id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
22,293 |
V \cdot x^{1/2} = V \cdot x^{\dfrac12}
|
3,271 |
10! \cdot \tfrac{1}{3! \cdot 2! \cdot 2!}/10 = \dfrac{1}{2! \cdot 2! \cdot 3!} \cdot 9!
|
-8,337 |
-\dfrac{6}{-1} = 6
|
23,616 |
\left(8 \times x + x = 45\Longrightarrow 45 = x \times 9\right)\Longrightarrow x = 5
|
7,288 |
\frac{1}{{4 \choose 2}} (-{2 \choose 2} + {3 \choose 2}) = \dfrac{1}{3}
|
2,897 |
y*2 |e| = y |e|*2
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-6,102 |
\frac{1}{8 \cdot (-1) + p \cdot 2} = \frac{1}{(p + 4 \cdot (-1)) \cdot 2}
|
-17,783 |
1 = 84 + 83\cdot \left(-1\right)
|
43,184 |
x^2 = 9 \cdot x \cdot x = 3 \cdot 3 \cdot x \cdot x + 0
|
7,562 |
1/6 = -\frac{4}{3} + \frac{3}{2}
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30,857 |
\sin{x\cdot 3} = \sin{(x + \dfrac{2}{3}\cdot \pi)\cdot 3}
|
18,162 |
1 + y + y^2 + y^3 = (y + 1)\times (y^2 + 1)
|
12,547 |
\phi^6 + (-1) = \left(2\phi + 1\right)^2 + (-1) = 4\phi^2 + 4\phi = 4\phi^3
|
22,704 |
-2/4 + 1 = 2/4
|
45,827 |
( X_1, Y_1)\cdot ( X_2, Y_2)\cdot ( X_3, Y_3) = ( X_1\cdot X_2, Y_1\cdot X_2 + Y_2)\cdot ( X_3, Y_3) = ( X_1\cdot X_2\cdot X_3, (Y_1\cdot X_2 + Y_2)\cdot X_3 + Y_3) = ( X_1\cdot X_2\cdot X_3, Y_1\cdot X_2\cdot X_3 + Y_2\cdot X_3 + Y_3)
|
-14,669 |
87 = \frac14 \cdot 348
|
11,542 |
\frac{7\cdot (-1) + 35}{(6 \cdot 6 + 3^2 + 2^2)^{\frac{1}{2}}} = 4
|
3,027 |
0.4\cdot n = (0.3 + 0.1)\cdot n
|
35,599 |
(-1) \cdot (-1) = (-1)\cdot (-1) = -1
|
-4,424 |
\dfrac{-4 \cdot z + 11 \cdot (-1)}{4 \cdot \left(-1\right) + z^2 + 3 \cdot z} = -\frac{1}{z + 4} - \frac{1}{(-1) + z} \cdot 3
|
34,742 |
218^2 + \left(-1\right) = (218 + 1) \cdot \left(218 + (-1)\right) = 219 \cdot 217 = 3 \cdot 73 \cdot 7 \cdot 31
|
32,665 |
\binom{2 + i}{2} = \binom{i + 3}{3} - \binom{i + 2}{3}
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7,192 |
x^{10} = (1 - x)*(13 - 21*x) = 21*x * x - 34*x + 13 = 21*(1 - x) - 34*x + 13 = 34 - 55*x
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-2,320 |
-2/11 + 4/11 = \tfrac{2}{11}
|
31,882 |
p\cdot 4 = 12 rightarrow p = 3
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-19,226 |
1/45 = \frac{F_s}{36\cdot \pi}\cdot 36\cdot \pi = F_s
|
22,022 |
-2 = (-1) + \eta \Rightarrow -1 = \eta
|
-6,511 |
\dfrac{6}{6}*\dfrac{2}{(7 + a)*\left(8 + a\right)} = \frac{12}{6*\left(a + 7\right)*(a + 8)}
|
-99 |
2(-1) - 9 = -11
|
-4,486 |
\dfrac{-x*6 + 18}{x * x - x*4 + 5*(-1)} = -\frac{2}{5*(-1) + x} - \frac{4}{1 + x}
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-4,702 |
\frac{5 - x}{6 + x^2 - 5\cdot x} = -\frac{3}{x + 2\cdot (-1)} + \frac{1}{x + 3\cdot (-1)}\cdot 2
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50,768 |
{2 \choose 1}\cdot {5 \choose 1}\cdot {4 \choose 1}\cdot {3 \choose 1}\cdot {1 \choose 1} = 120
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29,568 |
1 + r + r \times r + ... + r^x = \frac{1 - r^{(-1) + x}}{1 - r}
|
-622 |
e^{13*5i\pi/12} = (e^{5\pi i/12})^{13}
|
-18,956 |
\frac{11}{30} = \dfrac{A_s}{4 \cdot \pi} \cdot 4 \cdot \pi = A_s
|
22,933 |
\frac{1}{36}*\left((-1) + 37 * 37 * 37\right) = 3*7*67
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-4,702 |
\frac{2}{3\times \left(-1\right) + \theta} - \frac{3}{\theta + 2\times \left(-1\right)} = \frac{1}{\theta^2 - \theta\times 5 + 6}\times \left(5 - \theta\right)
|
-12,044 |
\frac{3}{4} = s/(16\cdot \pi)\cdot 16\cdot \pi = s
|
5,808 |
\binom{m}{2} \binom{2 \left(-1\right) + m}{j}/(\binom{m}{j}) = \binom{m - j}{2}
|
11,571 |
x^4 + 10 x^2 + 25 = \left(x * x + 5\right)^2 = (2*3^{1/2} x)^2 = 12 x^2
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-20,607 |
-7/5 \cdot \frac{(-1) + 5 \cdot x}{x \cdot 5 + (-1)} = \tfrac{-35 \cdot x + 7}{5 \cdot \left(-1\right) + x \cdot 25}
|
13,795 |
x - L + L^2 - L^3 + ... = \dfrac{1}{x + L}
|
-30,606 |
-12^{\frac{1}{2}} = -2*3^{1 / 2}
|
-20,003 |
\left(y + 9\right)/4\cdot 4/4 = \left(36 + y\cdot 4\right)/16
|
31,849 |
e^y = e^{(-1) + y} \cdot e
|
-10,321 |
10/10 \cdot \frac{1}{5 \cdot r} \cdot (5 \cdot r + 2) = \frac{20 + r \cdot 50}{r \cdot 50}
|
28,846 |
(x^2)^4 = (x^4)^2 = (x + 1)^2 = x^2 + 1
|
-21,068 |
\dfrac{1}{4}*2 = \frac{4}{8}
|
37,878 |
r^2 + 1 + r = 1 - 1 + r + (1 + r)^2
|
-6,128 |
\frac{3}{(j + 5 \cdot (-1)) \cdot \left(j + 9 \cdot (-1)\right)} = \frac{3}{45 + j^2 - 14 \cdot j}
|
33,715 |
1/2 + 0 = \frac{2}{4} < 2/\pi
|
-29,561 |
(x \cdot x \cdot x \cdot 4 - x^2 + 3)/x = 3/x + x^3 \cdot 4/x - \frac{x^2}{x}
|
-25,364 |
\dfrac{d}{dx}\left(\dfrac{\sin(x)}{x^2}\right)=\dfrac{x\cos(x)-2\sin(x)}{x^3}
|
33,645 |
3.14 = \dfrac{157}{50} = \frac{1}{7} \cdot 22 - 1/350
|
20,118 |
\tan^2{x} + \sin^2{x} + \cos^2{x} = \frac{\text{d}}{\text{d}x} \tan{x}
|
8,344 |
\frac{x\cdot \frac{1}{y}}{z}\cdot 1 = \frac{x\cdot \frac1z}{y} = \tfrac{x}{y\cdot z}
|
29,924 |
\dfrac{1}{100}95 = 5*19/100
|
-25,864 |
\dfrac{z^5}{z^2} = z^{5 + 2 \cdot (-1)} = z^3
|
124 |
\left(-Y*2 + Y^3\right)/Y = 2 (-1) + Y Y
|
-23,377 |
\dfrac{9}{32} = 3/4*3/8
|
37,724 |
(-f + a)^2 = a^2 + f^2 - a \cdot f \cdot 2 rightarrow a^2 + f^2 - (-f + a)^2 = 2 \cdot a \cdot f
|
21,258 |
X\cdot z = X\cdot z
|
-2,104 |
\frac{17}{12} \pi + 0 = \pi*17/12
|
34,911 |
\left(-1\right) + 11/12 = -1/12
|
15,065 |
0 = y + 2 (-1) rightarrow 2 = y
|
16,033 |
\sin(x) = -\cos(\dfrac{\pi}{2} + x)
|
9,800 |
47*((-1) + x*47) = 47^2 x + 47 (-1)
|
-9,228 |
11 r + 33 (-1) = -11\cdot 3 + 11 r
|
6,641 |
2\cdot (2 + z) = 2\cdot z + 4
|
-20,339 |
-\frac{36}{-8} = -4/\left(-4\right)\cdot \frac12\cdot 9
|
20,051 |
C*Q * Q = Q^2*C
|
-22,030 |
\frac{1}{7} \cdot 10 = \frac{1}{28} \cdot 40
|
-7,313 |
0 = \dfrac{1}{7} \cdot 2 \cdot 0
|
4,143 |
\frac{1}{2^k}\cdot 2 = \frac{1}{\frac12\cdot 2^k}
|
-22,232 |
27 \left(-1\right) + s \cdot s + 6s = (9 + s) (3\left(-1\right) + s)
|
-20,750 |
-\frac{14}{7 c + 42 (-1)} = \frac{7}{7} (-\dfrac{2}{c + 6 (-1)})
|
-23,162 |
-\dfrac14 = ((-1)\cdot 1/2)/2
|
13,285 |
\frac13/(1/3) = 1
|
10,838 |
4 = 2*x^2*\left(1 - \frac17\right) = 12/7*x^2
|
10,261 |
5 + 2 \sqrt{13} = \left(a + b \sqrt{13}\right) \left(a + b \sqrt{13}\right) \left(a + b \sqrt{13}\right) = a^2 a + 39 a b^2 + (3 a^2 b + 13 b^3) \sqrt{13}
|
-4,297 |
\frac{k \cdot k \cdot k\cdot 120}{80\cdot k \cdot k \cdot k} = 120/80\cdot \frac{1}{k^3}\cdot k \cdot k \cdot k
|
23,284 |
\frac{1}{b}\cdot a + g/h = \frac{1}{b\cdot h}\cdot (a\cdot h + b\cdot g) \neq a\cdot h + b\cdot g
|
-20,578 |
\frac{36 \cdot \left(-1\right) - i \cdot 4}{4 \cdot i + 12 \cdot (-1)} = 4/4 \cdot \dfrac{-i + 9 \cdot (-1)}{3 \cdot (-1) + i}
|
31,082 |
1 + \frac{1}{1 + 1/\left(5\cdot \frac{1}{3}\right)} = 1 + \frac{1}{1 + \frac{1}{1 + \frac23}}
|
13,195 |
11 * 11*3^2 = 1089
|
9,684 |
b \times a = a^3 \times b = a \times a \times a \times b = a \times b
|
40,043 |
5\cdot K = K + K + K + K + K
|
52,157 |
\frac{1}{(1 + z)^2} z = \dfrac{1 + z + (-1)}{(1 + z)^2} = \frac{1}{1 + z} - \frac{1}{(1 + z)^2}
|
-15,636 |
\frac{(\frac{1}{q^4})^5}{\frac{1}{p \cdot p^2}\cdot \tfrac{1}{q}} = \dfrac{1}{q^{20}\cdot \frac{1}{q\cdot p^3}}
|
-20,753 |
\tfrac{l}{8 \cdot \left(-1\right) + l \cdot 2} \cdot 14 = \frac{2}{2} \cdot \frac{7 \cdot l}{l + 4 \cdot (-1)}
|
-3,867 |
\tfrac{90}{x\cdot 10}\cdot x^4 = \frac{x^4}{x}\cdot 90/10
|
-3,346 |
176^{1 / 2} + 44^{\frac{1}{2}} = (4\cdot 11)^{1 / 2} + (16\cdot 11)^{1 / 2}
|
-6,097 |
\frac{2 \cdot p}{\left(p + 2\right) \cdot (2 + p)} \cdot 1 = \dfrac{2 \cdot p}{4 + p^2 + p \cdot 4}
|
-7,021 |
1/6 = 5/9\cdot 6/10\cdot \frac{1}{8}\cdot 4
|
-2,628 |
-\sqrt{7} + \sqrt{9\cdot 7} = -\sqrt{7} + \sqrt{63}
|
-4,448 |
6\cdot (-1) + x \cdot x + x = (2\cdot (-1) + x)\cdot (x + 3)
|
24,865 |
t^4 - t^2 + 2(-1) = (t^2 + 2(-1)) (1 + t^2)
|
8,406 |
\left(\frac{z}{c}\right)^2 = (z/c)^2
|
-698 |
-\pi \cdot 24 + \frac{76}{3} \pi = \pi \frac43
|
1,553 |
x + iy - z + ik = x - iy + (z - ik) (x - z) + y - k = x + z - y - k
|
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