id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-7,786
|
\frac{1}{32}(16 - 144 i - 16 i + 144 (-1)) = \left(-128 - 160 i\right)/32 = -4 - 5i
|
21,028
|
\sin(Z*2) = \sin\left(Z\right) \cos(Z)*2
|
12,312
|
F^2\times q\times x = q\times F^2\times x
|
13,862
|
(1 + z)^{n + 1} = (1 + z)\cdot (1 + z)^n \geq (1 + z)\cdot (1 + n\cdot z) = 1 + (n + 1)\cdot z + n\cdot z^2 \geq 1 + \left(n + 1\right)\cdot z
|
32,727
|
\left(2\cdot c + 2\cdot c + c\cdot 4 + 8\cdot c + 14\cdot c = 1 \Rightarrow 1 = 30\cdot c\right) \Rightarrow c = \dfrac{1}{30}
|
21,849
|
f\cdot g\cdot t = f\cdot \sqrt{\sin^2{t} + \cos^2{t}}\cdot g\cdot t
|
20,267
|
\left(a^4 \cdot h = a \cdot h \implies h = a^6 \cdot h = a^2 \cdot h \cdot a\right) \implies a \cdot h = a \cdot a \cdot a \cdot h \cdot a = h \cdot a
|
30,191
|
w^3 = 3 \cdot \left(x + y\right) \cdot (z - x) \cdot (z - y) = 3 \cdot (z + w) \cdot (y - w) \cdot (x - w)
|
28,935
|
\sqrt{3 \cdot 3 + 4 \cdot 4} = 5
|
-12,772
|
\frac{2}{3} = 18/27
|
3,839
|
g = \lim_{k \to \infty} g_k \Rightarrow \lim_{k \to \infty} |g_k| = |g|
|
4,038
|
\cos(5 \cdot y) = \cos(2 \cdot y + 3 \cdot y)
|
-20,511
|
8/8*\frac{7}{10 (-1) + p} = \dfrac{56}{80 (-1) + 8p}
|
-2,740
|
-\sqrt{4}*\sqrt{6} + \sqrt{25}*\sqrt{6} = -2*\sqrt{6} + 5*\sqrt{6}
|
47,975
|
18 + 20 + 20 + 18 + 14 = 90
|
11,240
|
J \cdot C/C = A \Rightarrow \dfrac{1}{A} = C \cdot \frac1J/C
|
12,509
|
1 - y + y^2/2 - ... = e^{-y}
|
-22,937
|
\dfrac{9 \cdot 9}{5 \cdot 9} = 81/45
|
35,035
|
5 = |-2 \cdot t + 16| \Rightarrow t = 5.5, 10.5
|
-11,797
|
(\frac{3}{2})^3 = \frac{27}{8}
|
-20,240
|
\frac{-5\times x + 7}{-5\times x + 7}\times (-7/1) = \frac{1}{-x\times 5 + 7}\times (49\times (-1) + 35\times x)
|
35,678
|
\left((-1)*\pi\right)/4 = -\frac{\pi}{4}
|
-16,491
|
\sqrt{50}\cdot 3 = \sqrt{25\cdot 2}\cdot 3
|
14,097
|
\overline{A} x_1 + \cdots + \overline{r_n} x_z = x_1 A + \cdots + r_n x_z
|
-19,423
|
\dfrac{7}{8}\cdot \tfrac19 = \dfrac{1}{9/7\cdot 8}
|
607
|
1/(A/C C) = C*1/(AC)
|
36,691
|
E = \frac{1}{1/E}
|
1,490
|
\left(z^2 - V^2 - 4z + 4 = 0 \implies -V^2 + (z + 2(-1))^2 = 0\right) \implies 0 = (z + 2(-1) - V) (z + 2(-1) + V)
|
5,326
|
u\frac{dw}{dx} + w\frac{du}{dx} = \frac{\partial}{\partial x} (uw)
|
-660
|
(e^{3 \cdot \pi \cdot i/2})^{11} = e^{\dfrac12 \cdot i \cdot \pi \cdot 3 \cdot 11}
|
20,590
|
a + b - x = -2\cdot x + a + b + x
|
16,158
|
(3 \cdot 5 \cdot 19)^2 \cdot 17 = 1380825
|
5,795
|
n \cdot 2^{n + (-1)} = (\sum_{k=0}^n \binom{n}{k}) \cdot k = (\sum_{k=1}^n \binom{n}{k}) \cdot k
|
-504
|
(e^{13\times i\times π/12})^{16} = e^{\frac{13}{12}\times π\times i\times 16}
|
-21,493
|
10/10\times 3/10 = \frac{30}{100}
|
10,102
|
\sin(\frac{1}{2} \cdot \pi - t) = \cos{t}
|
-2,876
|
\sqrt{13} \times (2 \times (-1) + 4) = \sqrt{13} \times 2
|
26,190
|
0 + 0 + 3\cdot \dfrac{s}{3} = s
|
9,198
|
1/f = f^{\tfrac{g}{y}}*f^{y/g} = f^{\frac{g}{y}}*f^y
|
40,412
|
(2 \cdot k + 1) \cdot (2 \cdot k + 1) + 8 = 4 \cdot k^2 + 4 \cdot k + 1 + 8 = 2 \cdot \left(2 \cdot k^2 + 2 \cdot k + 4\right) + 1
|
-17,549
|
29\cdot (-1) + 82 = 53
|
-9,239
|
-11 \times 2 \times 2 \times 2 - 3 \times 11 \times p = 88 \times (-1) - p \times 33
|
4,941
|
F\cdot A - F\cdot A = A\Longrightarrow A\cdot F\cdot A - A \cdot A\cdot F = A^2
|
10,515
|
\left((-1) + X\right)\times (X^2 + X + 1) = (-1) + X^3
|
6,214
|
(b + f'') z = (b + f'') \left(z - \pi/4\right) \sqrt{2}
|
29,838
|
x \cdot x + 1 = x \cdot x + xy + yz + xz = (x + y) \left(x + z\right)
|
-20,774
|
\frac{1}{12*\left(-1\right) + 3*m}*\left(20 - 5*m\right) = -\frac{1}{3}*5*\frac{m + 4*\left(-1\right)}{m + 4*(-1)}
|
-5,785
|
\frac{1}{4 (z + 5)} 2 = \frac{1}{z*4 + 20} 2
|
29,801
|
25 = 5^2 + 2*0^2
|
13,945
|
h^y = (\frac{1}{h})^{-y} = (\frac1h)^{-y}
|
-14,380
|
1 + (10 - 9 \cdot 10) \cdot 5 = 1 + (10 + 90 \cdot (-1)) \cdot 5 = 1 - 400 = 1 + 400 \cdot \left(-1\right) = -399
|
25,661
|
0 = \alpha - \beta + x\Longrightarrow x + \alpha = \beta
|
37,049
|
|b - c| = |c - b|
|
-29,339
|
\left(2x + 5\right) (2x + 5(-1)) = (2x) \cdot (2x) - 5 \cdot 5 = 4x \cdot x + 25 (-1)
|
-20,246
|
\tfrac{q*8}{6*q + 8}*1*5/5 = \frac{40*q}{30*q + 40}
|
13,554
|
12 = -2 \times 84 + (144 - 84) \times 3
|
40,020
|
G^m*G = G^{1 + m}
|
30,112
|
2\cdot \sin{\frac{\pi}{18}} = 2\cdot \cos{\frac{4}{9}\cdot \pi}
|
14,635
|
( f_1, g_1) + \left( f_2, g_2\right) = ( f_1 + f_2, g_1 + g_2) = ( f_2, g_2) + ( f_1, g_1)
|
30,693
|
c^x c^y = c^{x + y}
|
20,986
|
d \times d + d \times 2 + 1 = \left(d + 1\right)^2
|
49,336
|
1 \times 2 \times 6 = 12
|
2,643
|
1 = x + y + z \Rightarrow z = 1 - y + x
|
-30,596
|
-(7 \cdot (-1) + z^2) \cdot 4 = -z^2 \cdot 4 + 28
|
13,852
|
1/(\dfrac{1}{j}) = j
|
47,183
|
z \cdot 2 = z + z
|
3,726
|
7^2 \cdot 7 - 4 \cdot 7 + 9 = 18^2
|
-20,628
|
4/4 \cdot \frac{r \cdot 2}{3 \cdot (-1) - r} \cdot 1 = \frac{8 \cdot r}{-r \cdot 4 + 12 \cdot (-1)}
|
26,217
|
\frac{800}{1} \times \frac{1}{10} \times 800 = 80 \times 800
|
-10,538
|
-\frac{1}{16 \cdot r} \cdot 12 = 2/2 \cdot (-\frac{1}{r \cdot 8} \cdot 6)
|
-6,479
|
\frac{1}{(z + 2(-1)) (z + 5)}4*5/5 = \frac{20}{5(z + 5) (2\left(-1\right) + z)}
|
26,281
|
{26 \choose 3} = {-13\cdot 2 + 52 \choose 3}
|
-21,076
|
\tfrac14 \cdot 3 = 6/8
|
14,814
|
\dfrac{1}{36} \cdot 6 = 1/6
|
14,055
|
\dfrac{r_1}{r_2} = 1 = r_2/(r_1)
|
-11,564
|
-i*7 - 9 = -i*7 - 6 + 3(-1)
|
-16,527
|
5 \cdot 16^{\frac{1}{2}} \cdot 2^{\frac{1}{2}} = 5 \cdot 4 \cdot 2^{\frac{1}{2}} = 20 \cdot 2^{1 / 2}
|
31,956
|
1 + x^6 = (1 + 3^{\dfrac{1}{2}}\times x + x^2)\times (1 - x\times 3^{1/2} + x^2)\times (1 + x \times x)
|
51
|
(x + 1)^2 \left(x + 2\left(-1\right)\right) = 2\left(-1\right) + x^3 - 3x
|
18,413
|
j + \left(-1\right) = m\Longrightarrow j = m + 1
|
-5,823
|
\dfrac{4}{\left(q + 6\right)\cdot \left(q + 5\right)} = \frac{4}{30 + q^2 + 11\cdot q}
|
-28,895
|
\frac{1}{2} = \dfrac{3}{2 + 3 + 1}
|
9,129
|
-\sin^2{y/2}\cdot 2 + 1 = \cos{y}
|
29,083
|
\frac{20}{2\lambda} = \frac{10}{\lambda}
|
-29,559
|
\dfrac{6}{x} \cdot x^5 = 6 \cdot x^4
|
24,336
|
\left(-1\right) + z + 1 = z
|
35,731
|
4 \cdot 5 + 2\left(-1\right) = 18
|
-8,091
|
\frac{1}{i - 5} (-5 + i) \dfrac{-23 - i*15}{-i - 5} = \frac{1}{-5 - i} \left(-23 - i*15\right)
|
-20,551
|
8/8 \frac{a}{2(-1) - a}3 = \frac{a\cdot 24}{16 (-1) - 8a}1
|
-21,041
|
3/3*\frac{1}{4}*3 = \frac{1}{12}*9
|
6,984
|
\frac{1}{4^n} = \dfrac{1}{4^n} \cdot 1^n = (\frac14)^n
|
26,208
|
\frac{m}{(2 \cdot m)!} = \dfrac{m}{2 \cdot m \cdot \left(2 \cdot m + (-1)\right)!} = \frac{1}{2 \cdot (2 \cdot m + (-1))!}
|
17,228
|
w_q - w_{z \cdot z} \cdot b^2 = 0 \Rightarrow w_q \cdot w = b \cdot b \cdot w_{z \cdot z} \cdot w
|
35,957
|
x = -(-1) \cdot x
|
-20,523
|
\frac{1}{(-50)*x}*(45 - x*40) = \frac{1}{x*\left(-10\right)}*(-8*x + 9)*5/5
|
18,921
|
30 = 3\cdot 6 + 2\cdot 6
|
27,745
|
(1 + y)^4 = 1 + y^4 + 4 \cdot y^3 + 6 \cdot y \cdot y + 4 \cdot y
|
-22,284
|
(8*\left(-1\right) + p)*(p + 5*(-1)) = 40 + p^2 - 13*p
|
-12,996
|
9 = 14 + 5 \cdot (-1)
|
4,698
|
\left(x + 1\right)^{2n} = (1 + x)^n\cdot (1 + x)^n
|
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