id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-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
|
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