdot 3 + 2 = (y + 1)\cdot (y + 2) |
-26,544 | -9*z^2 + 100 = -\left(3*z\right)^2 + 10^2 |
28,560 | -1 = \omega \cdot \omega^r = \omega^{r+1} \quad(**) |
13,222 | y^6 = (1 - y)*\left(2 - 3*y\right) = 3*y^2 - 5*y + 2 = 3*\left(1 - y\right) - 5*y + 2 = 5 - 8*y |
14,943 | 2((q + (-1))/2 + 1) = q + 1 |
9,636 | -1/(\sqrt{2}) = \sin(\dfrac{1}{4}((-1) \pi)) |
9,646 | \dfrac12\pi - \frac{1}{4}\pi = \dfrac{1}{4}\pi |
2,180 | S + 15 = x - S\Longrightarrow x = S*2 + 15 |
-19,100 | \frac{5}{8} = \frac{G_q}{16 \pi}*16 \pi = G_q |
-2,092 | \pi \dfrac{23}{12} + \pi/2 = \frac{29}{12} \pi |
5,427 | (k + 1)! + (k + 1)!*(k + 1) = \left(k + 1\right)!*(1 + k + 1) = (k + 2)! |
-29,066 | 192.4 = 8\cdot 24.05 |
28,491 | \dfrac{1}{z\cdot (z + (-1))} = \frac{1}{z + (-1)} - \frac1z |
-12,015 | 4/5 = \frac{1}{8 \cdot \pi} \cdot s \cdot 8 \cdot \pi = s |
2,701 | \left(x \cdot 3 = \frac13 \cdot \left(x + y + z\right) \Rightarrow z + y = 8 \cdot x\right) \Rightarrow \tfrac12 \cdot \left(y + z\right) = x \cdot 4 |
-17,541 | 42 = 12 + 30 |
-11,887 | 8.395/1000 = 8.395 \cdot 0.001 |
37,847 | e z = e z |
24,822 | 616 = 2 ^ 3 \cdot 7 \cdot 11 |
8,532 | 1 + 3*m^2 - m*3 = m^3 - (m + (-1))^3 |
7,330 | \cos{\frac14 \cdot \pi} - \frac{\pi}{4 \cdot \sin{\dfrac14 \cdot \pi}} = \frac{\sqrt{2}}{2 \cdot (1 - \pi/4)} > 0 |
44,935 | 3^4*3^4 = 3^4 * 3^4 |
-19,471 | \dfrac{\frac17}{4 \cdot 1/9} \cdot 2 = 9/4 \cdot 2/7 |
-20,196 | \dfrac{1}{4 + z \cdot 4} \cdot \left(7 + 7 \cdot z\right) = \frac{1}{4} \cdot 7 \cdot \frac{1}{1 + z} \cdot (z + 1) |
-9,331 | 63 \cdot d + 63 = 3 \cdot 3 \cdot 7 + d \cdot 3 \cdot 3 \cdot 7 |
15,911 | \left(b + a\right)^2 = b^2 + a^2 + a\times b\times 2 |
-29,347 | -b^2 + c^2 = (c + b)\cdot (-b + c) |
32,433 | 1 + 3\cdot 8 = 5^2 |
13,862 | (1 + x)^{n + 1} = (1 + x) \cdot (1 + x)^n \geq (1 + x) \cdot (1 + n \cdot x) = 1 + (n + 1) \cdot x + n \cdot x^2 \geq 1 + (n + 1) \cdot x |
31,497 | \left\{0, 2, \ldots, 1\right\} = \mathbb{N} |
1,405 | \mathbb{E}[D \cdot v] = v \cdot D |
-20,038 | \dfrac{1}{72 + p\cdot 56}\cdot \left(-35\cdot p + 45\cdot \left(-1\right)\right) = -\dfrac{1}{8}\cdot 5\cdot \frac{9 + 7\cdot p}{7\cdot p + 9} |
-5,734 | \frac{3}{p \cdot 5 + 10 \cdot (-1)} = \tfrac{3}{5 \cdot (p + 2 \cdot \left(-1\right))} |
2,640 | \mathbb{E}(C_2 + C_1) = \mathbb{E}(C_1) + \mathbb{E}(C_2) |
29,727 | \frac{\mathrm{d}}{\mathrm{d}y} \sec(y) = \tan\left(y\right) \cdot \sec(y) |
-2,905 | \sqrt{48} + \sqrt{3} = \sqrt{3} + \sqrt{16\cdot 3} |
-1,245 | -10/12 = ((-10)\cdot \frac{1}{2})/(12\cdot 1/2) = -\frac{5}{6} |
15,541 | 2\cdot x + 5\cdot z + 1 = 2\cdot x + 5\cdot z + 5 + 4\cdot (-1) = 2\cdot (x + 2\cdot \left(-1\right)) + 5\cdot (z + 1) |
15,982 | 1 + 6^5 = \left(1 + 6\right)\cdot (6^3\cdot 5 + 6\cdot 5 + 1) |
16,323 | (H + A)\cdot (-H + A) = A \cdot A - H^2 |
47,327 | x \times \tan(\tfrac{\pi}{2 + x}) = \frac{1}{\tan(\pi/2 - \frac{\pi}{2 + x})} \times x = \frac{1}{\tan(\frac{\pi \times x}{2 \times x + 4})} \times x = \frac{\pi \times x \times \frac{1}{2 \times x + 4}}{\tan(\frac{\pi \times x}{2 \times x + 4} \times 1)} \times (2 \times x + 4)/\pi |
2,165 | \frac{1}{TS} = \frac{1}{ST} |
-29,520 | 4!/2! = \frac1224 = 12 |
-1,704 | -4/3 \pi + \frac{11}{6} \pi = \pi/2 |
33,761 | \mathbb{E}[V] + \mathbb{E}[B] = \mathbb{E}[V + B] |
7,670 | 1 + l + 2(-1) - i = l + 2(-1) - (-1) + i |
13,089 | 77/216 = \dfrac{1}{216}\cdot 5 + 2/27 + \dfrac{4}{27} + \frac{1}{9} |
7,228 | 8 + 8 \left(-1\right) + (1 + 8)*10 = 90 |
16,212 | 840 \cdot 883 + 882 = 840 \cdot 883 + 991 + 109 \cdot \left(-1\right) |
21,684 | (x + 1) \cdot (x + 1) - x^2 = 2 \cdot x + 1 = x + 1 + x |
-2,875 | \sqrt{3} + 4 \cdot \sqrt{3} = \sqrt{3} + \sqrt{16} \cdot \sqrt{3} |
-18,386 | \frac{(r + 2(-1)) (1 + r)}{r*(1 + r)} = \frac{r^2 - r + 2(-1)}{r^2 + r} |
-27,645 | 1 + 3 + 5\cdot \left(-1\right) = 4 + 5\cdot (-1) = -1 |
28,915 | x^3 + x^6 + x^5 + x^4 = (x + x^3) (x^2 + x^3) |
-20,637 | \frac{1}{-z*21 + 14}(z*18 + 12 \left(-1\right)) = \tfrac{1}{-z*3 + 2}(2 - 3z) \left(-6/7\right) |
-24,508 | 8 + 3^2 = 8 + 3*3 = 8 + 9 = 17 |
25,212 | 2 \cos{z} \sin{z} = \sin{z \cdot 2} |
-19,731 | \frac{1}{9}\cdot 49 = 7\cdot 7/(9) |
2,285 | \{g \frac{N}{g}, N\} \Rightarrow N = N/g g |
23,416 | 0 \cdot ( 1, 0) + 0 \cdot \left( 0, 1\right) = 0 \cdot \left( 1, 2\right) + 0 \cdot ( 3, 5) |
-24,755 | \frac14(-6^{1 / 2} + 2^{\frac{1}{2}}) = \cos\left(\frac{7\pi}{12}\right) |
-27,499 | 30 \cdot x^3 = 2 \cdot 3 \cdot 5 \cdot x \cdot x \cdot x |
-4,948 | \dfrac{10}{10^6} = \frac{10.0}{10^6} |
-20,895 | 4/9\cdot (-4/(-4)) = -16/\left(-36\right) |
32,666 | y^2 + 2 + \tfrac{1}{y^2} = (y + 1/y)^2 |
14,353 | z + (-1) + y + (-1) + y \cdot z - z - y + 1 = (-1) + y \cdot z + z - z + y - y + 1 + (-1) |
17,962 | \left(d \cdot b + c \cdot a\right)^2 + (a \cdot d - c \cdot b) \cdot (a \cdot d - c \cdot b) = (d^2 + c^2) \cdot (a^2 + b^2) |
-6,478 | \frac{2}{3\cdot (-1) + 3\cdot p} = \frac{2}{((-1) + p)\cdot 3} |
11,544 | l*w^2 = w*l*w |
-22,172 | \frac17\times 9 = 45/35 |
10,954 | -t \cdot t + t^4 = 2 + (1 + t^2)\cdot (t \cdot t + 2\cdot \left(-1\right)) |
30,044 | 1/2 + \frac{1}{3} + 1/6 = 1 |
-1,987 | \pi \cdot \frac{5}{12} + \pi \cdot \frac{7}{12} = \pi |
27,245 | 1000 = 18 \cdot 18 + 26^2 |
17,768 | \frac{1}{2} 3 d + d = d*5/2 |
20,432 | \sin{2\times t} = 2\times \sin{t}\times \cos{t} |
-9,314 | 45 - h\cdot 15 = -h\cdot 3\cdot 5 + 3\cdot 3\cdot 5 |
-20,998 | -3/(-3) \left(-\dfrac176\right) = \dfrac{18}{-21} |
31,914 | 21 x^{5/2} = x^2*21 \sqrt{x} |
-6,589 | \frac{1}{(m + 2\left(-1\right)) (7 + m)} = \frac{1}{m^2 + 5m + 14 (-1)} |
-7,385 | \frac{2}{12} \cdot 6/11 = 1/11 |
42,135 | e^{\log_e(s_1)} = s_1 |
15,348 | E\left(X - 2 \cdot (X + (-1)) \cdot (X + (-1))\right) = E\left(X - 2 \cdot (X \cdot X - 2 \cdot X + 1)\right) = E\left(-2 \cdot X^2 + 5 \cdot X + 2 \cdot (-1)\right) = -2 \cdot E\left(X \cdot X\right) + 5 \cdot E\left(X\right) + 2 \cdot \left(-1\right) |
-3 | -15 + 4 (-1) = -19 |
18,432 | 1/(a_2\cdot a_1) = \frac{1}{a_2\cdot a_1} |
14,989 | (2\cdot b \cdot b + a^2 - b\cdot a\cdot 2)\cdot (b^2\cdot 2 + a^2 + 2\cdot a\cdot b) = 4\cdot b^4 + a^4 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.