id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
---|---|
-1,602 | \frac34 \cdot \pi = -13/12 \cdot \pi + \pi \cdot 11/6 |
23,794 | (-1)^{2 + m} = (-1)^m |
18,390 | h_1^2 = c \cdot h_2 + h_2^2 rightarrow -h_2^2 + h_1^2 = c \cdot h_2 |
17,004 | \sqrt{\frac{7950}{30} - 16^2} = 3 |
14,981 | 8 - \dfrac89 = \dfrac{64}{9} |
54,578 | |x| = |x - y + y| \leq |x - y| + |y| |
54,998 | 2 + 6 + 120 = 128 = 2^7 |
14,671 | \left(2\cdot t^2\right)^2 = 2^2\cdot (t^2)^2 = 4\cdot t^4 |
-20,908 | \frac{8\cdot s + 3}{3 + s\cdot 8}\cdot \left(-\frac51\right) = \frac{-40\cdot s + 15\cdot (-1)}{s\cdot 8 + 3} |
-23,169 | -1 = -\dfrac13*3 |
-20,448 | \frac{4}{4} \cdot \frac{3 \cdot \left(-1\right) + y}{y + 3} = \frac{1}{y \cdot 4 + 12} \cdot (y \cdot 4 + 12 \cdot (-1)) |
27,338 | \{E_1, E_2\} \implies E_2 = E_1 \cup E_2 \setminus E_1 |
23,622 | (A*X)^2 = A*X*A*X = X*A*A*X = X*A^2*X |
20,960 | 2 + 7578/24541 = \frac{56660}{24541} |
-29,592 | \frac{\text{d}}{\text{d}y} (2 \cdot y^2) = 2 \cdot \frac{\text{d}}{\text{d}y} y^2 = 2 \cdot 2 \cdot y^1 = 4 \cdot y |
9,830 | (P(Y) + P(B))^2 = P\left(Y\right)^2 + 2 P(Y) P\left(B\right) + P\left(B\right) P\left(B\right) = 1 \implies P(B)^2 + P(Y)^2 = 0.9 |
15,431 | a^2 + b^2 = (b + a)^2 - 2ba |
30,208 | \left(p^2 \cdot p\right)^3 = (p^5)^5 = \left(p^7\right)^7 = p |
27,350 | a f = a f |
31,426 | 5 + 2 \cdot 6^{1/2} = (2^{1/2} + 3^{1/2}) \cdot (2^{1/2} + 3^{1/2}) |
24,279 | (c^3)^\beta + \beta = (c^3)^\beta + \beta^3 - \beta^3 + \beta = (c^\beta + \beta) \cdot ((c^2)^\beta - \beta \cdot c^\beta + \beta^2) - \beta^3 + \beta |
14,518 | (u - v \sqrt{V}) (u + v \sqrt{V}) = -v^2 V + u^2 |
11,784 | 1 - \dfrac12 - 1/5 = \frac{3}{10} |
4,023 | a^n = a^{n + 0} = a^n a^0 |
13,806 | ( r, z) \cdot ( t', \beta) := t' \cdot (-r) + \beta \cdot z |
30,259 | B = \sqrt{A*B} \Rightarrow B = 0\text{ or }B = A |
21,777 | x*(n + 1)*4 = x*(4 + 4n) |
15,723 | {l + k + \left(-1\right) \choose k + (-1)} = {(-1) + l + k \choose l} |
26,517 | (\left(-1\right) (-1) + 7)/2 = 4 |
1,398 | \frac{d_2^2}{a\cdot d_2 + a\cdot d_1}\cdot d_1^2 = \frac{a^2\cdot d_1 \cdot d_1}{a\cdot d_2 + d_2\cdot d_1} = \tfrac{a^2\cdot d_2^2}{d_2\cdot d_1 + a\cdot d_1} |
5,826 | (a + x)/2 = a + \dfrac{1}{2} \left(x - a\right) = x - (x - a)/2 |
35,942 | A \cdot A + A = 3\cdot A - I = A \cdot A \cdot A + I |
42,547 | 1/(\frac{1}{a}) = 1/(\dfrac1a) = 1/a\cdot a/(1/a) = \frac{1}{1/a\cdot a}\cdot a = a = a |
2,952 | \frac{2 x y}{x + y} = \frac{2}{\frac1x + \dfrac{1}{y}} \leq (x + y)/2 |
3,471 | h_1/(g_1) + \frac{h_2}{g_2} = \frac{1}{g_2 g_1} \left(g_2 h_1 + h_2 g_1\right) |
394 | 0*\ldots*2*π = 0 |
2,655 | a^4 + h^4 = \left(a + h\right)^4 - 4 \cdot h \cdot a^3 - 6 \cdot h^2 \cdot a^2 - h^3 \cdot a \cdot 4 |
-9,473 | 2\cdot t + t\cdot 2\cdot 2\cdot t = 4\cdot t^2 + 2\cdot t |
40,310 | x^q = x^{q + (-1)}*x = 2^{(q + (-1))/2}*x |
9,765 | g^Q g^m = g^{Q + m} |
-5,940 | \frac{1}{2\cdot d + 4}\cdot 5 = \frac{1}{2\cdot \left(2 + d\right)}\cdot 5 |
16,245 | d + b = 4\Longrightarrow d - b = 4 |
11,020 | 0 = x^2 + z^2 - x\cdot 2 - 2 b z + 8 (-1) \implies (\sqrt{b b + 9})^2 = (z - b)^2 + (x + (-1)) (x + (-1)) |
3,711 | z + 3\cdot \left(-1\right) = \frac{1}{2}\cdot (z\cdot 2 + 6\cdot (-1)) |
4,522 | \frac{9}{29} \cdot \tfrac{1}{30} \cdot 30 = \frac{1}{29} \cdot 9 |
27,337 | (p^2 - p)\cdot (\left(-1\right) + p^2) = (p + 1)\cdot ((-1) + p)^2\cdot p |
-19,438 | 8/3\cdot \frac29 = \frac{8\cdot 2}{3\cdot 9} = 16/27 |
10,102 | \sin(\frac{\pi}{2} - t) = \cos{t} |
36,002 | e^{D + B} = e^D \cdot e^B = e^B \cdot e^D |
7,255 | 1 + z^4 + z^2 = (z \cdot z + z + 1) \cdot (z^2 - z + 1) |
30,606 | z^2 + z + 8 = z^2 - 9 \cdot z + 8 = (z + (-1)) \cdot (z + 8 \cdot (-1)) = (z + 9) \cdot \left(z + 2\right) |
-11,494 | 16 - 24 \cdot i = -24 \cdot i - 4 + 20 |
23,282 | \tfrac{1}{H_1 \cdot H_2} \cdot \left(C \cdot H_1 + A \cdot H_2\right) = \frac{1}{H_2} \cdot C + A/(H_1) |
8,319 | x^2\cdot 2 = (x\cdot \sqrt{2})^2 |
28,426 | ((-5)^2)^{\tfrac{1}{2}} = |-5| = 5 |
-26,464 | \phi \cdot \phi + 4^2 - \phi\cdot 4\cdot 2 = (4 - \phi)^2 |
12,962 | 135^2 = 3^2\cdot 45^2 = 9\cdot 2025 < 9\cdot 2040 |
22,446 | c^2 \cdot d^2 = \left(d \cdot c\right) \cdot \left(d \cdot c\right) |
-3,858 | \frac{x^5}{x^5}\cdot 63/54 = \frac{x^5\cdot 63}{54\cdot x^5}\cdot 1 |
20,358 | \tfrac{1}{b \cdot b} \cdot \tfrac{1}{b \cdot b} + (b^2)^2 = b^4 + \dfrac{1}{b^4} |
6,546 | -397\cdot 1027776565^2 + 20478302982^2 = -1 |
27,172 | \left(\sin(b + a) + \sin(a - b)\right)/2 = \sin(a)\cdot \cos(b) |
10,088 | a^3 - c^3 = (c^2 + a \times a + a\times c)\times (a - c) |
34,256 | 1/3 = \dfrac{3}{9} |
9,639 | (a*x)^2 = a^2*x^2 |
19,414 | (g + f)^2 - fg \cdot 2 = f^2 + g^2 |
15,401 | -h^3 + z^3 = (z - h) (h^2 + z^2 + hz) |
10,694 | z^2 = z^2 + (-1) + 1 = \left(z + 1\right)*\left(z + (-1)\right) + 1 |
-26,624 | s^2 \cdot 81 - 144 \cdot s \cdot t + t \cdot t \cdot 64 = \left(9 \cdot s - 8 \cdot t\right) \cdot \left(9 \cdot s - 8 \cdot t\right) |
18,575 | \frac19 + 1/8 = \dfrac{17}{72} |
22,857 | \left(m + 1\right)^2 - 31\times m + 257 = m^2 + 2\times m + 1 - 31\times m + 257 = m^2 - 29\times m + 258 |
21,360 | (z_2 \cdot z_2 + z_1^2)^2 = (z_2^2 - z_1^2)^2 + (2z_2 z_1) \cdot (2z_2 z_1) = 5^2 + 12 \cdot 12 = 13^2\Longrightarrow z_2^2 + z_1^2 = 13 |
443 | a_{n + 1} = \left(1 + a_n\right)*(n + 1) \Rightarrow 1 + n = \frac{a_{1 + n}}{a_n + 1} |
35,814 | \theta\times n\times \dfrac{1}{(n + \left(-1\right))!}\times (n + 2\times (-1))! = \frac{n}{n + (-1)}\times \theta |
-9,973 | 0.01 (-4) = -\frac{4}{100} = -0.04 |
28,832 | 3/8 + \dfrac28 = \frac{5}{8} |
-19,795 | 125\% = \dfrac{125}{100} = 1.25 |
32,357 | 10^l = (2 \cdot 5)^l |
-2,766 | \sqrt{7} + \sqrt{9}\cdot \sqrt{7} = \sqrt{7} + \sqrt{7}\cdot 3 |
24,682 | r*(r + 1) = r^2 + r |
12,212 | \frac{x}{x} \cdot s = s \cdot x/x |
-6,388 | \frac{20}{(6 + p)*(p + 4*(-1))*4} = \dfrac{5}{(4*(-1) + p)*(p + 6)}*\dfrac{4}{4} |
46,291 | 105 = 53 + 52 |
31,915 | 1 + x^2 - 2\times x = (x + (-1))^2 rightarrow x^2 - 2\times x = \left(x + (-1)\right)^2 + (-1) |
-20,512 | \dfrac{1}{10 p + 60 (-1)}(10 + 10 p) = \dfrac{10}{10} \frac{1 + p}{6(-1) + p} |
25,348 | \int_{-2}^{-1} (5(-1) + y^2 c)\,\mathrm{d}y = 0 rightarrow \int\limits_1^2 (cy^2 + 5(-1))\,\mathrm{d}y = 0 |
19,983 | 2/(1/2\cdot x) = 4/x |
3,332 | \frac{x^2}{x + 9 \cdot (-1)} = x + \dfrac{81}{x + 9 \cdot (-1)} + 9 |
46,839 | (\sqrt{z + 7} - \sqrt{14}) \cdot (\sqrt{z + 7} + \sqrt{14}) = z + 7 + 14 \cdot (-1) = z + 7 \cdot (-1) |
31,552 | x^3+1=x^3-1=(x-1)(x^2+x+1)=(x+1)(x^2+x+1) |
18,305 | (2^{20})^{10} = 2^{20}\cdot 2^{20}\cdot \ldots\cdot 2^{20} |
423 | (-1) + \frac{1}{Y - b} \cdot \left(t - b\right) = \frac{t - Y}{-b + Y} |
13,531 | \dfrac{13!}{7!} - \frac{12!}{7!} = 1140480 |
6,129 | 1/3 + 1/(4\cdot 3) = -1/(3\cdot 4) + \frac{1}{2} |
32,298 | -(x - e) = e - x |
37,088 | \frac{1}{2} \cdot (1 + 5^{1/2}) = \frac{1}{2} \cdot 5^{1/2} + \dfrac12 |
12,886 | \dfrac{1}{9}\cdot 2 + \dfrac{5}{18} + 5/18 = 7/9 |
8,820 | g \times e \times f = g \times e \times f |
-5,688 | \frac{1}{(\left(-1\right) + \xi) (\xi + 2)}4 = \dfrac{4}{\xi^2 + \xi + 2\left(-1\right)} |
10,285 | D_1^2 \times D_2^3 = D_1 \times D_1 \times D_2^3 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.