id
int64
-30,985
55.9k
text
stringlengths
5
437k
-19,696
\frac{27}{7} = \frac{3*9}{7}
34,659
177 = 10^2 + 6 \cdot 6 + 5^2 + 4^2
-20,544
\frac{1}{z*10 + 90}*(30*(-1) + 10*z) = 10/10*\frac{z + 3*(-1)}{9 + z}
25,370
1^2 + \left(2 + s\right)^2 = 5 + s s + 4 s
-20,508
\frac{1}{70 + l*10}*\left(l*(-40)\right) = \dfrac{1}{l + 7}*((-4)*l)*\dfrac{1}{10}*10
30,264
b + x \neq 0\Longrightarrow -b \neq x
24,233
-(k + (-1)) + n = n - k + 1
-18,444
5 \cdot t + 4 \cdot (-1) = 8 \cdot (t + 8) = 8 \cdot t + 64
2,518
e^{z + (-1)} = \frac{e^z}{e}
16,755
x\cdot p = \frac{1}{2}\cdot (-(x \cdot x + p \cdot p) + (p + x)^2)
-8,660
\dfrac{7}{8} - \dfrac{8}{10} = {\dfrac{7 \times 5}{8 \times 5}} - {\dfrac{8 \times 4}{10 \times 4}} = {\dfrac{35}{40}} - {\dfrac{32}{40}} = \dfrac{{35} - {32}}{40} = \dfrac{3}{40}
41,170
(-1) + A + 1 = A
13,028
t^2-2xt+1=0 \Rightarrow t=x \pm \sqrt{x^2-1}
18,045
5*5 = 25 = 7
35,427
\frac{d}{dc} e^c = e^c
4,824
32/9 = -(5 - 8/3)^2 + 9
21,470
\frac{2}{2*(-1) + 100} = \frac{1}{49}
-17,470
19 = 32 (-1) + 51
15,491
|E \cdot A| = |E \cdot A|
37,783
\int\limits_{-\pi}^\pi f\,\mathrm{d}z = (\int_0^\pi f\,\mathrm{d}z) \cdot 2
25,799
\frac{2}{1 - t^2} = \frac{1}{-t + 1} + \frac{1}{t + 1}
1,876
\tfrac{x}{5} + 1/4 = \frac{1}{20} \cdot (5 + 4 \cdot x)
12,081
y + y \times z \times z = z \times y^2 + z \Rightarrow z = y
1,028
\frac{1}{\varphi \cdot x} \cdot U \cdot V = U/\varphi \cdot V/x
23,404
(1 + \tfrac1n)^k = (1 + 1/n)\cdot (1 + \frac{1}{n})^{k + (-1)} \geq (1 + 1/n)^{k + (-1)}
649
-a + (x + j) \cdot (x + j) = x^2 + 2 \cdot x \cdot j + j^2 - a
48,314
{20 \choose 2} = 190
14,867
(n + 1)^3 - n n n = 3 n^2 + n \cdot 3 + 1
30,479
92 = 4 \cdot (2 \cdot 8 + 7)
14,857
180 = \binom{3}{2}*\binom{5}{2}*\binom{2}{1}*\binom{3}{1}
30,659
1 + k^2 + k*2 = (k + 1)*(1 + k)
10,801
\frac{1}{3}\pi = \frac{\pi}{6}2
-23,508
\dfrac{1}{10}3 = 3 \cdot \tfrac15/2
4,197
z^g*H*z = (z^g*H*z)^g = z^g*H^g*z
14,716
s^{t\times u} = s\times t\times u/(t\times u) = \frac1t\times s\times t\times u/u = s^t\times u/u = (s^t)^u
17,319
2 = 2\cos\left(0\right)
-4,413
(x + 2\times (-1))\times (4\times (-1) + x) = x^2 - 6\times x + 8
6,712
0 = 50\cdot 0 + C_4 \Rightarrow 0 = C_4
40,720
225 = 15 \cdot 15 = (3 \cdot 5) \cdot (3 \cdot 5) = 3 \cdot 3 \cdot 5^2
10,826
M M x x = M x M x
-10,418
-\dfrac{25}{20 \cdot n} = -\frac{1}{n \cdot 4} \cdot 5 \cdot 5/5
2,087
\left(-1\right) + y^5 = (y^4 + y^3 + y^2 + y + 1) (y + (-1))
-1,821
-\pi\cdot 13/12 = -\frac{23}{12}\cdot \pi + \pi\cdot \frac{5}{6}
8,684
\left(\phi^{16}\right)^{\frac{1}{4}} = \left(\phi^{16}\right)^{1/4} = \phi^{16/4} = \phi^4
7,306
\frac{\mathrm{d}}{\mathrm{d}q} \sqrt{q^2 + 1} = \frac{q}{\sqrt{1 + q^2}}
10,672
1 - \sin^2(p/2)\cdot 2 = \cos(p)
37,740
23^{\frac{1}{2}} = 5*(23/25)^{1 / 2} = 5*\left(1 - \frac{2}{25}\right)^{\frac{1}{2}}
-3,204
9^{1/2} \cdot 2^{1/2} + 25^{1/2} \cdot 2^{1/2} = 2^{1/2} \cdot 5 + 3 \cdot 2^{1/2}
-22,991
\frac{33}{44} = 3*11/(4*11)
27,401
\frac57\cdot 65 = \frac{1}{7}325
23,134
\cos(\pi + \pi z) = -\cos{z\pi}
460
((-1) + y)\cdot \left(1 + y^2 + y\right) = (-1) + y^3
37,160
\binom{x + 2}{2} = (x + 2)!/(2!\cdot x!) = \frac{(x + 1)\cdot x!}{2\cdot x!}\cdot (x + 2) = \left(x + 2\right)\cdot (x + 1)/2
30,257
4^{2\cdot k} + \left(-1\right) = 16^k + (-1) = (16 + \left(-1\right))\cdot (16^{k + (-1)} + 16^{k + 2\cdot (-1)} + \cdots + 1)
3,377
\sin{x} \times \cos{b} + \cos{x} \times \sin{b} = \sin(b + x)
-20,621
7/7\cdot \frac{x\cdot (-1)}{-10\cdot x + 3\cdot (-1)} = \frac{(-1)\cdot 7\cdot x}{-70\cdot x + 21\cdot (-1)}
40,407
\tfrac{1}{4 + (-1)}\cdot (11 + 7\cdot (-1)) = \frac43
21,539
\mathbb{E}[V] + \mathbb{E}[A] = \mathbb{E}[V + A]
7,612
\sqrt{15}*\mathrm{i} + 5 = 5 + \sqrt{-15}
25,916
\frac{1}{20} = \frac{1}{x}\Longrightarrow x = 20
12,132
-\cos(X) = \sin(-X + \dfrac{3}{2} \cdot \pi)
22,643
1^2 = 1^3
7,826
a I = I a
28,914
\dfrac{\binom{8}{2}*7!}{9!}2! = \frac{7}{9}
-26,589
4 \cdot x^2 = (2 \cdot x)^2
5,105
x\cdot \beta\cdot \alpha = \alpha\cdot x\cdot \beta
18,583
\frac12 - 1/\left(4*3\right) = 5/12
-3,721
\dfrac{x}{x^3} = \frac{x}{x\cdot x\cdot x} = \dfrac{1}{x^2}
27,849
256 = 16 + {10 \choose 1} \cdot {4 \choose 1} \cdot {4 \choose 2}
-1,120
-\frac{8}{2} = \frac{1}{2*\frac{1}{2}} ((-8)*1/2) = -4
-19,044
\dfrac58 = A_s/\left(4*\pi\right)*4*\pi = A_s
-2,586
-\sqrt{6} + \sqrt{6} \times \sqrt{4} = 2 \times \sqrt{6} - \sqrt{6}
3,960
\frac{1}{z^2}\cdot \sin^2(3\cdot z) = 9\cdot (\frac{\sin(z\cdot 3)}{z\cdot 3})^2
1,319
35^{\frac{1}{2}}/7 = \left(5/7\right)^{\frac{1}{2}}
5,883
y_2 \cdot t + t \cdot y_1 = (y_1 + y_2) \cdot t
-12,587
48 = 128 \left(-1\right) + 176
2,431
\frac23 \cdot 3 \cdot 8 = 16
10,272
4 + 7 \cdot n = 7 \cdot (n + 1) + 3 \cdot (-1)
11,483
42 = 2\cdot \left(1 + ((2 + 0)\cdot 2 + 1)\cdot 2\cdot 2\right)
-23,355
3/10 = \dfrac{3}{2}\frac15
25,039
B \cdot Z = Z - B = Z \cdot B
-24,892
2/15 = p/\left(12\cdot \pi\right)\cdot 12\cdot \pi = p
-11,697
36^{-\dfrac{1}{2}} = (1/36)^{\frac12} = \dfrac16
-189
\frac{10!}{(5*(-1) + 10)!*5!} = \binom{10}{5}
-20,798
8/8 \cdot \frac{1}{x + \left(-1\right)} \cdot (-x \cdot 9 + 9 \cdot (-1)) = \frac{1}{x \cdot 8 + 8 \cdot \left(-1\right)} \cdot (72 \cdot (-1) - 72 \cdot x)
31,991
\dfrac14 = \dfrac{1}{2^6} \cdot 2^4
-7,645
\frac{1}{5 - i} (5 - i) \frac{1}{5 + i} (17 - i\cdot 7) = \frac{1}{5 + i} (17 - 7 i)
-7,159
5/78 = 5/12 \cdot 2/13
-16,635
-1 = -(-3)\times s - 1 = 3\times s - 1 = 3\times s + (-1)
32,875
\left(2 \cdot (-1) + x\right) \cdot \left(x + 2\right) = x^2 + 4 \cdot (-1)
-13,881
1 + \frac13 27 = 1 + 9 = 1 + 9 = 10
32,360
(y^{\frac13})^3 = y
-12,395
8 = \frac{1}{1.5}12
-4,244
\frac{63 \cdot n}{n^5 \cdot 54} = 63/54 \cdot \dfrac{n}{n^5}
-28,215
\frac{\mathrm{d}}{\mathrm{d}z} \csc{z} = -\cot{z} \csc{z}
16,481
z \cdot z + 2z + 25 = (z + 1) \cdot (z + 1) + 24
17,056
\mathbb{E}(X_x)\cdot \mathbb{E}(Z_x) = \mathbb{E}(X_x\cdot Z_x)
-6,309
\frac{4}{\left(9 \left(-1\right) + a\right) \left(a + 5 (-1)\right)*2} = 2/2*\frac{2}{(a + 9 (-1)) (a + 5 (-1))}
14,240
2 + 4 + 6*\dotsm + (1 + k)*2 = 2^{1 + k}
-4,410
((-1) + z)\cdot (4 + z) = 4\cdot (-1) + z^2 + 3\cdot z