id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
20,277 |
1/16\cdot 2 = \frac18
|
2,514 |
x^{16} = ((x \cdot x \cdot x \cdot x)^2)^2
|
19,869 |
\sqrt{1 - x_\omega^2} = x_\omega
|
18,333 |
\tfrac{1}{z \cdot z} = \dfrac{1}{z \cdot z}
|
-12,026 |
1/18 = \frac{s}{6 \cdot \pi} \cdot 6 \cdot \pi = s
|
5,241 |
g^{d + c} = g^c \times g^d
|
489 |
y^5 \cdot y^4 \cdot y^3 \cdot y^5 = y^{17}
|
23,594 |
3 \cdot l^2 + l \cdot 3 + 1 = -l^3 + (l + 1)^3
|
-26,496 |
12 x = 6x*2
|
21,791 |
\frac{\mathrm{d}}{\mathrm{d}x} \sin{\tfrac{1}{2}*x} = \dfrac{\cos{x/2}}{2}
|
6,965 |
\tfrac{1}{x + 2\cdot (-1)}\cdot (x^3 - x\cdot U\cdot y - 2\cdot x^2 + 2\cdot x\cdot y + y\cdot U) = \frac{1}{2\cdot (-1) + x}\cdot (y\cdot 4 - y\cdot U) + x^2 - y\cdot U + 2\cdot y
|
24,420 |
\left(\varepsilon + 1\right)^{1 / 2}\times 2 - 2\times \varepsilon^{1 / 2} = \left((\varepsilon + 1)^{1 / 2} - \varepsilon^{\frac{1}{2}}\right)\times 2
|
21,026 |
x^2 = 36 + (6 + x)^2 - 12 \cdot \left(6 + x\right)
|
29,551 |
a^4 \cdot y = y = a^3 \cdot y
|
20,190 |
H \cdot A = 0 \Rightarrow A = 0\text{ or }0 = H
|
27,574 |
(1 + Y) \cdot \left(1 + Y^2\right) \cdot (1 + Y^4) \cdot (1 + Y^8) \cdot \ldots = 1 + Y + Y^2 + Y^3 + Y^4 + \ldots = \dfrac{1}{1 - Y}
|
-22,054 |
10/7 = \dfrac{20}{14}
|
9,148 |
0 = A \cdot C - A \cdot C = \dfrac{A}{k} \cdot B - B \cdot C/n = \frac{1}{n \cdot k} \cdot (A \cdot B \cdot n - k \cdot B \cdot C)
|
11,876 |
-\pi*2 + \frac{\pi*5}{4} = \frac14((-3) \pi)
|
21,872 |
33 = 4*8 + 1
|
16,162 |
\frac{7\times 6}{2} + 14\times (-1) = 7 \lt 14
|
8,628 |
\tfrac{1}{3} (3 (-1) + 13 + 1)\cdot 78 = 286
|
-637 |
\pi \frac{5}{12} = 437/12 \pi - 36 \pi
|
19,605 |
\dfrac{1}{b*g} = 1/(b*g)
|
30,668 |
0.6 \cdot (1 - 0.4) ((-1) \cdot 0.2 + 1) = 0.288
|
4,480 |
y \cdot (x + 3 \cdot \left(-1\right)) = 6 \cdot e^x + C\Longrightarrow y = \frac{C + 6 \cdot e^x}{3 \cdot (-1) + x}
|
4,013 |
(b + 1) \cdot (a + 1) = a \cdot b + a + b + 1
|
-21,055 |
\dfrac{2}{2} \cdot \frac{3}{4} = \frac{6}{8}
|
29,573 |
240/20 + 1 = 13
|
19,386 |
\varphi = 1 + z \times 3\Longrightarrow z = \left(\varphi + (-1)\right)/3
|
30,972 |
-(-63)\cdot 10 + 23\cdot (-27) = 9
|
8,730 |
Z B = 0 = B Z
|
24,087 |
\frac{\partial}{\partial t} (e + f) = \frac{\mathrm{d}e}{\mathrm{d}t} + \frac{\mathrm{d}f}{\mathrm{d}t}
|
35,096 |
2310 = 2*3*5*7*11 = (1 + (-2309)^{\frac{1}{2}})*(1 - (-2309)^{\frac{1}{2}})
|
24,566 |
n\cdot 2 + (-1) = -\left((-1) + n\right)^2 + n^2
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35,359 |
3/4*y * y + \left(5*y/2 + z\right) * \left(5*y/2 + z\right) = z^2 + y*z*5 + 7*y^2
|
8,662 |
(q - r)\cdot 2 = 2\cdot q + 1 - 1 + r\cdot 2
|
-15,859 |
9/10 - 10 \cdot 9/10 = -\dfrac{1}{10} \cdot 81
|
4,659 |
\tfrac{H}{x} = H/x
|
14,052 |
m/2 + 1 = m/2 + 2/2 = \left(m + 2\right)/2
|
12,089 |
0 = y^2 - y + 380*\left(-1\right) = (y + 19)*\left(y + 20*(-1)\right)
|
-30,629 |
4\cdot (-1) + y\cdot 12 = (y\cdot 3 + (-1))\cdot 4
|
17,441 |
(-i + 3)/z + z = 3 \Rightarrow 3 - i + z^2 - 3\times z = 0
|
11,923 |
9*8*7*6*5*4*3*2 = \frac{1}{1!}*9!
|
-6,697 |
\dfrac{1}{100}5 + \frac{1}{100}70 = 5/100 + \frac{1}{10}7
|
37,923 |
3 + 4*0 - 5 (-2) = 3 + 10 = 13
|
-22,764 |
20/45 = \dfrac{4 \cdot 5}{5 \cdot 9}
|
-6,641 |
\frac{4}{(1 + x)\cdot (7 + x)} = \frac{4}{x^2 + 8\cdot x + 7}
|
31,934 |
3 \cdot 7/45 = \frac{3}{\frac{1}{7} \cdot 45}
|
-4,590 |
\left(x + 5\right)*(3*(-1) + x) = x^2 + x*2 + 15*(-1)
|
-7,953 |
\frac{1}{-4 - i}(10 + i*11) = \frac{1}{i - 4}(-4 + i) \frac{i*11 + 10}{-i - 4}
|
6,848 |
2 + (t + 1)\cdot (t + 2\cdot (-1)) = t^2 - t
|
48,202 |
1\cdot 2 = 3 - 1
|
-20,113 |
\tfrac{1}{4}\cdot 4\cdot (R + 1)/(-2) = \dfrac{1}{-8}\cdot (4 + 4\cdot R)
|
21,196 |
BA = x\Longrightarrow BA = x
|
45,435 |
1 + 7 + 7 = 15
|
35,525 |
(2^{5250}+1)^2=2^{10500}+2^{5251}+1
|
16,797 |
(-2 x + q)^2 = q^2 - x q\cdot 4 + 4 x^2
|
-2,692 |
6\times 3^{1/2} = (5 + 1)\times 3^{1/2}
|
18,417 |
r x_i s = s r x_i
|
33,062 |
4^m = (2^2)^m = 2^{2\cdot m}
|
19,475 |
2240 + 1876 \cdot \left(-1\right) + 324 + 240 + 96 \cdot (-1) + 4 + 4 \cdot (-1) = 832
|
15,117 |
0 \cdot f = \left(0 + 0\right) \cdot f = 0 \cdot f + 0 \cdot f
|
28,324 |
2\cdot \left(48 + 6\right) = 108
|
18,766 |
(a^2 + ab + b^2) (-b + a) = -b^3 + a^3
|
7,577 |
\frac{1}{y^2 + 1} (2 y y + y) = 1 + \frac{1}{y^2 + 1} (y y + y + (-1)) = 1 + \dfrac{1}{2 (y^2 + 1)} (2 y^2 + 2 y + 2 \left(-1\right))
|
19,443 |
4 \cdot 6 \cdot 5/216 = \dfrac59
|
-26,429 |
10/3\cdot \dfrac12\cdot 3 = 5
|
21,876 |
2\cdot (-1) + 50 + 1 - 2\cdot (-7) + 1^2 - 2\cdot 2\cdot \left(-1\right) + 2\cdot (-7) + 2^2 = 58
|
-4,632 |
(x + 4 \cdot (-1)) \cdot \left(5 \cdot \left(-1\right) + x\right) = 20 + x^2 - x \cdot 9
|
-25,053 |
\frac{5}{10}*4/9 = \tfrac{20}{90} = \frac{2}{9}
|
16,615 |
8/11 = \dfrac{1}{2} + 1/6 + 1/22 + \dfrac{1}{66}
|
31,352 |
d \cdot \cos^2{h} = f - \cos{h}\Longrightarrow \cos^2{h} \cdot d + \cos{h} - f = 0
|
24,898 |
\frac{(-1) \cdot (1 + u)}{-u + 1} = \dfrac{1 + 1/u}{-1/u + 1}
|
7,297 |
b \cdot x = 0 \implies 0 = x\text{ or }b = 0
|
-18,383 |
\dfrac{1}{y \cdot y - 8\cdot y + 16}\cdot (-4\cdot y + y^2) = \frac{(4\cdot (-1) + y)\cdot y}{(4\cdot (-1) + y)\cdot \left(y + 4\cdot (-1)\right)}
|
-1,805 |
π*7/12 - 3/4 π = -π/6
|
8,985 |
\dfrac{1}{V\cdot U} = 1/\left(V\cdot U\right)
|
38,016 |
1030000 = 10^4 \times 103
|
-10,375 |
\frac{4}{12 \times (-1) + q \times 20} = 2/2 \times \frac{1}{6 \times \left(-1\right) + 10 \times q} \times 2
|
21,408 |
1 = \cot^2(\frac14*3*\pi)
|
-5,176 |
0.69 \cdot 10 \cdot 10 \cdot 10 = 10^{7 + 4 \cdot \left(-1\right)} \cdot 0.69
|
5,422 |
((-1) + x) x = x^2 - x
|
-2,028 |
\frac{\pi}{4} = \frac{2}{3} \cdot \pi - \frac{1}{12} \cdot 5 \cdot \pi
|
-5,887 |
6/6*\frac{1}{(x + 2\left(-1\right)) (3\left(-1\right) + x)}5 = \frac{30}{(2(-1) + x) (x + 3(-1))*6}
|
46,720 |
12.7 = 161.29^{1/2}
|
1,808 |
\frac{3}{5} - 6 \cdot 36/96 + 3 = \tfrac{1}{20}27
|
18,141 |
e\cdot (x + u) = x\cdot e + u\cdot e
|
21,886 |
(-k_1)^{1 / 2}\cdot (-k_2)^{\dfrac{1}{2}} = k_1^{\dfrac{1}{2}}\cdot i\cdot k_2^{1 / 2}\cdot i = (k_1\cdot k_2)^{\dfrac{1}{2}}\cdot i^2 = -(k_1\cdot k_2)^{\tfrac{1}{2}}
|
-1,120 |
-8/2 = \frac{1}{2*\frac{1}{2}}*(\left(-8\right)*1/2) = -4
|
22,028 |
16 = -25\cdot 4 + 116
|
41,319 |
1 = 22 + 21 \cdot \left(-1\right)
|
55,371 |
{6\choose3}=20
|
-22,369 |
k^2 - 2k - 35 = (k + 5)(k - 7)
|
32,851 |
c\cdot i = i\cdot c
|
-22,178 |
(z + 8)\cdot (10\cdot (-1) + z) = 80\cdot (-1) + z^2 - 2\cdot z
|
7,104 |
a^b*a^r = a^{r + b}
|
18,932 |
x = x + x \cdot 2 + x \cdot 4 + 8 \cdot ...
|
7,031 |
\left(x^{45} = x^{46}/x = \tfrac1x \implies \dfrac1x = 8\right) \implies x = \frac{1}{8} = 6
|
11,936 |
1 - 2 \cos\left(z\right) + (-1) = 2 - 2 \cos(z) = 2 \cdot (1 - \cos(z))
|
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