id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
17,384
|
\frac34 + (-1/2 + y)^2 = 1 + y^2 - y
|
8,152
|
|F \times H| = |F \times H|
|
-13,498
|
8 + \frac{12}{6} = 8 + 2 = 10
|
6,492
|
b*x = (x*b)^1
|
11,438
|
0 = \frac{0^2 \cdot 2}{3 + 0}
|
7,908
|
y \cdot y + y + 1 = y^2 + y + 1
|
10,855
|
g^{i + 2} c^{i + 2} = (gc)^{i + 2} = (gc)^{i + 1} gc = g^{i + 1} c^{i + 1} gc
|
9,349
|
\frac13 \cdot 26 = 2 + 4 + \dfrac83
|
-13,760
|
7\cdot 10 + 7\cdot 2/2 = 7\cdot 10 + 7 = 70 + 7 = 70 + 7 = 77
|
17,237
|
\frac{k}{x} = \frac{1}{i}*x = \dfrac{k - x}{x - i}
|
-18,431
|
\frac{1}{z\cdot (z + 7\cdot (-1))}\cdot (z + 3)\cdot \left(7\cdot (-1) + z\right) = \frac{1}{z^2 - 7\cdot z}\cdot \left(z^2 - 4\cdot z + 21\cdot \left(-1\right)\right)
|
26,063
|
n^8 = (n^2 \cdot n^2)^2
|
12,072
|
e^{-u} = -u*6 \implies -u*6 = \frac{1}{e^u}
|
14,895
|
a^{T + c} = a^T*a^c
|
34,892
|
n \cdot 4 + 4 \cdot (-1) = (n + (-1)) \cdot 4
|
-12,003
|
\frac{14}{15} = s/\left(10\times \pi\right)\times 10\times \pi = s
|
27,577
|
\left(-a\right)^2 = (-a)^2 = (-1)^2\cdot a^2 = a^2
|
1,678
|
q^2 - xq \cdot 4 + 4x^2 = (q - x \cdot 2) \cdot (q - x \cdot 2)
|
-5,801
|
\frac{100\cdot (-1) + 26\cdot x}{600\cdot (-1) + 15\cdot x^2 - 45\cdot x} = \frac{30 + 20\cdot x + 160\cdot (-1) + 6\cdot x + 30}{15\cdot x^2 - x\cdot 45 + 600\cdot (-1)}
|
1,448
|
n = x\cdot 3/2 \implies x = \frac{2}{3}\cdot n
|
18,598
|
\pi/6 + \frac{1}{4} \cdot \pi = \frac{5}{12} \cdot \pi
|
17,289
|
\left(-|v\cdot F^2| + |F^2\cdot v_x|\right)\cdot (|v\cdot F^2| + |F^2\cdot v_x|) = -|v\cdot F^2|^2 + |F^2\cdot v_x|^2
|
21,489
|
(g^j)^1*1^{j + \left(-1\right)} = g^j
|
-30,842
|
8 = 2 \cdot \left(-1\right) + 10
|
3,806
|
3 = (a + 1/a) * (a + 1/a) = a^2 + \frac{1}{a^2} + 2
|
29,234
|
\frac{x^2}{2\cdot (-1) + x} = x + 2 + \frac{4}{x + 2\cdot (-1)}
|
31,256
|
(84*(-1) + 87)/3 = 1
|
-3,058
|
5*\sqrt{7} - 2*\sqrt{7} = -\sqrt{4}*\sqrt{7} + \sqrt{25}*\sqrt{7}
|
-6,670
|
\dfrac{1}{2*p + 10*(-1)}*5 = \frac{5}{2*(p + 5*(-1))}
|
13,776
|
\left(a + 1\right)*(1 - a + a^2) = a^3 + 1
|
8,648
|
\left(9 + 6 \times \left(-1\right)\right) \times 10 = 30
|
5,431
|
1 + s^5 + s^3 + s * s = \left(1 + s * s - s\right)*(1 + s^2)*\left(1 + s\right)
|
7,697
|
\lim_{z \to -3} \frac{1}{z^2 + 9 \cdot (-1)} \cdot (z + 3) = \lim_{z \to -3} \frac{1}{(z + 3 \cdot (-1)) \cdot \left(3 + z\right)} \cdot (3 + z)
|
-5,227
|
12.0*10^{5 + 0} = 12.0*10^5
|
3,068
|
a^{q + p} = a^q\cdot a^p
|
30,226
|
y = \|y\| \cdot \frac{y}{\|y\|}
|
-1,157
|
\frac{(-1)*7*1/3}{1/4*(-1)} = -\frac13*7*(-\dfrac{4}{1})
|
18,995
|
1 = y + 1/y \Rightarrow y^2 - y + 1 = 0
|
13,770
|
\frac12(|x - x'| + x + x') = \max{x, x'}
|
40,564
|
11 + 4 + 4 + 4 + 4 + 4 = 31
|
-22,322
|
x^2 + x \cdot 3 + 18 \cdot \left(-1\right) = (6 + x) \cdot (3 \cdot (-1) + x)
|
-23,299
|
-1/7 + 1 = \frac{6}{7}
|
-5,738
|
\frac{5}{16 + q^2 - 10 q} = \dfrac{5}{\left(q + 8 (-1)\right) (q + 2 \left(-1\right))}
|
23,547
|
(\sqrt{5} + (-1))/2 = \cos(\tfrac{2}{5}\cdot \pi)\cdot 2
|
921
|
\frac{15}{51} = \frac{16 + (-1)}{(-1) + 52}
|
25,394
|
z\cdot \tfrac1y/1 = z/y
|
40,081
|
1+\frac1{1+\frac1{1+\frac1{\frac32}}}=1+\frac1{1+\frac1{1+\frac1{1+\frac12}}}
|
17,018
|
b^2 + \frac{1}{b^2} + 1 = (b + 1/b)^2 + \left(-1\right) = (b + \frac1b + 1) \cdot \left(b + 1/b + (-1)\right)
|
-6,714
|
3/10 + \frac{1}{100}8 = \frac{1}{100}8 + 30/100
|
19,481
|
(A^X*A)^X = A^X*(A^X)^X = A^X*A
|
32,232
|
3*e^{z^3}*z^2 = d/dz e^{z^3}
|
9,150
|
z = |z|\cdot e^{i\cdot t} = |z|\cdot (\cos\left(t\right) + i\cdot \sin\left(t\right))
|
-6,776
|
168 = 7 \cdot 2 \cdot 12
|
344
|
\frac{1}{2^4}*2 = 1/8
|
21,198
|
\left(y^2 + y + 10 \cdot (-1)\right) \cdot (11 \cdot \left(-1\right) + y^2 - y) = y^4 - y^2 \cdot 22 - y + 110
|
13,662
|
g\cdot j\cdot \frac{X}{q} = \frac{g}{q}\cdot j\cdot X
|
19,143
|
(z + 1)^4 - z^4 = ((z + 1)^2 + z^2) \times ((z + 1)^2 - z \times z) = (2 \times z^2 + 2 \times z + 1) \times (2 \times z + 1)
|
-17,462
|
30 + 5\times \left(-1\right) = 25
|
22,624
|
GA^2 = GA^2
|
10,939
|
0 = a\sin(k) + h\cos(k)\cdot 0 = -a\sin(k) + h\cos(k)
|
10,795
|
\frac{1}{g^{1/2}}g^{2/2} = g^{2/2 - \dfrac{1}{2}}
|
19,481
|
(H^x*H)^x = H^x*\left(H^x\right)^x = H^x*H
|
15,487
|
r\cdot r = \frac{1}{0\cdot 0} = \frac{1}{0} = r
|
-7,124
|
\frac{6}{11}*5/10 = 3/11
|
29,252
|
(-1)^{-n} = \frac{1}{\left(-1\right)^n} = \left(\dfrac{1}{-1}\right)^n = (-1)^n
|
10,378
|
\frac{1}{1! \cdot 2! \cdot 4!}7! = \frac{7!}{4! \cdot 3!} \frac{1}{0! \cdot 1!}1! \frac{1}{1! \cdot 2!}3!
|
11,896
|
(\left(-1\right) + e^{-x})^2 = (1 - x + \frac{x^2}{2!} + \cdots + (-1))^2
|
-18,944
|
\frac{7}{9} = \frac{A_s}{4 \cdot \pi} \cdot 4 \cdot \pi = A_s
|
16,329
|
9072 = 6*9*9*8*7/3
|
26,380
|
\frac{1}{5^2}*\left(12^2 - 5^2\right) = 2*(-1) + \frac{13^2}{5^2}
|
2,535
|
r' = q^2\Longrightarrow q = \sqrt{r'}
|
7,362
|
\lim_{z \to 0} \frac{\sin(z)*\cos\left(z\right)}{\sin(z)} = \lim_{z \to 0} \cos(z)
|
14,607
|
\left(2 + n\right)! = (n + 1)! \cdot (2 + n)
|
15,252
|
\lim_{l \to ∞}(h_l - b_l) = 0 \implies \lim_{l \to ∞} \frac{h_l}{b_l} = 1
|
-1,113
|
-\frac{1}{35}*35 = ((-35)*\frac{1}{35})/(35*1/35) = -1
|
-22,280
|
(3 + y) (y + 9) = 27 + y * y + y*12
|
1,873
|
(xf)^2 = f \cdot f x \cdot x
|
19,333
|
0 = x - y + z \Rightarrow -z + y = x
|
-4,840
|
\frac{7.2}{10} = \frac{1}{10}7.2
|
-23,895
|
\tfrac{22}{5 + 6} = \frac{22}{11} = \frac{22}{11} = 2
|
-26,386
|
z^{-m + l} = \frac{z^l}{z^m}
|
-1,771
|
-11/12\cdot \pi + 2\cdot \pi = \frac{13}{12}\cdot \pi
|
26,847
|
0 = f_x + a_x \cdot f_z \Rightarrow -\frac{f_x}{f_z} = a_x
|
32,864
|
\cosh\left(s\right) = \frac{d}{ds} \sinh\left(s\right)
|
18,670
|
-n*2 + 4*n = n*2
|
-26,061
|
\frac15\cdot (-2 - 16\cdot i + i + 8\cdot (-1)) = \left(-10 - 15\cdot i\right)/5 = -2 - 3\cdot i
|
10,241
|
5 \cdot N = 11 \Rightarrow 11/5 = N
|
-9,350
|
P \cdot 2 \cdot 2 \cdot 3 \cdot 7 + 2 \cdot 2 \cdot 3 \cdot 7 = 84 \cdot P + 84
|
-2,996
|
\sqrt{250} + \sqrt{90} = \sqrt{25 \times 10} + \sqrt{9 \times 10}
|
-13,626
|
\dfrac{84}{6 + 8} = \frac{84}{14} = \frac{1}{14} \cdot 84 = 6
|
-27,714
|
\frac{\mathrm{d}}{\mathrm{d}y} (-\cos{y}*10) = 10*\sin{y}
|
13,055
|
n\cdot 4 = 2\cdot 2n
|
-17,180
|
{4} = 6p^{2} - 14p + ({4} \times{3p}) + ({4} \times{-7}) = 6p^{2} - 14p + 12p - 28
|
-20,335
|
\tfrac{8 - y\cdot 4}{14\cdot (-1) + y\cdot 7} = \dfrac{y + 2\cdot (-1)}{2\cdot (-1) + y}\cdot (-\dfrac47)
|
-6,020
|
\dfrac{1}{2\cdot (x + 8\cdot \left(-1\right))}\cdot 2 = \frac{2}{x\cdot 2 + 16\cdot (-1)}
|
18,537
|
\frac13*(a + 2) = 2 \implies a = 4
|
-6,128
|
\frac{3}{(m + 5 \cdot (-1)) \cdot \left(m + 9 \cdot (-1)\right)} = \frac{3}{m^2 - 14 \cdot m + 45}
|
-7,181
|
1/7 = 1/7 \cdot 3/3
|
21,357
|
\cos(\cos\left(\theta + \pi\right)) = \cos(\cos{\theta})
|
16,272
|
(2 + 2*l)! = (l*2 + 2)*(2*l)!*\left(1 + 2*l\right)
|
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