id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-26,468 |
20 + 5\cdot z^2 - z\cdot 20 = 5\cdot \left(4 + z^2 - 4\cdot z\right)
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-16,506 |
2\cdot \sqrt{25}\cdot \sqrt{7} = 2\cdot 5\cdot \sqrt{7} = 10\cdot \sqrt{7}
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38,300 |
\frac{1}{57} \times 113 = 2 - \frac{1}{57}
|
9,756 |
q \cdot A^T = (q \cdot A)^T = (q \cdot \omega \cdot A)^T = A^T \cdot q \cdot \omega
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-10,702 |
\frac{1}{12}\times 12\times (-\frac{3}{4\times g + 4}) = -\frac{36}{48\times g + 48}
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-10,942 |
6 = \frac{84}{14}
|
1,212 |
x = \frac12(-i\cdot (1 - x^2)^{1/2} + x) + (x + i\cdot (1 - x \cdot x)^{1/2})/2
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-10,649 |
-15 = -y + 3 + 20\cdot (-1) = -y + 17\cdot \left(-1\right)
|
23,301 |
\frac{1}{y}\cdot 4 = 2\cdot y \Rightarrow 4 = y^2\cdot 2
|
24,187 |
1 + i + (-1) + k' + (-1) = (-1) + i + k'
|
-18,531 |
-\frac{81}{14} = -\tfrac{81}{14}
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-22,908 |
\frac{40}{24} = 8*5/(3*8)
|
6,983 |
-z_p \cdot x_p + x_p \cdot z_p = -x_p \cdot z + x \cdot z_p
|
-15,667 |
\tfrac{1}{\frac{1}{k\cdot s^3}\cdot (k^2 \cdot k/s)^2} = \dfrac{s^3\cdot k}{k^6\cdot \dfrac{1}{s^2}}
|
-10,269 |
\frac{1}{24*s + 12*\left(-1\right)}*(6*(-1) + s*9) = \frac33*\frac{1}{4*(-1) + 8*s}*(s*3 + 2*\left(-1\right))
|
5,013 |
1 \cdot 2 \cdot ... \cdot (k + (-1)) \cdot k \cdot \left(k + 1\right) = (k + 1)!
|
22,005 |
34 = 5^2 + 3 \cdot 3
|
-12,077 |
7/8 = s/(16\cdot \pi)\cdot 16\cdot \pi = s
|
9,912 |
B = B^{\frac{1}{2}}*B^{\frac{1}{2}}
|
17,294 |
5/34*34*5/34 = \dfrac{25}{34}
|
30,061 |
e^{-\lambda\cdot 2 - \lambda} = e^{-\lambda\cdot 3}
|
10,548 |
f - -c = f + c
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-7,786 |
(16 - 144*i - 16*i + 144*\left(-1\right))/32 = (-128 - 160*i)/32 = -4 - 5*i
|
22,267 |
-\sin(\pi/3) = \sin(\frac43 \cdot \pi)
|
1,680 |
4 \cdot \cot(\theta) = \sqrt{3} \cdot (\cot^2(\theta) + 1) = \sqrt{3} \cdot \csc^2\left(\theta\right)
|
-1,116 |
-40/42 = \frac{(-40)*1/2}{42*\frac12} = -20/21
|
10,833 |
10^{f + h} = 10^f*10^h
|
-27,714 |
\sin(z)*10 = \frac{\mathrm{d}}{\mathrm{d}z} \left(-\cos(z)*10\right)
|
6,709 |
e^{-ax} = \left(e^{-x}\right)^a \approx \left(1 - x\right)^a
|
2,391 |
C = G + C\cdot H \implies G = C - H\cdot C
|
8,812 |
x = ((-1) + x)/2 + (1 + x)/2
|
10,149 |
\sin(13*\pi/6) = 1/2
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-20,182 |
-\frac{1}{81 \times s + 18 \times (-1)} \times 36 = \frac19 \times 9 \times (-\dfrac{1}{9 \times s + 2 \times (-1)} \times 4)
|
16,378 |
\frac{1}{x_1*x_2}*(r_1*x_2 + x_1*r_2) = \frac{r_2}{x_2} + \tfrac{r_1}{x_1}
|
310 |
\frac{1}{S^2}\cdot (-x + S) = -\dfrac{x}{S^2} + 1/S
|
1,288 |
y^{(-1) + n} \times n = \frac{\partial}{\partial y} y^n
|
23,504 |
\pi/2 = \operatorname{asin}\left(1\right)
|
23,416 |
( 0, 1) \cdot 0 + ( 1, 0) \cdot 0 = ( 1, 2) \cdot 0 + 0 \cdot ( 3, 5)
|
7,677 |
\left(-x,x\right) = (-x, x)
|
4,441 |
\sqrt{1^{1.5}} = \sqrt{1^{3/2}}= \sqrt{1} = 1
|
22,988 |
x + g = e + h rightarrow x + g = h + e
|
-6,250 |
\frac{1}{3 \cdot z + 9} \cdot 4 = \frac{1}{\left(z + 3\right) \cdot 3} \cdot 4
|
-29,346 |
(3 \cdot v + 7) \cdot (3 \cdot v + 7 \cdot (-1)) = (3 \cdot v)^2 - 7^2 = 9 \cdot v^2 + 49 \cdot \left(-1\right)
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34,698 |
\sqrt{2 \cdot y^2 - 4 \cdot y + 4} = \sqrt{y^2 + \left(y + 2 \cdot (-1)\right)^2} \geq \sqrt{y^2} = |y| \geq y
|
11,016 |
-\frac23 \cdot w + y = 0 rightarrow y = w \cdot \frac23
|
15,280 |
(b\cdot a)^n = (a\cdot b)^n
|
7,381 |
x \cdot x + x = x^2 + 2 \cdot x - x = x^2 - x + 2 \cdot x = x \cdot x - x + 2 \cdot x
|
32,339 |
(a\cdot e_2 + e_1\cdot e_2 + e_1\cdot a)\cdot 2 + 23 = 49 \Rightarrow 13 = e_2\cdot a + e_1\cdot e_2 + a\cdot e_1
|
-22,804 |
18*3/\left(4*18\right) = 54/72
|
-3,362 |
\sqrt{13} + \sqrt{13} \sqrt{4} = \sqrt{13} + \sqrt{13}*2
|
6,832 |
\sin{3\cdot y} = \sin\left(5\cdot y - 2\cdot y\right) = \sin{5\cdot y}\cdot \cos{2\cdot y} - \sin{2\cdot y}\cdot \cos{5\cdot y}
|
33,207 |
-h^2 + W^2 = \left(h + W\right)*(W - h)
|
9,640 |
\lim_{z \to 2} \frac{2\cdot (-1) + z}{z^2 + 4\cdot (-1)} = \lim_{z \to 2} \frac{1}{2 + z}
|
29,488 |
1 - 2\cdot 2^n - 2^n = 1 - 2^n\cdot \left(2 + \left(-1\right)\right) = 1 - 2^n
|
12,364 |
4^2 + 2 \times 2 + 3^2 = 29
|
1,742 |
3 = 2 - d\Longrightarrow d = -1
|
-2,974 |
\sqrt{11}\cdot \left(3 + 5\right) = \sqrt{11}\cdot 8
|
-5,585 |
\frac{k}{k^2 + k\cdot 13 + 30} = \frac{1}{(3 + k)\cdot (k + 10)}\cdot k
|
5,039 |
\left(-2\right)^{1/2} = i\cdot 2^{1/2} = i\cdot |-2|^{1/2}
|
-4,441 |
(4 + x)\cdot (x + 1) = x \cdot x + 5\cdot x + 4
|
25,141 |
\left(A * A\right)^T = (AA)^T = A^T A^T = (A^T)^2
|
-20,363 |
\tfrac{4\cdot q + 36}{63 + 7\cdot q} = 4/7\cdot \frac{q + 9}{9 + q}
|
7,684 |
F^2 A^2 = (FA)^2
|
26,191 |
h_2 h_1 h_1 = h_1 h_2 h_1
|
-30,233 |
\frac{84}{8} = 21/2
|
-4,632 |
20 + x^2 - x\cdot 9 = (x + 5\cdot (-1))\cdot (4\cdot \left(-1\right) + x)
|
-1,727 |
\frac13*\pi - 7/6*\pi = -\tfrac16*5*\pi
|
-1,846 |
-\tfrac{1}{12}*19*\pi + \pi*2 = \pi*5/12
|
27,953 |
-n \cdot (-n) = n \cdot n
|
22,042 |
\frac{1}{n} \cdot (n + 2 \cdot (-1)) = -\frac{2}{n} + 1
|
43,189 |
10 = 50\cdot (-1) + 20\cdot 3
|
24,843 |
-17 \cdot (a + 4) + (a + 7)^2 = a \cdot a - a \cdot 3 + 19 \cdot (-1)
|
3,843 |
x = D\cdot Z \implies x = D\cdot Z
|
-1,502 |
\frac{\left(-9\right)\cdot 1/2}{2\cdot \frac19} = 9/2\cdot (-\tfrac{9}{2})
|
5,498 |
s - \frac{s}{3} = \dfrac23 s
|
16,761 |
\frac{dy}{dy} - r = \frac{\partial}{\partial y} (y - r)
|
5,037 |
\mathbb{E}[T\cdot Z] = \mathbb{E}[Z]\cdot \mathbb{E}[T]
|
41,255 |
(-1)^3 + 1 = 0
|
9,078 |
d^{g + h} = d^h \cdot d^g
|
17,498 |
\tfrac{y}{(1 + y \cdot 6)^2} = y \cdot \frac{\mathrm{d}}{\mathrm{d}y} \left(-\frac{1}{6 \cdot (y \cdot 6 + 1)}\right)
|
-11,703 |
\frac{1}{81} \cdot 256 = (4/3)^4
|
-20,767 |
\frac{4}{t + 5}*\dfrac{1}{3}3 = \frac{1}{3t + 15}12
|
25,899 |
52 = \frac26 \times 52 \times 3
|
19,261 |
1 + 6\cdot \rho + \rho^2\cdot 14 + \rho^3\cdot 16 + 9\cdot \rho^4 + 2\cdot \rho^5 = \left(\rho\cdot 2 + 1\right)\cdot \left(1 + \rho\right)^4
|
20,246 |
(2(-1) + y^3)^2 = y^6 - y^3*4 + 4
|
39,040 |
\frac{1}{\pi}\pi = 1
|
-7,624 |
\frac{10 - 5\cdot i}{2\cdot i + 1}\cdot \frac{1 - i\cdot 2}{-2\cdot i + 1} = \frac{10 - 5\cdot i}{1 + 2\cdot i}
|
23,721 |
(\frac18 + t)^2\cdot 64 = t^2\cdot 64 + 16 t + 1
|
28,568 |
\frac{1}{4} \cdot \pi = \tan^{-1}{1}
|
-5,451 |
2.7\cdot 10 \cdot 10^2 = 10^{-1 + 4}\cdot 2.7
|
-9,590 |
0.01 \cdot \left(-87\right) = -87/100 = -0.875
|
-16,494 |
4\cdot 48^{1 / 2} = 4(16\cdot 3)^{\dfrac{1}{2}}
|
-6,252 |
\frac{1}{z^2 - 3 \cdot z + 18 \cdot (-1)} \cdot 4 = \frac{1}{(z + 6 \cdot \left(-1\right)) \cdot (3 + z)} \cdot 4
|
38,183 |
1 \times 10^2 = 100
|
9,109 |
x * x - z * z = (x - z) (x^{1 + 0(-1)} z^0 + x^{1 + (-1)} z^1) = (x - z) \left(x + z\right)
|
-3,173 |
10^{1/2} \cdot 6 = 10^{1/2} \cdot (4 + 2)
|
-6,395 |
\frac{1}{27 + i \cdot 3} = \frac{1}{3 \cdot (9 + i)}
|
-26,620 |
6 \cdot 6 - x^2 = (6 + x) \cdot (6 - x)
|
-510 |
e^{i\pi \cdot 3/4 \cdot 3} = \left(e^{\frac{3i\pi}{4}}\right)^3
|
25,344 |
800 = {17 + \left(-1\right) \choose 2} + {17 + \left(-1\right) \choose 2} + {17 + (-1) \choose 3}
|
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