id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
20,031 |
1 + \left(5 \times p + 1\right) \times 19 = x \times 5 \Rightarrow 19 \times p + 4 = x
|
8,546 |
(n + 1)^2 = n^2 + 2*n + 1 = (n + \left(-1\right))^2 + 2*n + (-1) + 2*n + 1 = (n + (-1))^2 + 4*n
|
9,817 |
190 = (20 + (-1))*20/2
|
26,669 |
|(t + \frac{1}{2}) * (t + \frac{1}{2}) + \dfrac74|/(\sqrt{2}) = \frac{1}{\sqrt{1^2 + 1^2}}*|t * t + 2 + t|
|
17,209 |
0 = \dfrac{0}{1 + 0^2}
|
4,658 |
\int\limits_{-1}^1 \left(a + h\right)^2\,dz = \int (a * a + \int (h^2 + 2\int ah\,dz)\,dz)\,dz = \int (a^2 + \int h^2\,dz)\,dz
|
-10,754 |
10 = -6 + 5*a + 7*(-1) = 5*a + 13*(-1)
|
10,436 |
\dfrac{x}{z} = \frac{x}{z}
|
9,906 |
41625 = \frac{1}{5}125*(1 + 2 + 3 + 4 + 5)*111
|
639 |
z^2 - 10 z + 25 = (z + 5 (-1))^2
|
18,917 |
{8 \choose 5}\cdot 5 = 280
|
46,701 |
72-32=40
|
13,167 |
x = \tfrac{1}{2}(x + y - z + x + z - y) \geq \sqrt{(x + y - z) (z + x - y)}
|
23,937 |
1 - 1/36 - \frac{20}{36} = \frac{1}{36}\cdot 15
|
437 |
\left(b + g\right) \cdot (b + g) = b^2 + g^2 + b \cdot g + b \cdot g
|
-10,694 |
\tfrac{30}{z*15 + 12} = \frac133*\dfrac{10}{z*5 + 4}
|
36,341 |
180 + 30 \cdot (-1) - 48.59 = 101.41
|
22,318 |
4*(-1) + a^3 - a^2*3 + 5*a = (a + (-1))^3 + 2*(a + (-1)) + (-1)
|
24,774 |
29 \cdot 29 + 29 \cdot 37 + 37^2 = 49 \cdot \left(2^2 + 2 \cdot 7 + 7^2\right) = 49 \cdot 67
|
18,806 |
(s*2)^2 = s^2*4
|
-10,780 |
-15 = 35 + 2 \cdot t + 9 = 2 \cdot t + 44
|
4,235 |
\sin(\beta + \alpha) = \sin(\beta) \times \cos(\alpha) + \cos(\beta) \times \sin(\alpha)
|
4,712 |
(z + \frac{z^2}{2!} + \frac{1}{3!} \cdot z \cdot z \cdot z + \ldots)^{-1} = \frac{1}{e^z + \left(-1\right)}
|
25,013 |
\sqrt{a * a + b^2} = (b^2 + a^2)^{\frac12}
|
10,276 |
a^2\cdot \dfrac{\frac{1}{a}\cdot 1/b}{b^2}\cdot 1\cdot b^6 = \frac{1}{b\cdot \dfrac{1}{b^6\cdot a^2}\cdot b \cdot b\cdot a}
|
-20,323 |
4/4 \cdot \frac{1}{-10} \cdot (z \cdot 2 + 2) = \left(z \cdot 8 + 8\right)/\left(-40\right)
|
21,571 |
h = h*d = d\Longrightarrow h = d
|
30,570 |
{5 \choose 2}*{9 \choose 2} = 360
|
22,671 |
(x^2)^3 + 64 = (x \cdot x)^3 + 4^3 = (x^2 + 4)\cdot \left(x^4 - 4\cdot x^2 + 16\right)
|
4,333 |
5 \cdot (-1) \cdot (-5) \cdot (-25) \cdot \left(-110\right) = 68750
|
17,323 |
\left(t + p\right) (a \frac{p}{p + t} + b \dfrac{t}{p + t}) = a p + b t
|
24,817 |
\lim_{x \to 1}(3*x^2 - 4*x + 1) = 0 = \lim_{x \to 1}(x + \left(-1\right))
|
15,511 |
\operatorname{asin}(\theta) = \frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)}
|
22,508 |
(x^3 + 0x^2 + 1x + 0) = (x^2 + 0x + 1) * (x + 0)
|
28,410 |
2 = (i + 1)^1 + (1 - i)^1
|
-21,019 |
8/8*\frac{7*t}{t*6 + 4} = \tfrac{56*t}{32 + 48*t}
|
13,873 |
e^{1/x} = 1 + \frac1x + \tfrac{1}{2 \cdot x^2} + \ldots > \dfrac{1}{2 \cdot x^2}
|
-22,303 |
q^2 - q \times 6 + 8 = (q + 2 \times \left(-1\right)) \times (4 \times (-1) + q)
|
31,575 |
-10 x + 3x + 12 x = 15 x - 10 x = 5x
|
21,795 |
\dfrac{4}{2\cdot (2\cdot x + 1)} = \dfrac{1}{2\cdot x + 1}\cdot 2 = \frac{1}{x + 1} + \dfrac{1}{(x + 1)\cdot (2\cdot x + 1)}
|
20,579 |
1 - \frac{1}{2^5}(\binom{5}{0} + \binom{5}{2}) = 1 - \frac{1}{32}(1 + 5) = 0.8125
|
4,302 |
a^2*M + I + M*a^2 = I + 2*M*a * a
|
12,177 |
\sin(\frac12 \cdot \pi + k) = \cos{1/k} \geq 1 - \dfrac{1}{k^2}
|
-17,640 |
28 = 35 + 7*(-1)
|
22,230 |
\frac{2^k*6}{\left(2^k*6\right)^2} = \frac{1}{2^k*6}
|
1,119 |
1 - \frac{1}{K + 1} = \frac{1}{K + 1}*K = \frac{1}{1 + 1/K}
|
8,808 |
\left|{D^t\times D}\right| = \left|{D\times D^t}\right|
|
-12,835 |
2/7 = 6/21
|
31,631 |
\frac{1}{\frac12 \cdot 6} = 1/3
|
-3,324 |
\sqrt{7} + \sqrt{112} - \sqrt{63} = -\sqrt{9 \cdot 7} + \sqrt{7} + \sqrt{16 \cdot 7}
|
29,454 |
\tan(y + 2\times \pi) = \tan(y)
|
19,288 |
1 + 2 + 3 + \cdots + 21 = 21\times 22/2 = 231
|
38,634 |
\pi^{-1}[\pi[U]] = U
|
19,706 |
(4 \cdot x + z) \cdot (z + x) = x \cdot x \cdot 4 + 5 \cdot x \cdot z + z \cdot z
|
5,953 |
1 = \cos^2{\dfrac{\pi}{2}} + \sin^2{\pi/2}
|
8,601 |
\frac{1000}{2 + (-1)} + \frac{1}{1 + 0(-1)}0 = 1000
|
37,239 |
x \cdot 3 + 3 \cdot y = (x + y) \cdot 3
|
-14,357 |
10 + \frac1210 = 10 + 5 = 15
|
27,322 |
\sin(\tan^{-1}(y)) = \frac{y}{(y^2 + 1)^{1 / 2}}
|
35,186 |
y + ly^2 + l^2 y^3 + \dotsm = (ly + (ly)^2 + (ly)^3 + \dotsm)/l = \frac{1}{1 - ly}
|
950 |
11 - k\cdot 4 = 3\Longrightarrow k = 2
|
-18,269 |
\frac{1}{-3 l + l^2} (15 (-1) + l^2 + 2 l) = \frac{(3 (-1) + l) (l + 5)}{(l + 3 (-1)) l}
|
22,363 |
(1 + n + 1)\cdot (n + 1)! = (1 + n + 1)\cdot (n + 1)!
|
14,124 |
F + B = -(-B + 180 - F) + 180
|
26,137 |
12 \times 16^0 + 5 \times 16^1 + 16^2 = 348
|
20,734 |
9/8 = 3/2*\dfrac{1}{4}*3
|
1,367 |
1/256 = \left((1/2)^2\right)^4
|
21,901 |
(x^2 + z^2) \cdot (x + z) \cdot (-z + x) = x^4 - z^4
|
8,643 |
(T + 1)^2 = T^2 + 2*T + 1 > T^2 + 1
|
26,804 |
\sqrt{5/3} = \sqrt{\frac{1}{12}20}
|
6,402 |
1 \leq 4 \cdot x < 2 \implies 4 \cdot x = 4 \cdot x + 1
|
32,456 |
(s * s)^2 = s^4
|
-3,325 |
2*\sqrt{7} = \sqrt{7}*(3*(-1) + 1 + 4)
|
14,876 |
(c + a)*\left(a - c\right) = a * a - c^2
|
6,948 |
\sqrt{1 + s} = 1 + s/2 + \ldots
|
12,252 |
2^{d + f} = 2^d\cdot 2^f
|
16,616 |
xv vx = (vx) * (vx) xv\Longrightarrow 1 = vx
|
68 |
4 + z^4 - z^2\cdot 5 = ((-1) + z)\cdot (z + 2\cdot (-1))\cdot (z + 1)\cdot (z + 2)
|
22,613 |
z_0^4 - z_0^2*2 + 1 = 0 \implies (z_0^2 + (-1))^2 = 0
|
8,892 |
(z + (-1) + 1)^{\dfrac12} = \sqrt{z}
|
23,059 |
29/3 = -\dfrac{2}{3}*2 + 35 - 8*3
|
30,173 |
\frac{8 + y}{8 - y} = 1 + \frac{2 \cdot y}{8 - y} = 1 + \frac{1}{8/y + \left(-1\right)} \cdot 2
|
-14,317 |
\frac{65}{8 + 5} = \frac{1}{13}65 = 65/13 = 5
|
21,109 |
A*z = z/(1/A)
|
9,090 |
-(l + 1)! + (2 + l)! = (l + 1)!\cdot (l + 1)
|
30,604 |
\cos(-G) = \cos\left(G\right)
|
17,018 |
b^2 + \frac{1}{b * b} + 1 = (b + \tfrac1b)^2 + (-1) = (b + \frac{1}{b} + 1)*(b + \tfrac{1}{b} + (-1))
|
4,045 |
\frac{l_2}{l_1} = \frac{1}{l_1}l_2
|
-3,191 |
\sqrt{3} \cdot (4 + 2 + 3(-1)) = \sqrt{3} \cdot 3
|
-4,015 |
120/36*\dfrac{1}{r^4}*r^5 = \frac{r^5*120}{36*r^4}*1
|
4,480 |
\left(3\times (-1) + x\right)\times y = C + e^x\times 6 \Rightarrow y = \frac{C + e^x\times 6}{3\times (-1) + x}
|
16,191 |
4^{\frac23} = 2^{1/3}*2
|
13,434 |
a \cdot h = -a \cdot (-h)
|
3,697 |
d_1^2 - d_2^2 = (d_1 + d_2) (-d_2 + d_1)
|
26,926 |
f^{-x}*b = \tfrac{1}{f^x}*b
|
4,403 |
5^{20} \cdot \binom{19}{9} = 5 \cdot 5^{19} \cdot \binom{19}{9}
|
22,003 |
2/31 = 1/31 + \frac{1}{30} \cdot 30 \cdot 1/31
|
9,775 |
\left(k + \left(-1\right)\right) (k + 1) k \ldots = (1 + k)!
|
29,167 |
ak = ai \Rightarrow a^k = a^i
|
35,930 |
\mathbb{Var}[S_m] = \mathbb{E}[(S_m - \mathbb{E}[S_m]) * (S_m - \mathbb{E}[S_m])] = \mathbb{E}[(S_m + 5*\left(-1\right))^2]
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.