id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-3,821 |
2 \cdot f^4 = 2 \cdot f^4
|
41,208 |
11 \times 73 \times 101 \times 137 = 11111111
|
-11,258 |
(y + a)^2 = (y + a) \left(y + a\right) = y^2 + 2 a y + a^2
|
29,611 |
0 = (-3*2 + 2) + 3*\left(2*(-1) + 3\right) - 1*(2*(-1) + 1)
|
-15,724 |
\frac{t^9\cdot \dfrac{1}{l^{15}}}{1/t\cdot l^3} = \dfrac{1}{\dfrac{1}{t\cdot \frac{1}{l^3}}}\cdot (\frac{1}{l^5}\cdot t \cdot t \cdot t)^3
|
1,682 |
\dfrac{y + 2*(-1)}{1 - y + 2 + 2*(-1)} = \frac{y + 2*(-1)}{-1 - y + 2*(-1)} = -\frac{y + 2*(-1)}{1 + y + 2*(-1)}
|
5,065 |
-(i + 1) + (1 + i)^3 = i^3 + 3\cdot i^2 + 2\cdot i
|
42,485 |
108 = 9 \cdot 12
|
-3,613 |
\frac{n}{4}\cdot 5 = n\cdot \frac14\cdot 5
|
-15,264 |
\dfrac{i\cdot \gamma^2}{\frac{1}{\tfrac{1}{\gamma^8}\cdot i^8}} = \frac{\gamma^2}{\gamma^8\cdot \frac{1}{i^8}}\cdot i
|
-26,429 |
5 = 3/2 \cdot 10/3
|
20,633 |
h^2 \times x + 3 \times a^2 \times x = x \times \left(h \times 2 + a \times 3\right) \times a + h \times x \times (-2 \times a + h)
|
-16,354 |
6 \cdot 25^{1 / 2} \cdot 3^{\frac{1}{2}} = 6 \cdot 5 \cdot 3^{\frac{1}{2}} = 30 \cdot 3^{1 / 2}
|
15,357 |
p^2 = 4*a*u \Rightarrow 4*a*u = p * p
|
-1,380 |
-7/9 \times (-9/7) = \frac{1/7 \times (-9)}{\left(-1\right) \times 9 \times \frac17}
|
-1,086 |
7/4 \cdot (-4/3) = \frac{\dfrac{1}{4}}{(-3) \cdot 1/4} \cdot 7
|
26,235 |
6^{1/2}/2 = (3/2)^{1/2}
|
18,189 |
|3\times \pi\times \frac23\times \pi + 5| = 2\times \pi \times \pi + 5 \neq 3
|
8,923 |
0 = \left(-1\right) + v^6 - v^3\cdot 4 rightarrow v^3 = 2 \pm \sqrt{5}
|
18,546 |
\cos\left(h\right) = \cos\left(-h\right)
|
20,056 |
det\left(5E^3\right) = 5^4 det\left(E \cdot E \cdot E\right) = 5^4 det\left(E\right)^3
|
25,621 |
(2^2 \cdot 2 + 4(-1)) \cdot (2^2 \cdot 2 + 4(-1)) \cdot (2^2 \cdot 2 + 4(-1)) = 4^3
|
-28,658 |
6x * x + 36 x + 78 = 6(x * x + 6x + 13) = 6(x^2 + 6x + 9 + 4) = 6\left((x + 3)^2 + 4\right) = 6\left((x + 3) * (x + 3) + 2^2\right)
|
50,583 |
50 \times (0.79 \times 2 + 0.06 \times 3 + 0.05 \times 2 + 0.11 \times 16) = 181
|
535 |
H\cdot x_0 = b \Rightarrow \frac{b}{H} = x_0
|
19,785 |
{m \choose x} = \frac{m!}{x! \cdot (m - x)!} = \dfrac{1}{\left(m - x\right)!} \cdot 156
|
5,167 |
2^c \cdot 2^x = 2^{c + x}
|
15,273 |
\tfrac{b}{x}\cdot x = b\cdot \frac{x}{x}
|
-20,216 |
\frac{1}{-x*45 + 72*(-1)}*(35*x + 56) = -\dfrac19*7*\frac{1}{-x*5 + 8*\left(-1\right)}*(-x*5 + 8*\left(-1\right))
|
42,219 |
0 = -g + 1 \implies g = 1
|
17,798 |
\frac{30}{1.15} + \tfrac{30}{1.3} + 40/1.5 = 26.1 + 23.1 + 26.7 = 75.9
|
31,306 |
\dfrac{1}{\frac{1}{81}} = \frac{1}{\frac{1}{3^4}} = 3^4
|
-23,422 |
4*1/7/2 = \frac{2}{7}
|
25,141 |
(F^2)^T = (F\times F)^T = F^T\times F^T = (F^T)^2
|
19,736 |
\left\{1, 2, 3, 4\right\} = \left\{3, 2, 1, 4\right\}
|
1,058 |
341444579376 = 342527319476 + 1082740100 \left(-1\right)
|
17,098 |
x\cdot 90 \lt 92\cdot c rightarrow 2\cdot c > 90\cdot (x - c) \geq 90\cdot 2 = 180
|
-2,728 |
4 \cdot \sqrt{11} = \left(5 + 1 + 2 \cdot (-1)\right) \cdot \sqrt{11}
|
37,122 |
\lceil\sqrt[4]{4000}\rceil=8
|
18,150 |
1=3(xyz)^{\frac{2}{3}} -2\leq xy+yz+zx-2
|
-27,721 |
-\csc(\tau) \cdot \cot(\tau) = \frac{d}{d\tau} \csc(\tau)
|
15,126 |
(g/f f)^k = fg^k/f
|
1,901 |
\sqrt{2}\cdot \dfrac{2}{2 + \sqrt{2}}\cdot \sqrt{2} = \frac{1}{2 + \sqrt{2}}\cdot 4
|
3,478 |
z^2 + z + 6(-1) = (z + 3) (z + 2(-1))
|
12,469 |
-\sin{x} = \cos(x + \dfrac{\pi}{2})
|
31,080 |
|9*(-1) + 8| = 1
|
-6,095 |
\tfrac{3}{5*\left(8 + t\right)} = \frac{3}{40 + 5*t}
|
-2,177 |
\frac{7}{12} - \dfrac{4}{12} = \frac{3}{12}
|
8,542 |
1/(2*2) + 1/2 = 3/4
|
5,001 |
2/9 = \frac{4}{2}\cdot 1/9
|
19,365 |
0 = |f| \Rightarrow 0 = f
|
10,523 |
6666*(120/2)=6666*60
|
-4,354 |
\dfrac{1}{6z^3} = \frac{1}{6z^3}
|
-9,429 |
-q \cdot q \cdot 2 \cdot 5 \cdot q = -q^3 \cdot 10
|
19,213 |
d/dy \tan^{-1}(\tanh(y)) = \dfrac{d/dy \tanh(y)}{1 + \tanh^2(y)}
|
3,399 |
63\%\cdot z + z\cdot 24\% = z\cdot 87\%
|
9,727 |
x^3 + d^3 + h^3 - d\cdot x\cdot h\cdot 3 = (h + x + d)\cdot (x^2 + d^2 + h^2 - x\cdot d - h\cdot x - d\cdot h)
|
10,254 |
(z + \chi)^2 = \chi^2 + 2\cdot z\cdot \chi + z \cdot z
|
31,225 |
3^2\cdot 2^2 \cdot 2\cdot 5\cdot 7 = 2520
|
16,575 |
299.5 \times 36 = 10782
|
33,589 |
b\cdot (x + 1) + (x + 1)\cdot e = (1 + x)\cdot (e + b)
|
26,412 |
1 = y^p + x^p \Rightarrow y = (1 - x^p)^{\tfrac1p}
|
21,841 |
i^3 = i \cdot i \cdot i = w \cdot w^2 \cdot i \cdot i \cdot i = (i \cdot w)^3
|
20,941 |
q^2 - 2 \cdot q + 2 = 1 + ((-1) + q)^2
|
19,469 |
\left(z + 3\right)*(z + 2*\left(-1\right)) = 6*(-1) + z * z + z
|
-22,715 |
\frac{30}{18} = \frac{6 \cdot 5}{6 \cdot 3}
|
15,284 |
-30 = 15 (-1) - 15
|
-8,826 |
\pi\times 4 + 4\times \pi + 20\times \pi = 28\times \pi
|
17,171 |
27 (-1) + 259^3 \cdot 4 \cdot 4225513 = 17136391^2
|
28,844 |
\dfrac{6}{d^2} \cdot b \cdot 2 \cdot \frac{k^4}{b^4} \cdot R^4 = \frac{12 \cdot k^4 \cdot R^4}{b^3 \cdot d^2} \cdot 1
|
20,349 |
\dfrac{1}{z \cdot e^{-t}} = e^t + K\Longrightarrow \frac{1}{e^t} \cdot (e^t + K) = 1/z
|
-2,028 |
2/3 \cdot π - 5/12 \cdot π = π/4
|
25,029 |
\sum_{i=0}^n f^i = \sum_{i=0}^{(-1) + n + 1} f^i
|
-19,357 |
\dfrac17\cdot 2/(1/5\cdot 2) = 5/2\cdot 2/7
|
17,972 |
\tfrac1w(wz + x) = x/w + z + w*0
|
42,882 |
1 - \frac1b = \dfrac{1}{\frac{1}{(-1) + b} + 1}
|
20,104 |
7 \cdot 2^4 - 7 \cdot 2 \cdot 2^2 = 7 \cdot 2^3 \cdot (2 + (-1)) = 56
|
-20,442 |
(-7 \cdot x + 6 \cdot (-1))/\left(-2\right) \cdot 4/4 = (24 \cdot (-1) - 28 \cdot x)/(-8)
|
28,836 |
8^2 - 4^2 = -1^2 + 7^2
|
-22,957 |
\dfrac{36}{54} = \dfrac{2 \cdot 18}{ 3\cdot 18}
|
11,144 |
\|x\|^2 = x \times x^\xi = x \times x^\xi
|
29,228 |
P(k) := \frac{1}{x^k} := (1/x)^k
|
3,547 |
x * x * x - z^3 = (x^2 + x*z + z^2)*(x - z)
|
12,911 |
(1 + y) \cdot \left(y + (-1)\right) \cdot (1 + y^2) = y^4 + (-1)
|
6,228 |
\frac{a \cdot a}{a + a - b} = \frac{a \cdot a}{2\cdot a - b}
|
-29,343 |
\left(a + b\right)*(a - b) = -b^2 + a^2
|
37,136 |
B^4 + 1 = B^4 - 2B^2 + 1 - B \cdot B = (B^2 + (-1))^2 - B^2 = \left(B^2 - B + \left(-1\right)\right) (B^2 + B + 1)
|
28,869 |
\sum_{l=1}^\infty \sin{l} = \sin{1} + \sin{2} + \sin{3} + ... + \sin{l}
|
19,541 |
-9 = 2 \cdot 2 + 9\left(-1\right) \cdot \left(-1\right) - 4 \cdot 2 + 18 \left(-1\right) + 4
|
26,611 |
T*a*(x + \varphi)*2 = g*f*a rightarrow \frac{g}{T*a}*f = 2*\left(x + \varphi\right)/a
|
16,608 |
19*\left(-5\right) + 12*8 = 1
|
-4,029 |
s/6 = s/6
|
378 |
\phi^2 - f^2 = \left(-f + \phi\right)\cdot (f + \phi)
|
-4,481 |
\frac{1}{x^2 + 6\cdot x + 8}\cdot (14\cdot (-1) - x\cdot 5) = -\frac{2}{x + 2} - \dfrac{3}{x + 4}
|
-2,784 |
\sqrt{3} \cdot 7 = \left(4 + 2 + 1\right) \cdot \sqrt{3}
|
3,935 |
\left(a + b\right)^2 = a^2 + 2 \cdot b \cdot a + b^2
|
29,812 |
a^4 = \frac{m^2}{9} \Rightarrow a^2 = |m|/9
|
28,170 |
a^2 + b^2 = (b + a) \cdot (b + a) - 2\cdot a\cdot b
|
1,493 |
0 = \left(m \cdot I - D\right)^2 \cdot x_2 = (m \cdot I - D) \cdot (m \cdot I - D) \cdot x_2
|
30,938 |
m^2 + (-1) = ((-1) + m)\cdot (1 + m)
|
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