id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
6,401 |
(q - p)^2 = (p - q) * (p - q)
|
27,273 |
\frac12\cdot (1 + 5^{1/2}) = 5^{1/2}/2 + 1/2
|
12,339 |
n = \left\{1, ..., n\right\}
|
19,120 |
m*2 + 3(-1) = m + \left(-1\right) + m + 2(-1)
|
26,694 |
\frac{1}{-10}\cdot 48 = -24/5
|
8,589 |
n^5 + (-1) = (n + (-1)) \cdot \left(n^4 + n^3 + n^2 + n + 1\right)
|
17,594 |
\frac{1}{12} = 7/z rightarrow 84 = z
|
2,765 |
kv + wk = k \cdot (w + v)
|
40,916 |
121^2 - 17*54 54 = 14641 + 49572 (-1) = -34931
|
-20,889 |
\tfrac{1}{-2 \cdot k + 20} \cdot (-k \cdot 10 + 4) = \frac{1}{-k + 10} \cdot (-5 \cdot k + 2) \cdot \frac12 \cdot 2
|
109 |
\frac12\left(-\cos(2x) + 1\right) = \sin^2(x)
|
4,902 |
\varepsilon/F = X/H \implies \frac{1}{H}\cdot X = \varepsilon/F = \frac{X - \varepsilon}{H - F}
|
-15,058 |
\frac{1}{\frac{1}{y^4 x^6} y^5} = \frac{(\frac1y)^5}{\frac{1}{y^4 x^6}}
|
-22,719 |
\frac{5 \cdot 8}{7 \cdot 8} = 40/56
|
16,260 |
\left(z - y_2\right)\cdot (z - y_1) = y_2\cdot y_1 + z \cdot z - (y_1 + y_2)\cdot z
|
-10,643 |
3/(t*12) = \frac{1}{4*t}*1
|
-23,921 |
\dfrac{15}{1 + 4} = \frac15\cdot 15 = \frac{15}{5} = 3
|
711 |
\sqrt{\frac{1 + t}{1 - t}} = \frac{1}{\sqrt{1 - t^2}} \cdot (1 + t) = (1 + t) \cdot \mathbb{E}[t]
|
-2,585 |
((-1) + 4 + 5)\cdot \sqrt{13} = 8\cdot \sqrt{13}
|
14,759 |
(-y + x)\cdot \left(y + x\right) = x \cdot x - y^2
|
9,718 |
0 = u \cdot (-\lambda \cdot I + B \cdot A)\Longrightarrow u \cdot B \cdot (B \cdot A - \lambda \cdot I) = 0
|
-10,488 |
\dfrac{1}{x}(4x + 1)*3/3 = (x*12 + 3)/(3x)
|
10,034 |
(b_z + \left(-1\right))*(b_z + 1) = b_z^2 + \left(-1\right)
|
-536 |
\pi\cdot 3/2 = \pi\cdot \frac{1}{2}\cdot 35 - \pi\cdot 16
|
24,092 |
N^{x_0} = Nk \Rightarrow N^{x_0 + (-1)} = k
|
5,836 |
\frac{4}{51}\cdot \frac{48}{52} = \dfrac{16}{221}
|
-22,178 |
80\cdot (-1) + z^2 - 2\cdot z = (10\cdot \left(-1\right) + z)\cdot (8 + z)
|
13,823 |
b^4 - a^4 = (b^2 - a \cdot a)\cdot (b^2 + a^2) = (b - a)\cdot (b + a)\cdot (b \cdot b + a^2)
|
-797 |
491/10000 = 1/10000 + 0 + \frac{0}{10} + \frac{4}{100} + 9/1000
|
21,645 |
\cos\left(x + z\right) = -\sin(x)\cdot \sin\left(z\right) + \cos\left(z\right)\cdot \cos\left(x\right)
|
21,777 |
y\cdot 4\cdot \left(1 + l\right) = (l\cdot 4 + 4)\cdot y
|
-7,164 |
\frac{1}{24}\cdot 7 = \dfrac19\cdot 6\cdot \dfrac{7}{10}\cdot 5/8
|
14,817 |
\left(\cos{z} = i\cdot \sin{z} \Rightarrow 0 = -i\cdot \sin{z} + \cos{z}\right) \Rightarrow e^{-z\cdot i} = 0
|
-7,293 |
3/9\cdot \frac{2}{10} = \frac{1}{15}
|
7,939 |
20 \pi/8 = \frac{\pi\cdot 5}{2}
|
-8,978 |
104.7\% = \frac{1}{100} \cdot 104.7
|
-20,878 |
\dfrac{-10y - 3}{y - 1} \times \dfrac{7}{7} = \dfrac{-70y - 21}{7y - 7}
|
-20,466 |
-9/4*\frac{1}{t + 10}*\left(t + 10\right) = \dfrac{1}{t*4 + 40}*(-t*9 + 90*(-1))
|
11,995 |
4 + x^2 = 4 \cdot \left(1 + x^2/4\right)
|
240 |
\frac14 = -\frac23 + 11/12
|
-11,637 |
16*i - 16 + 3 = i*16 - 13
|
1,061 |
0 = b + 2 \cdot (-1) \Rightarrow 2 = b
|
5,848 |
1/(g\cdot f) = 1/\left(f\cdot g\right)
|
-5,827 |
\dfrac{5}{4 \cdot (p + 5)} = \frac{1}{4 \cdot p + 20} \cdot 5
|
18,149 |
1 = \frac{z}{z} rightarrow \frac1z = 1/z
|
18,959 |
\cos^2(x) - \sin^2\left(x\right) = 2 \cdot \cos^2(x) + \left(-1\right) = 1 - 2 \cdot \sin^2(x)
|
38,378 |
0^{2^{k + 1 + 1}} = 0^{2^k*2*2}
|
-17,470 |
19 = 32\cdot \left(-1\right) + 51
|
18,586 |
\frac{15}{45} + \frac{24}{45}*\frac{1}{2} = \frac{1}{3} + \frac{4}{15} = \frac15 3
|
35,108 |
(n + 1)/n! = 1/n! + \frac{1}{\left(n + (-1)\right)!}
|
-7,426 |
\frac{9}{91} = \dfrac{3}{13}*6/14
|
17,790 |
\frac{x^2 + y^2}{x \cdot y} = \frac{1}{x \cdot y} \cdot (\left(x + y\right)^2 - 2 \cdot x \cdot y) = \frac{(x + y)^2}{x \cdot y} + 2 \cdot (-1)
|
-4,455 |
-\frac{1}{(-1) + x} - \frac{1}{4 \cdot (-1) + x} \cdot 4 = \dfrac{1}{x \cdot x - 5 \cdot x + 4} \cdot \left(-5 \cdot x + 8\right)
|
16,393 |
\frac{y}{y + h} = 1 - \frac{h}{y + h}
|
-25,312 |
\dfrac{d}{dx}\left(\dfrac1x\cos(x)\right)=\dfrac{-\cos(x)-x\sin(x)}{x^2}
|
10,305 |
\left(b + a = b*a \Rightarrow a*b - a - b = 0\right) \Rightarrow 1 = (a + (-1))*((-1) + b)
|
21,168 |
3/8 = 3/4\cdot \dfrac14\cdot 2
|
15,310 |
A_1 B_0 + B_1 A_0 = -A_1 B_1 + (A_0 + A_1) (B_1 + B_0) - A_0 B_0
|
-9,177 |
x \cdot 54 + 18 \cdot (-1) = x \cdot 2 \cdot 3 \cdot 3 \cdot 3 - 2 \cdot 3 \cdot 3
|
6,448 |
3^x \cdot 2 + 3 \cdot 3^x \cdot c_{k+1} = c_{k+1} \cdot 3^{1 + x} + 2 \cdot 3^x
|
23,421 |
\frac12 = \frac{1}{4}*2
|
37,475 |
3^{11} = 3^2 \cdot 3\cdot 3^8 = 10\cdot (-1) = 7
|
28,603 |
(x + q)*(-q + x) = -q^2 + x^2
|
3,172 |
x*261 + 1073 = 29*9 x + 1073
|
33,915 |
\frac{1 + n}{\sqrt{n + 1}} = \sqrt{n + 1}
|
14,894 |
\epsilon + \epsilon\cdot (1 + \epsilon) = \epsilon^2 + \epsilon\cdot 2
|
-30,292 |
\frac{1}{2}\cdot (-1 + 7) = \tfrac62 = 3
|
7,587 |
A \setminus G = A - A \cap G = A \cup G - G
|
-486 |
\left(e^{\pi i*11/6}\right)^{19} = e^{\frac16 11 i \pi*19}
|
40,799 |
\binom{9}{6} + 7\cdot (-1) = 77
|
7,387 |
\tan^{-1}{w} = G + x \implies \tan(G + x) = w
|
43,488 |
V\cdot 2 = V + V
|
-2,260 |
\dfrac{1}{12} = 2/12 - \dfrac{1}{12}
|
13,377 |
\dfrac{1}{(f^2 + y^2)^2}\cdot y\cdot y = \dfrac{1}{(y^2 + f^2)^2}\cdot y^2
|
27,863 |
7 \cdot i - 1 = \frac14 \cdot (-7 + i \cdot 24 + 3 + i \cdot 4)
|
12,409 |
{52 \choose 13} = \frac{1}{13}52 {51 \choose 12} = 4{51 \choose 12}
|
36,265 |
35 - x^3 = t^3 \implies x = (-t \cdot t \cdot t + 35)^{1/3}
|
-24,111 |
2 + 2\cdot \frac{24}{6} = 2 + 2\cdot 4 = 2 + 2\cdot 4 = 2 + 8 = 10
|
30,036 |
\frac{1}{b^2} \cdot a \cdot a = p \Rightarrow a^2 = b \cdot b \cdot p
|
16,246 |
y + 8*(-1) = -4*(x + 1) = -4*x + 4*(-1) \Rightarrow 0 = y + x*4 + 4*(-1)
|
35,776 |
\frac13\cdot 192 = 64
|
30,964 |
\cos{b} \cos{f} + \sin{f} \sin{b} = \cos\left(f - b\right)
|
-20,462 |
\frac{d + 9}{2 - d\cdot 2}\cdot \dfrac{7}{7} = \frac{63 + d\cdot 7}{14 - 14 d}
|
32,500 |
\int \tan{x}\,dx = \int \frac{\sin{x}}{\cos{x}}\,dx
|
14,644 |
\tfrac{m^2}{m + 1} > \frac{m^2 + \left(-1\right)}{m + 1} = \frac{1}{m + 1}\cdot (m + 1)\cdot (m + (-1)) = m + (-1)
|
20,841 |
x - \dfrac{1}{2} + 5/2 = 0 \Rightarrow x = -2
|
27,985 |
|x + (-1)| = |1 - x| \geq |1| - |x| = 1 - |x| \Rightarrow \dfrac{3}{4} \leq |x|
|
14,629 |
x/y = \frac{2*x}{2*y}
|
24,974 |
((-1) + B) \cdot (B + 1) = (-1) + B^2
|
35,151 |
A^n\cdot A = A^{1 + n}
|
29,789 |
0.99 = -1/100 + 1
|
23,019 |
(-1) + \tfrac{1}{g}\cdot (d + f + g) = (f + d)/g
|
-30,903 |
50 = 10 + 20\cdot 2
|
2,100 |
1 + z + z \cdot z + ... = \dfrac{1}{1 - z}
|
-20,976 |
-3/2\cdot (x\cdot (-4))/((-4)\cdot x) = x\cdot 12/\left(x\cdot (-8)\right)
|
-12,901 |
\dfrac{15}{25} = \frac35
|
27,611 |
(y^2 + (-1)) \cdot (y^2 + 1) = (-1) + y^4
|
5,056 |
g^2 + 2 \cdot g \cdot a + a^2 = (g + a)^2
|
18,154 |
(N + 2 \cdot (-1)) \cdot (N + 2 \cdot (-1)) + (\dfrac{1}{2} \cdot (3 + N)) \cdot (\dfrac{1}{2} \cdot (3 + N)) = N \cdot N + ((5 \cdot (-1) + N)/2)^2
|
15,548 |
43361 = (13*10 + 1) \left(3*11*10 + 1\right) = 131*331
|
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