id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-15,404
|
\dfrac{{q^{15}}}{{q^{-20}x^{8}}} = \dfrac{{q^{15}}}{{q^{-20}}} \cdot \dfrac{{1}}{{x^{8}}} = q^{{15} - {(-20)}} \cdot x^{- {8}} = q^{35}x^{-8}
|
8,505
|
25 = (x + y + z)^2 = x^2 + y^2 + z^2 + 2\cdot (x\cdot y + x\cdot z + y\cdot z) = x^2 + y^2 + z \cdot z + 16
|
37,175
|
\sqrt {x^2}=49\implies |x|=7 \implies \pm x = 7 \implies x =\pm 7
|
-18,784
|
5 = \frac{1}{3} \cdot 15
|
5,539
|
x\cdot C = C\cdot h \implies x\cdot C = C\cdot h
|
16,328
|
(1 + n)\cdot n! = \left(1 + n\right)!
|
-19,009
|
\frac{11}{60} = \dfrac{x_s}{100 \cdot \pi} \cdot 100 \cdot \pi = x_s
|
27,148
|
11/6 + 1/4 = \frac{50}{24} = \frac{1}{12}*25
|
10,552
|
1 + \frac{6}{x + 5\cdot (-1)} = \frac{1}{x + 5\cdot (-1)}\cdot \left(1 + x\right)
|
41,826
|
3\times 3 + (-1) = 8
|
19,985
|
\frac{1}{\left(1 + 0\right)*x} = \frac{1}{x}
|
-15,786
|
-3/10 \times 5 + 7/10 \times 8 = \tfrac{41}{10}
|
34,269
|
-x = (-4x)^2 + x^2 = 17 x^2
|
-22,769
|
\frac{10\cdot 7}{10\cdot 3} = \frac{1}{30}70
|
7,203
|
120 = 128 + (-1) + 7(-1)
|
7,596
|
\frac{1}{12} + \frac{1}{16} = \dfrac{4}{48} + 3/48 = 7/48
|
11,239
|
(g^k)^l = g^{k*l} = g^{l*k}
|
15,656
|
(3*\left(-1\right) + z)*(2*(-1) + z) = z^2 - 5*z + 6
|
-6,745
|
6/100 + \dfrac{4}{10} = \frac{1}{100}*6 + 40/100
|
-20,415
|
-\frac{45}{35 + 5*q} = -\frac{1}{7 + q}*9*\tfrac55
|
-27,592
|
4*1/9/4 = 1/9
|
-6,086
|
\tfrac{5}{4\cdot x + 40} = \frac{1}{4\cdot (x + 10)}\cdot 5
|
-743
|
(e^{\frac{\pi i}{6} 1})^{16} = e^{\frac{\pi}{6} i*16}
|
23,227
|
r^i = e^{\log_e\left(r^i\right)} = e^{i\cdot \log_e(r)}
|
27,118
|
\frac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{1}{y^2} + 4 \times (-1) = \dfrac{1}{y^2} \times (1 - 4 \times y^2)
|
21,201
|
\frac{1}{z^2 + z + 1} = \dfrac{1 - z}{1 - z^3} = \dfrac{1 - z}{1 - z^2 \times z}
|
19,218
|
126000 = 3^2\cdot 2^4\cdot 5^3\cdot 7
|
1,184
|
\pi \cdot \frac{\gamma}{\pi} = \gamma
|
30,106
|
1 - \frac{1}{2^4} = (\frac{1}{2^2} + 1) (1 - \frac{1}{2^2})
|
-7,181
|
1/7 = 3 \cdot 1/7/3
|
-8,879
|
-5^2 \cdot 5 = (-5)\cdot (-5)\cdot (-5)
|
41,377
|
\dfrac{1}{495}\cdot 1234 = \frac{2468}{990}
|
7,658
|
-(1 - \dfrac{1}{1 + z}) + 1 = \frac{1}{1 + z}
|
18,722
|
\frac{1}{52} \times 8 = 8/52 = 2/13
|
14,162
|
\cos{2 \times y} = 2 \times \cos^2{y} + (-1)
|
9,827
|
-(l + \left(-1\right))^2 = (-1) - l^2 + l \cdot 2
|
9,556
|
E(|Z_2| + |Z_1|) = E(|Z_1|) + E(|Z_2|)
|
13,368
|
\frac13\cdot (1 + 3\cdot t) + (-t + 1)/4 + \frac{1}{6}\cdot (-t\cdot 2 + 1) = 3/4 + \frac{t}{12}\cdot 5
|
2,192
|
t = pq \Rightarrow p = qt
|
7,120
|
\left(2 + \mathrm{i}\right) \times (2 - \mathrm{i}) = 5
|
4,117
|
d/dz \operatorname{arcosh}\left(z\right) = \frac{1}{(\left(-1\right) + z z)^{1/2}}
|
11,941
|
(-h + d)\cdot (d + h) = -h^2 + d \cdot d
|
5,192
|
\left|{V}\right| \cdot \left|{-V \cdot Z + \beta}\right| = \left|{-V \cdot Z + \beta}\right| \cdot \left|{V}\right|
|
-635
|
(e^{\frac{17}{12} \times i \times \pi})^3 = e^{3 \times \frac{1}{12} \times i \times 17 \times \pi}
|
12,337
|
(ab)^{-1} = b^{-1}a^{-1} \neq a^{-1}b^{-1}
|
19,712
|
\sin(-\theta + \frac{1}{2} \cdot \pi) = \cos{\theta}
|
-1,581
|
\pi \cdot 23/12 + \pi/6 = 25/12 \cdot \pi
|
-5,368
|
0.56 \times 10 \times 10 = 0.56 \times 10^{0 - -2}
|
-14,123
|
4 + \frac{48}{8} = 4 + 6 = 10
|
-12,080
|
1/5 = \dfrac{p}{12 \cdot \pi} \cdot 12 \cdot \pi = p
|
54,813
|
13 * 13 = 169
|
35,367
|
4 \times 4^2 - 6\times 4^2 - 2\times 4 + 40 = 64 + 96\times (-1) + 8\times (-1) + 40 = 0
|
-20,570
|
\frac{n\cdot 24}{6 + 27\cdot n}\cdot 1 = \frac{3}{3}\cdot \dfrac{n\cdot 8}{2 + n\cdot 9}
|
28,808
|
(2 \cdot \phi - z) \cdot 3 = 6 \cdot \phi - z \cdot 3
|
12,267
|
\frac{1}{k} \leq 1 \Rightarrow 2 \geq 1 + 1/k
|
2,347
|
x^y = y \Rightarrow y^{\frac{1}{y}} = x
|
3,471
|
\dfrac{1}{a_2 \cdot a_1} \cdot \left(f_1 \cdot a_2 + a_1 \cdot f_2\right) = \frac{f_2}{a_2} + \dfrac{f_1}{a_1}
|
-22,240
|
42\cdot \left(-1\right) + r^2 + r = \left(6\cdot (-1) + r\right)\cdot (r + 7)
|
37,585
|
k!\cdot k + k! = \left(k + 1\right)\cdot k! = (k + 1)!
|
5,968
|
\frac{x^2 + 4}{x + 2} + 2\cdot (-1) = \frac{1}{x + 2}\cdot \left(x^2 + 4 - 2\cdot x + 4\cdot (-1)\right) = \frac{1}{x + 2}\cdot (x^2 - 2\cdot x)
|
27,975
|
D \cdot D \cdot D = D \cdot D^2
|
-26,213
|
\left(6 - 14 \times x\right) \times e^{6 \times x - 7 \times x^2} = d/dx e^{6 \times x - 7 \times x^2}
|
28,834
|
\cos(x) = 2 \cdot \cos^2\left(x/2\right) + \left(-1\right) = 1 - 2 \cdot \sin^2(\dfrac{x}{2})
|
15,939
|
c^2 + d^2 + 2*c*d = (c + d)^2
|
345
|
c - b = 2 \cdot \tfrac{c}{2} - b
|
15,234
|
z^4 + 1 = z^4 + 2*z * z + 1 - 2*z^2 = (z^2 + 2^{1/2}*z + 1)*(z^2 - 2^{1/2} + 1)
|
13,727
|
\left(R + r\right) (R^2 + r^2 - rR) π \cdot 4/3 = 4π/3 (R^3 + r^3)
|
14,085
|
(a^2 - h\cdot a + h^2)\cdot (h + a) = a^3 + h^3
|
-12,188
|
\frac{1}{45}\cdot 44 = r/(6\cdot \pi)\cdot 6\cdot \pi = r
|
18,303
|
4! - 3! \cdot 5 + 5 \cdot 2! - 5 \cdot 1! + 1 + \left(-1\right) = -1
|
21,492
|
x^5 + x + 1 = (x^3 - x^2 + 1)\cdot (1 + x \cdot x + x)
|
-20,243
|
\frac{1}{x*6 + 8}*(8 + 6*x)*8/5 = \frac{1}{40 + 30*x}*(64 + x*48)
|
-1,092
|
8/5 \cdot (-\frac{1}{3} \cdot 8) = \frac{(-1) \cdot 8 \cdot \dfrac{1}{3}}{5 \cdot 1/8}
|
-3,246
|
\sqrt{4}\cdot \sqrt{5} + \sqrt{5} = 2\cdot \sqrt{5} + \sqrt{5}
|
3,655
|
2*(\frac{1}{2} + 1/2) = 2
|
16,252
|
1/16 + \frac{1}{16} + 1/4 = \dfrac{3}{8}
|
39,097
|
(g - x)^2 = -(h - f)^2 \Rightarrow \left(-x + g\right)^2 + \left(-f + h\right) * \left(-f + h\right) = 0
|
51,430
|
\tfrac{\sqrt{x^4 + 1}}{\left(x^6 + 1\right)^{\frac{1}{3}}} = \frac{x^2\cdot \sqrt{1 + \frac{1}{x^4}}}{x^2\cdot (1 + \frac{1}{x^6})^{1/3}} = \frac{1}{(1 + \frac{1}{x^6})^{1/3}}\cdot \sqrt{1 + \frac{1}{x^4}}
|
-3,409
|
\sqrt{11} \cdot (5 + 4 \cdot (-1) + 1) = 2 \cdot \sqrt{11}
|
-2,583
|
3^{1/2}\cdot 5 + 3\cdot 3^{1/2} = 3^{1/2}\cdot 9^{1/2} + 25^{1/2}\cdot 3^{1/2}
|
-9,495
|
q\cdot 3\cdot 3\cdot 5 - 2\cdot 3\cdot 5 = 30\cdot \left(-1\right) + 45\cdot q
|
14,609
|
\left(\cos{y} + i\cdot \sin{y}\right)/\cos{y} = i\cdot \tan{y} + 1
|
18,682
|
\left(n + 1\right)^3 = n^3 + n \cdot n\cdot 3 + n\cdot 3 + 1
|
21,737
|
(C + 2\cdot (-1)) \cdot (C + 2\cdot (-1))\cdot (8\cdot (-1) + C) = 32\cdot \left(-1\right) + C^3 - 12\cdot C \cdot C + 36\cdot C
|
5,657
|
( a'\cdot a - g\cdot x, a\cdot x + a\cdot x) = \left( a, g\right)\cdot (x + a')
|
41,099
|
32 = 198\cdot \left(-1\right) + 230
|
-1,692
|
-2 \cdot π + \frac73 \cdot π = \frac13 \cdot π
|
-12,018
|
19/24 = s/\left(12\cdot \pi\right)\cdot 12\cdot \pi = s
|
34,415
|
31 \cdot 2 \cdot 64 \cdot 24 \cdot 720 = 68567040
|
11,209
|
c^p + 1 = (1 + c)*(c^{(-1) + p} - c^{2*(-1) + p}*...*... + 1)
|
-4,276
|
\frac{k^5}{k^5} \times 132/110 = \frac{k^5 \times 132}{110 \times k^5}
|
1,568
|
3 + 1^2 + 4\cdot (-1) = 0
|
34,754
|
h_1^3 - h_2^3 = (-h_2 + h_1) \cdot (h_1 \cdot h_1 + h_1 \cdot h_2 + h_2^2)
|
-5,369
|
0.52\cdot 10^0 = 0.52\cdot 10^{0 + 0\cdot (-1)}
|
3,671
|
(x^{t/q}*x^{r/g})^{q*g} = x^{t*g}*x^{r*q} = x^{t*g + r*q}
|
4,546
|
|Y| \cdot |X| = |Y \cdot X|
|
25,499
|
(z^3)^{1/2} = (z^3)^{\frac12} = z^{3/2} = z*z^{\dfrac12} = z*z^{1/2}
|
17,725
|
(a + d)^n = a^n + a^{n + (-1)} d {n \choose 1} + \ldots
|
15,070
|
32 = 2\cdot \left(-1\right) + 34
|
-15,749
|
\frac{y^5}{\frac{1}{\frac{1}{y^{10}}\cdot z^6}} = \frac{1}{y^{10}\cdot \frac{1}{z^6}}\cdot y^5
|
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