id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
31,997 |
d + g + a = g + a + d
|
23,424 |
10 = (1 + 1) (4 + 1)
|
3,364 |
3\cdot x \cdot x/(3\cdot x) = x
|
2,145 |
(x + (-1))\cdot (x + 1) = (x + \left(-1\right))\cdot x + (x + (-1)) = x^2 - x + x + \left(-1\right) = x^2 + (-1)
|
2,307 |
x = (\frac{m}{l})^{x + \left(-1\right)} = l/m\cdot (m/l)^x
|
16,012 |
\sqrt{\frac{1}{\dfrac{5}{13} + 1}\cdot 2} = \sqrt{13}/3
|
27,132 |
\dfrac{2 + z}{z + 1} = \frac{1}{z + 1} + 1
|
669 |
y \in [0,1]\Longrightarrow \left\{y\right\} = y
|
14,056 |
\frac{\zeta}{2^{\dfrac{1}{3}}}2^{\tfrac13} = \zeta
|
-10,366 |
-\frac{50}{20*(-1) + 10*a} = 5/5*(-\dfrac{10}{2*a + 4*(-1)})
|
-3,802 |
\frac{88\cdot q^4}{55\cdot q^2} = \dfrac{1}{q \cdot q}\cdot q^4\cdot \frac{1}{55}\cdot 88
|
422 |
1/2 = \frac{3}{2 \cdot 3}
|
29,748 |
\frac12\cdot 9900 = 4950
|
52,887 |
3 + 4 + 10 = 17 < 18
|
21,072 |
6 + z^2 - z\cdot 5 = \left(z + 2\cdot (-1)\right)\cdot (z + 3\cdot (-1))
|
13,221 |
|a_n + b_n - b_{k + n} + a_{n + k}| = |b_n - b_{k + n} + a_n - a_{k + n}|
|
-19,226 |
\dfrac{1}{45} = b_x/(36*\pi)*36*\pi = b_x
|
15,017 |
\frac{1}{e^{-z} + 1} = \frac{e^z}{e^z + 1}
|
-20,365 |
\dfrac{5}{5} \cdot \dfrac{t + (-1)}{1 + 6 \cdot t} = \frac{1}{30 \cdot t + 5} \cdot \left(5 \cdot (-1) + 5 \cdot t\right)
|
27,414 |
y - \frac{1}{2}\cdot y \cdot y + y^3/3 - \frac{y^4}{4} + \dots = \ln\left(y + 1\right)
|
-3,952 |
\dfrac{1}{r^2} \cdot r \cdot r \cdot \dfrac{1}{4} \cdot 8 = \frac{8}{4 \cdot r^2} \cdot r \cdot r
|
26,334 |
52 = 91 + 39\cdot (-1)
|
9,135 |
x^2 + 2 \times x + 4 = x \times x + 2 \times x + 1 + 3 = (x + 1)^2 + 3
|
1,044 |
\sin\left(z + 180\right) = \sin\left(z\right) \cdot \cos(180) + \sin(180) \cdot \cos(z) = -\sin(z)
|
-12,133 |
\dfrac{44}{45} = \tfrac{p}{6\times \pi}\times 6\times \pi = p
|
38,164 |
46^2 \cdot 46 - 37^3 = 46683 = 27 \cdot 27^2 + 30^3 = 3^3 + 36^3
|
13,476 |
p^4 - p \cdot p \cdot p + p^2 - p = p^4 - p^3 - p^2 + p = (p^2 + \left(-1\right))\cdot (p \cdot p - p)
|
41,569 |
2(3+1)=8
|
-26,356 |
-1/4 \cdot (-\frac14) = \tfrac{1}{16}
|
7,779 |
\dfrac{1}{2} \cdot (\left(-1\right) + 11) = 5
|
14,866 |
12/99 = 12 \cdot \dfrac{1}{99}
|
18,864 |
\cos{2 \cdot π} = \sin{\tfrac{1}{2} \cdot π}
|
2,916 |
\dfrac{11}{11}*\frac{2}{9} = \frac{1}{99}*22
|
-25,586 |
\frac{1}{x^2} 3 = d/dx \left(-\frac3x\right)
|
25,105 |
\cos{3*x} = \cos(x + 2*x) = \cos{x}*\cos{2*x} - \sin{x}*\sin{2*x}
|
4,067 |
3 - 2x = z^2 + x^2 \Rightarrow 4 = \left(1 + x\right) * \left(1 + x\right) + z^2
|
14,994 |
U^W*x^3*x^3*U = x^3*U^W*x^2 * x*U
|
-6,175 |
\frac{t\cdot 3}{4 + t^2 + t\cdot 4} = \frac{3\cdot t}{(t + 2)\cdot (2 + t)}\cdot 1
|
33,509 |
2^t = 4/4 = 1 rightarrow 0 = t
|
-19,388 |
1/5 \cdot 4/\left(1/8\right) = \frac{8}{1} \cdot 4/5
|
28,774 |
1 + 3^2 = 10
|
440 |
(-b + c)^2 = c \cdot c - 2bc + b^2
|
27,109 |
0^2 + \left(1 \cdot 1 + 2^2\right)^2 = 0 + (1 + 4)^2 = 0 + 5^2 = 0 + 25 = 25
|
5,308 |
2\cdot x + (-1) = 2\cdot (-1) + \frac{1 - 4\cdot x^2}{-x\cdot 2 + 1}
|
18,022 |
\left(F \cdot x = b \Rightarrow F \cdot x/F = \tfrac1F \cdot b\right) \Rightarrow x = \frac{1}{F} \cdot b
|
11,043 |
\mathbb{E}\left[X^2\right] = \mathbb{E}\left[X\right]^2 + Var\left[X\right]
|
-6,595 |
\dfrac{26}{j^2 + 5 \cdot j + 14 \cdot (-1)} = \frac{(-1) + 3 \cdot j + 21 - j \cdot 3 + 6}{14 \cdot \left(-1\right) + j^2 + 5 \cdot j}
|
24,387 |
((-1) + n)! = \frac1n \cdot n!
|
19,928 |
b + 2 = d + 2 \Rightarrow b = d
|
12,298 |
1 = (y \cdot b)^3 = y^3 \cdot b^{y^2} \cdot b^y \cdot b = b^{\frac{1}{y}} \cdot b^y \cdot b
|
15,473 |
\left(x^3\right)^2 = x^6 = x^2 \cdot x^2 \cdot x^2
|
19,132 |
3 \cdot \left(-1\right) + z \geq 0 \implies z \geq 3
|
-22,897 |
\dfrac{1}{70} \cdot 63 = \frac{7 \cdot 9}{10 \cdot 7}
|
-11,645 |
-3 + 5 - i \times 8 = 2 - 8 \times i
|
-23,082 |
-\frac12*3*(-2) = 3
|
16,813 |
x_2 - x_3 = 4\Longrightarrow -x_3\cdot 2 + 2\cdot x_2 = 8
|
31,572 |
-\frac{\pi}{2} = (\pi \cdot (-1))/2
|
20,066 |
(x + \left(-1\right)) \cdot (z + (-1)) = x + (-1) + z + (-1) + (x + \left(-1\right)) \cdot (z + \left(-1\right)) = x \cdot z + (-1)
|
38,686 |
\frac{1000}{90} = \frac{1}{9}\cdot 100
|
-6,020 |
\frac{2}{2 \cdot z + 16 \cdot \left(-1\right)} = \frac{2}{(z + 8 \cdot (-1)) \cdot 2}
|
13,737 |
9 \cdot \xi^2 + 36 \cdot (-1) = 3 \cdot \xi^2 - 6 \cdot 6 = (3 \cdot \xi + 6) \cdot (3 \cdot \xi + 6 \cdot (-1)) = 3 \cdot (\xi + 2) \cdot (3 \cdot \xi + 6 \cdot \left(-1\right)) = 9 \cdot \left(\xi + 2\right) \cdot (\xi + 2 \cdot (-1))
|
-19,309 |
\frac{9}{1/7}\cdot 1/2 = \frac{1}{2}\cdot 9\cdot 7/1
|
23,882 |
-\frac{3}{4} = (-2 + \dfrac{1}{2})/2
|
8,814 |
(z + y)^3 = (z + y)\cdot (z + y)\cdot \left(z + y\right) = z\cdot z\cdot z + z\cdot z\cdot y + z\cdot y\cdot z + z\cdot y\cdot y + y\cdot z\cdot z + y\cdot z\cdot y + y\cdot y\cdot z + y\cdot y\cdot y
|
-10,468 |
-\dfrac{6}{5\cdot x + 5}\cdot \frac{1}{10}\cdot 10 = -\frac{1}{50 + 50\cdot x}\cdot 60
|
14,242 |
27 = 28*(-1) + 55
|
-941 |
\frac23 = \frac{2}{3}
|
28,091 |
\sin(F) \cdot \cos(Y) + \sin(Y) \cdot \cos(F) = \sin(Y + F)
|
8,824 |
\sin^2\left(z\right) = \sin(z\times 2)
|
25,240 |
fg ex = gf ex
|
19,834 |
\left(x^2\right)^3 = (x \cdot x \cdot x)^2 = \left(x + 1\right)^2 = x \cdot x + 1
|
-6,129 |
\frac{1}{(x + 4) \cdot 5}2 = \frac{1}{5x + 20}2
|
14,479 |
x\cdot x^n\cdot C = x\cdot x^n\cdot C = x^{n + 1}\cdot C
|
14,833 |
1 + q + q^2 + ... + q^{(-1) + m} = \frac{1}{(-1) + q}*((-1) + q^m)
|
632 |
\frac{\text{d}x}{\text{d}t}\cdot y + \frac{\text{d}y}{\text{d}t}\cdot x = \frac{\partial}{\partial t} (y\cdot x)
|
-14,418 |
6 + 7*5 - 4*10 = 6 + 35 - 4*10 = 41 - 4*10 = 41 + 40*\left(-1\right) = 1
|
38,335 |
\left(5 + h\right)^2 + 25 \times \left(-1\right) = 25 + 2 \times 5 \times h + h^2 + 25 \times \left(-1\right) = 2 \times 5 \times h + h^2
|
-2,756 |
\sqrt{7} \cdot (3 + 1) = 4 \cdot \sqrt{7}
|
21,779 |
(1 + x^2)^4 = 1 + (x^4)^2 = 1 + (x + 1) * (x + 1) = 1 + x^2 + 1
|
1,284 |
3^{\frac{1}{2}}*3^{\dfrac12} = 3
|
38,508 |
X^T\cdot X = X\cdot X^T
|
36,326 |
(-1) + 2^6 = 3^2\cdot 7
|
1,951 |
\binom{m + 2}{3} = \binom{m + 1}{2} + \binom{m + 1}{3}
|
52,530 |
12 = 3*2*2
|
8,637 |
\frac{h - d}{d \times h} = -\frac{1}{h} + \tfrac{1}{d}
|
-19,502 |
\frac17\cdot 8/(1/8\cdot 7) = 8/7\cdot \dfrac{1}{7}\cdot 8
|
6,447 |
\binom{1 + z}{q} = \binom{z}{q} + \binom{z}{q + (-1)}
|
13,285 |
1 = \tfrac13/(\frac{1}{3})
|
9,824 |
\frac{b^l}{x}x = (\frac{bx}{x}1)^l
|
41,602 |
V^4 + 1 = V^4 - a \cdot a = \left(V^2 + a\right)\cdot \left(V^2 - a\right)
|
27,048 |
8/17 = 12/17*\frac23
|
-27,179 |
\sum_{x=1}^\infty \frac{(x + 5)\cdot (-5)^x}{x^2\cdot 5^x} = \sum_{x=1}^\infty \frac{\left(-1\right)^x\cdot 5^x}{x^2\cdot 5^x}\cdot (x + 5) = \sum_{x=1}^\infty (-1)^x\cdot \dfrac{1}{x^2}\cdot (x + 5)
|
-19,657 |
\frac{5*5}{9} = \frac{25}{9}
|
23,274 |
\tfrac{4}{(2 + n)\cdot (n + 1)} = \frac{1}{n + 1}\cdot 4 - \frac{4}{n + 2}
|
8,357 |
10!/(2!\cdot 2!) = 6! {10 \choose 2} {8 \choose 2}
|
23,311 |
\left(2 + 1\Longrightarrow \cos(A)\cdot x + k\cdot \sin(A) = 1\right)\Longrightarrow (-k\cdot \sin(A) + 1) \cdot (-k\cdot \sin(A) + 1) = (\cos(A)\cdot x)^2
|
23,297 |
\pi = 142\times l\times \pi/k \Rightarrow 142\times l = k
|
2,253 |
2\cdot (-1) + \left(y + 1/y\right)^2 = \frac{1}{y^2} + y \cdot y
|
24,281 |
(X + 2)^2 = X^2 + X \cdot 4 + 4
|
-9,258 |
-2\times 2\times r\times r = -r^2\times 4
|
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