id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
19,657 |
\mathbb{N} = \left\{2, 1, 3, 0, \ldots, 4\right\}
|
1,527 |
2\times k = n \implies n\times 3 + (-1) = \left(-1\right) + 6\times k
|
-11,742 |
(8/9) \cdot (8/9) = \frac{1}{81}\cdot 64
|
-580 |
\pi*\frac13*80 - 26*\pi = 2/3*\pi
|
26,934 |
\frac13\cdot (1 + 2 + 1) = \dfrac43
|
-10,600 |
5/5 \cdot \frac{1}{x + 3 \cdot (-1)} \cdot 10 = \frac{50}{15 \cdot (-1) + x \cdot 5}
|
27 |
\sin^2(y) \times \cos^2(y) = \frac{\sin^{22}(y)}{4} = \left(1 - \cos(4 \times y)\right)/8
|
-4,803 |
10^{2*\left(-1\right) + 4}*0.69 = 0.69*10^2
|
16,746 |
(2*g + 3*(-1))*\left(3*g + 2*(-1)\right) = g^2*6 - 13*g + 6
|
-28,798 |
150 = \frac{2*\pi}{\dfrac{1}{150}*2*\pi}*1
|
-17,175 |
6 t = 6 t\cdot \left(-t\right) + 6 t = -6 t^2 + 6 t = -6 t^2 + 6 t
|
16,893 |
-g_2 \cdot g_1 \cdot 4 + \omega^2 = d^2 \Rightarrow 4 \cdot g_1 \cdot g_2 = (\omega - d) \cdot (d + \omega)
|
29,363 |
(C_\tau * C_\tau + C_\tau^2)/2 = C_\tau^2
|
31,870 |
1 + 3 + 5 = 9 = 3 \cdot 3
|
34,124 |
(5^{1/2} + 1)/2 = \frac12 + 5^{1/2}/2
|
27,852 |
11 = 69 + 58 (-1)
|
17,140 |
a^2*h^2 = (h*a)^2
|
-7,047 |
\dfrac{1}{20} = \dfrac14 \cdot 1 / 5
|
15,936 |
(3 + r)*(r + 3*(-1)) = (3*(-1) + r)*\left(r - -3\right)
|
17,624 |
h^{m + x} = h^x\cdot h^m
|
32,919 |
\frac{1}{x\cdot N\cdot \omega}\cdot (N\cdot x + x\cdot \omega + \omega\cdot N) = \tfrac1N + 1/x + 1/\omega
|
21,774 |
0 = \dfrac{1}{A + I} \cdot (A + I) \cdot (A - I) = A - I\Longrightarrow I = A
|
11,832 |
26 + x^4 - x^3 + 3x^2 + 31 x = \left(x \cdot x - 4x + 13\right) (x + 2) (x + 1)
|
22,199 |
a \cdot b \cdot k = k \cdot a \cdot b
|
-29,936 |
\frac{\text{d}}{\text{d}z} (-z\cdot 8 - z^3 + 5\cdot z^2) = -3\cdot z^2 + 10\cdot z + 8\cdot (-1)
|
13,618 |
1 + z^8 + 6z^4 = 0 \implies z^4 = -3 ± 2^{\frac{1}{2}}*2
|
10,217 |
2^{-2 k} = \frac{1}{2^{k \cdot 2}}
|
6,589 |
21 = 1\cdot 2^4 + 0\cdot 2^3 + 1\cdot 2^2 + 0\cdot 2^1 + 1\cdot 2^0
|
-15,257 |
\tfrac{q \cdot q}{q^8 \dfrac{1}{x^8}} = \tfrac{q^2}{\frac{1}{\tfrac{1}{q^8} x^8}}
|
13,952 |
1\cdot (-i + 2) = -i + 2
|
5,406 |
\dfrac{n!}{m!} = \left((n + 1)\cdot (n + 2)\cdot \cdots\cdot m\right)^{-1} \lt n^{n - m}
|
4,579 |
(2 \cdot x + 1) \cdot (3 \cdot x + 2) = 6 \cdot x^2 + 7 \cdot x + 2 = x + 2
|
-519 |
e^{4\cdot \pi\cdot i/3\cdot 14} = \left(e^{4\cdot i\cdot \pi/3}\right)^{14}
|
-15,085 |
\frac{1}{\frac{1}{g^9\cdot \dfrac{1}{x^{12}}}\cdot g^6} = \frac{1}{g^6\cdot \frac{x^{12}}{g^9}}
|
12,175 |
z^2 + 16 \cdot (-1) = \left(z + 4\right) \cdot (4 \cdot (-1) + z)
|
9,010 |
k!*\left(k + 1\right) = (k + 1)!
|
25,012 |
0.985 = -0.85\cdot 0.9 + 0.9 + 0.85
|
-6,135 |
\frac{3}{70 (-1) + q^2 + q*3} = \frac{3}{(7 (-1) + q) \left(q + 10\right)}
|
-6,346 |
\frac{1}{\left(k + 7 \cdot (-1)\right) \cdot 5} \cdot 3 = \frac{3}{35 \cdot (-1) + k \cdot 5}
|
-4,705 |
\tfrac{1}{x^2 + 2*x + 8*(-1)}*(-x*5 + 2*(-1)) = -\frac{2}{2*(-1) + x} - \frac{3}{4 + x}
|
15,556 |
16\cdot k^2 = 4\cdot 4\cdot k^2 = 4 + 4\cdot ((2\cdot k)^2 - (-1) \cdot (-1))
|
-22,103 |
\frac74 = \dfrac{1}{12} \cdot 21
|
12,389 |
-\frac{1}{2} \cdot 9 = -\frac92
|
24,280 |
N \geq x \cdot \frac{N}{x} \Rightarrow N \leq \dfrac{N}{x} \cdot x
|
8,182 |
1/\left(a\cdot c\right) = 1/(a\cdot c)
|
9,372 |
\tfrac{1}{2}(35 (-1) - 7) = -21
|
15,416 |
x \cdot \beta = \sqrt{-6}\Longrightarrow x, \beta
|
-17,680 |
20 = 23 + 3(-1)
|
17,991 |
\int x\,\mathrm{d}v = x\cdot v = \int v\,\mathrm{d}x
|
-9,491 |
2\cdot 2\cdot 11 - 2\cdot 2\cdot 2\cdot 2\cdot x = -16\cdot x + 44
|
2,779 |
|x^2 + 2 \times x \times d + d \times d| = |x^2 + x \times d + d^2 + x \times d| = |0 + x \times d| = |x \times d|
|
-10,528 |
\frac{9}{k + 3 \cdot (-1)} \cdot 4/4 = \dfrac{36}{4 \cdot k + 12 \cdot (-1)}
|
11,575 |
(-b + a) \times \left(a + b\right) = a^2 - b^2
|
-2,836 |
-\sqrt{9} \cdot \sqrt{2} + \sqrt{2} \cdot \sqrt{16} = 4 \cdot \sqrt{2} - 3 \cdot \sqrt{2}
|
21,560 |
b = \sqrt{2^2 - x^2} \Rightarrow 2^2 = x \times x + b \times b
|
38,086 |
(1 + 6 + 15 + 12)^l = 34^l
|
6,525 |
\left(-N + N^{x_0} = Nk \Rightarrow k = (-1) + N^{x_0 + (-1)}\right) \Rightarrow N^{(-1) + x_0} = 1 + k
|
7,208 |
\frac38 = 44\cdot x - 20\cdot x = 24\cdot x
|
-19,117 |
35/36 = \dfrac{Z_t}{9 \cdot \pi} \cdot 9 \cdot \pi = Z_t
|
11,292 |
n*2 + 2 = (-1) + 3 + 1 + n + (-1) + n
|
24,338 |
k^4 = (k^2)^2
|
-5,537 |
\frac{4}{(n + 7) \cdot (5 \cdot \left(-1\right) + n)} = \dfrac{4}{35 \cdot (-1) + n^2 + 2 \cdot n}
|
21,657 |
10 t + k = 10 t - 200 k + 201 k = 10 (t - 20 k) + 3*67 k
|
14,216 |
x * x + \left(-1\right) = (x + 1) \left(x + \left(-1\right)\right)
|
21,575 |
112 = \frac{1}{3} \cdot (3333 + 3000 \cdot (-1)) + 1
|
25,868 |
\int \frac{A}{D + x^2} \cdot x^2\,dx = A \cdot \int \frac{x^2 + D - D}{D + x \cdot x}\,dx = A \cdot \int 1\,dx - A \cdot D \cdot \int \frac{1}{D + x \cdot x}\,dx
|
33,783 |
k^2 + 3 = 4 + (1 + k)*\left(k + (-1)\right)
|
18,637 |
2/3 \cdot f + 2 \cdot c \Rightarrow -3 \cdot c = f
|
13,782 |
\sin(90 - \theta) = -\sin\left(90 \cdot (-1) + \theta\right)
|
24,612 |
x = \frac{5^{\frac{1}{3}}\cdot x}{5^{\dfrac13}}\cdot 1
|
4,028 |
(-a + b)\cdot (1 + c) = -a\cdot c + b + b\cdot c - a
|
24,375 |
x^{2^{n_0}} + \left(-1\right) = (x + (-1))*(x + 1)*(x^2 + 1)*(1 + x^{2 * 2})*\cdots*\left(x^{2^{\left(-1\right) + n_0}} + 1\right)
|
31,304 |
\dfrac{1}{8}\cdot \left(2 + 1 + 1 + 2 + 2 + 1 + 1 + 2\right) = \frac12\cdot 3
|
917 |
u_2*y + u_1*y = y*(u_1 + u_2)
|
3,970 |
11 - \tfrac{49}{n + 4} = \frac{1}{4 + n}*(n*11 + 5*(-1))
|
26,127 |
HX + Hx = H*(X + x)
|
-30,909 |
(32 - m)*470 = 470*(-m + 32)
|
2,393 |
7!/(2!*2!*1!*2!) = {1 \choose 1} {3 \choose 2} {5 \choose 2} {7 \choose 2}
|
33,352 |
{6 \choose 2}*4! = 6!/(2!*4!)*4! = 6!/2! = 360
|
2,887 |
v^l v_{l + 1} x = v^l xx = v^l xv_{l + 1}
|
4,817 |
d = g \Rightarrow g^4 = d^4
|
-10,564 |
\tfrac{120}{60\cdot (-1) + y\cdot 15} = \frac{1}{4\cdot (-1) + y}\cdot 8\cdot \dfrac{1}{15}\cdot 15
|
76 |
z \cdot l + t \cdot z = \left(t + l\right) \cdot z
|
1,617 |
H \geq F_1 \geq F_2 \Rightarrow \dfrac{F_1}{F_2}\cdot \frac{H}{F_1} = H/(F_2)
|
22,526 |
q^3 \cdot \frac{16}{3} = \frac{4}{\pi} \cdot 4/3 \cdot q^3 \cdot \pi
|
18,567 |
x^2\cdot 2 \cdot 2 = x^2\cdot 4
|
24,614 |
\{H,B\} \Rightarrow H = B \cap H
|
19,968 |
q^4 - q^3 - q^2 + q = (-q + q q) ((-1) + q q)
|
38,434 |
\tan{\theta} = 1/\cot{\theta}
|
17,387 |
r\cdot f\cdot 5000\cdot h\cdot j = h\cdot j\cdot 3750\cdot 4\cdot r\cdot f/3
|
-26,579 |
x^2 - 8 * 8 = x^2 + 64*(-1)
|
36,721 |
\sqrt{a^2 + x^2} = \sqrt{a^2 + x \cdot x}
|
23,279 |
x = x \times z + z \Rightarrow x = \frac{z}{-z + 1}
|
5,206 |
x \gt 1 \implies x^3 + 7x^2 + 8(-1) \gt 1^3 + 7*1^2 + 8\left(-1\right) = 1 + 7 + 8(-1) = 0
|
3,846 |
\left(\sqrt{b} \times \sqrt{a}\right)^2 = a \times b
|
10,940 |
(-m + 2\cdot W_m)/(\sqrt{m}) = (-\frac{m}{2} + W_m)/(\sqrt{m}\cdot \tfrac{1}{2})
|
492 |
\frac{7 - b}{-a - 1} = -2\times a \implies 7 - b = a\times 2 + a^2\times 2
|
-20,851 |
\frac{1}{36 + x \cdot 9} \cdot (-x \cdot 8 + 32 \cdot (-1)) = -\frac89 \cdot \dfrac{x + 4}{x + 4}
|
31,216 |
\cos^2{E} = 1 - \sin^2{E}
|
15,460 |
-\int\limits_1^z \ldots\,\mathrm{d}z = \int\limits_z^1 \ldots\,\mathrm{d}z
|
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