id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-16,520 |
(25*13)^{1/2}*4 = 4*325^{1/2}
|
11,866 |
\lambda_e\cdot x = \lambda_e\cdot x
|
16,709 |
\mathbb{N} = \left\{1, 2, ..., 3\right\}
|
-18,271 |
\dfrac{4 \cdot p + p^2}{p^2 - p \cdot 6 + 40 \cdot (-1)} = \frac{p}{(10 \cdot (-1) + p) \cdot (4 + p)} \cdot (4 + p)
|
-7,706 |
\frac{1}{5 - i}\cdot (-25\cdot i - 5) = \frac{1}{-i + 5}\cdot (-i\cdot 25 - 5)\cdot \frac{1}{i + 5}\cdot (i + 5)
|
14,842 |
z^{d + h} = z^h\cdot z^d
|
-19,500 |
\dfrac76*\dfrac{1}{7} 4 = \frac{\frac{1}{6}*7}{7*1/4}
|
9,718 |
0 = v \cdot (B \cdot G - x \cdot I) \implies 0 = v \cdot B \cdot \left(G \cdot B - x \cdot I\right)
|
22,338 |
(\sqrt{a} + \sqrt{b})^2 = a + b + 2 \cdot \sqrt{a \cdot b} \gt a + b
|
21,154 |
\mathbb{Var}\left[V\right] = \operatorname{Cov}\left[V,V\right]
|
-29,591 |
6\cdot (-1) + 4\cdot x = \frac{d}{dx} (5 + 2\cdot x^2 - x\cdot 6)
|
13,141 |
g \lt \varepsilon + x \implies g - x \lt \varepsilon
|
43,841 |
253 + 4^{256} = 4^{4^4} + 253
|
8,406 |
(\dfrac{x}{a}) \cdot (\dfrac{x}{a}) = \left(\frac{x}{a}\right)^2
|
21,606 |
(1 - x) \cdot (-1 - x) - \sqrt{2} \cdot (-\sqrt{2}) = x \cdot x + \left(-1\right) + 2 = x^2 + 1
|
-3,760 |
\frac{4}{5} = \frac{4}{5}
|
2,742 |
c_1^l\cdot c_2/(c_2) = (c_2\cdot c_1/(c_2))^l
|
-15,167 |
\frac{z^5}{\frac{1}{\tfrac{1}{q^{10}} \cdot \frac{1}{z^{10}}}} = \dfrac{1}{q^{10} \cdot z^{10}} \cdot z^5
|
48,121 |
\sin\left(B\right) - \cos(A) = \cos(\pi/2 - B) - \cos(A) = -2\sin(\dfrac{1}{2}\pi + A - B) \sin\left(\frac{\pi}{2} - B - A\right)
|
31,140 |
47 \cdot 23 - 9 \cdot 120 = 1
|
8,247 |
\cos{2z} = (-1) + \cos^2{z}*2
|
21,070 |
9 + 5*\left(-1\right) = 4
|
-590 |
(e^{\frac{i \pi}{12}})^7 = e^{\dfrac{i \pi}{12}*7}
|
-23,819 |
\dfrac{40}{3 + 1} = 40/4 = \tfrac{40}{4} = 10
|
-30,279 |
\dfrac{x^2+7x+12}{x+2}=x+5+\dfrac{2}{x+2}
|
34,500 |
15\cdot c + 9\cdot c = 24\cdot c
|
25,025 |
0 = A^{100} rightarrow A^2 = 0
|
24,557 |
30 = 2^3*3 + 1^3*6
|
31,477 |
(2 \cdot n)^2 + (2 \cdot n + 2)^2 + (2 \cdot n + 4) \cdot (2 \cdot n + 4) = (5 + n^2 \cdot 3 + 6 \cdot n) \cdot 4
|
29,956 |
40 = \tfrac{1000}{25}
|
26,101 |
\frac{1}{(1/3 + 1/6 + \frac{1}{3}) \cdot 6} = 1/5
|
13,332 |
7 \cdot 7 + 24^2 = 25 \cdot 25
|
28,750 |
E(g) \cdot E(c) = E(g \cdot c) = 0 \implies 0 = g \cdot c
|
19,682 |
2*\frac{1}{1 + \left(2*y\right) * \left(2*y\right)}/3 = \frac{d}{dy} \left(\frac{\operatorname{atan}(2*y)}{3}\right)
|
-23,157 |
81/4 = \frac32 \cdot 27/2
|
25,437 |
G \cdot 2890 = G \cdot 289 \cdot 10
|
19,052 |
2^n + 2^n + 1 = 1 + 2^{1 + n}
|
6,602 |
x\cdot y - x\cdot z + z\cdot y = \frac{1}{4}\cdot (y + x)^2 - (-x + y - 2\cdot z)^2/4 + z^2
|
-5,656 |
\frac{4}{32 (-1) + 4 t} = \frac{1}{4 (8 (-1) + t)} 4
|
17,466 |
(2 + x)\cdot (1 + x)! = (x + 1)!\cdot (1 + 1 + x)
|
5,362 |
j*m = j*m
|
6,439 |
(-b + a) \times \left(b^2 + a^2 + a \times b\right) = a \times a \times a - b^3
|
24,415 |
(m + 1) (1 + m)! + (1 + m)! = (m + 1)! (m + 1 + 1)
|
13,177 |
3 (l + (-1)) + 3 = l\cdot 3
|
21,633 |
2 \cdot \frac15/4 = \frac{1}{10}
|
31,275 |
\frac14*\left(4*n + 6\right) = n + \frac64 = n + 1 + 1/2
|
20,075 |
\left(-1\right) + x = x + 2 (-1) + 1
|
2,725 |
e^x \sin(x) = \Im{(e^x e^{ix})} = \Im{(e^{(1 + i) x})}
|
368 |
\frac{5}{12} = \frac{1}{2 \cdot 2} + \frac{1}{2 \cdot 3}
|
3,696 |
y \cdot m = 1 \implies y = 1/m
|
-3,764 |
x^2\cdot 11/9 = x^2\cdot 11/9
|
4,524 |
(h_1\cdot h_2)^k = (h_1\cdot h_2)^k
|
-12,772 |
\dfrac{18}{27} = \frac{2}{3}
|
36,246 |
780 = {5 \choose 4} {12 \choose 1} {13 \choose 1}
|
-20,902 |
\frac{3\cdot z}{z + 3\cdot (-1)}\cdot \frac14\cdot 4 = \frac{12\cdot z}{12\cdot (-1) + z\cdot 4}
|
11,347 |
x_2 + x_3 + \ldots + x_k + x_{1 + k} = x_2 + x_3 + \ldots + x_k + x_{k + 1}
|
23,875 |
a_n + S_{(-1) + n} = S_n \Rightarrow S_n - S_{(-1) + n} = a_n
|
18,692 |
(1 + A)*(t + A) = (t + A)*(1 + A) = t + A
|
1,336 |
d/dz (\frac{1}{z + (-1)}e^z) = e^z \tfrac{1}{(z + (-1)) * (z + (-1))}(z + 2(-1))
|
11,123 |
\cos(\arcsin{\omega}) = \sqrt{1 - \omega^2}
|
4,337 |
5^{3\cdot l} + 2\cdot 5^{2\cdot l} - 5^l + 2\cdot (-1) = \left(5^l + 2\right)\cdot (5^{2\cdot l} + (-1)) = (5^l + 2)\cdot \left(5^l + (-1)\right)\cdot (5^l + 1)
|
-21,059 |
\dfrac48 = \frac24
|
6,385 |
720 = 6 \cdot 4 \cdot 3 \cdot 2 \cdot 5
|
24,970 |
4^x = (2 \times 2)^x = 2^{2\times x} = (2^x)^2
|
-11,557 |
18 i - 13 = -5 + 8 (-1) + i*18
|
25,105 |
\cos{3 \cdot M} = \cos(M + 2 \cdot M) = \cos{M} \cdot \cos{2 \cdot M} - \sin{M} \cdot \sin{2 \cdot M}
|
17,450 |
\frac{(-1) + 4}{4 + (-1) + 8}\cdot \frac{4}{4 + 8}\cdot 0.4\cdot 0.4 = 4/275
|
30,800 |
z^2*3/4 + (\frac{z}{2} + x)^2 = z^2 + x x + x z
|
37,913 |
(x + z) * (x + z) - 4*x*z = \dots = \left(x - z\right)^2
|
5,791 |
\mathbb{E}(Y_j) \mathbb{E}(Y_i) = \mathbb{E}(Y_i Y_j)
|
24,724 |
g_1/3 \cdot y^3 + y^2 \cdot b/2 + g_2 \cdot y = \int (y \cdot y \cdot g_1 + y \cdot b + g_2)\,\mathrm{d}y
|
15,248 |
{l \choose 4}\times 3 + 3\times {l \choose 3} = {{l \choose 2} \choose 2}
|
11,956 |
\frac{1}{\dfrac{1}{y + 1}} \cdot (1 + y) = (y + 1)^2
|
7,211 |
\frac{dy}{dt} \cdot z + \frac{dz}{dt} \cdot y = \frac{\partial}{\partial t} (y \cdot z)
|
5,647 |
(2 \cdot (-1) + z^2)^2 + 2 \cdot \left(-1\right) = z^4 - 4 \cdot z^2 + 2
|
-6,388 |
\dfrac{1}{(4 (-1) + p) (6 + p)*4} 20 = \dfrac14 4*\frac{1}{(6 + p) (p + 4 (-1))} 5
|
15,062 |
\sum_{j=1}^n j^2 = \frac{1}{2}\cdot \sum_{j=1}^n (j + n)\cdot \left(n + 1 - j\right)
|
10,178 |
\dfrac{1}{x \times z} = \tfrac{1}{z \times x}
|
-26,552 |
2*x * x - 40*x + 200 = 2*(x^2 - 20*x + 100) = 2*(x + 10*(-1)) * (x + 10*(-1))
|
1,203 |
-\sin{z} = \cos(z + \frac12\cdot \pi)
|
15,315 |
i\cdot (-\alpha)^{1 / 2} = i\cdot i\cdot \alpha^{\frac{1}{2}}\cdot \ldots
|
24,450 |
((3^3*2*5)^2*2*587)^{1/2} = (\left(2*3^2 * 3*5\right)^2)^{1/2}*\left(2*587\right)^{1/2}
|
6,121 |
x = c_1\cdot u + c_2/u \Rightarrow u^2\cdot c_1 - x\cdot u + c_2 = 0
|
10,780 |
1 + 1/n = \frac{1}{-\frac{1}{n + 1} + 1}
|
18,980 |
1 + \sqrt{5}\cdot \mathrm{i} = 1 + \sqrt{-5}
|
4,502 |
4/5 = \dfrac{h + b}{h \cdot b} = 1/h + \frac{1}{b}
|
18,585 |
\cos(1/x)\cdot x = x - 1/(2!\cdot x) + \frac{1}{(x^{34})!} - \ldots
|
-1,908 |
-\pi \cdot \frac{1}{3} \cdot 5 = -5/3 \cdot \pi + 0
|
25,238 |
\cot(\tfrac{\pi}{4} - x) = \tan(x + \frac14 \cdot \pi)
|
30,303 |
E\left(Y\cdot U\right) = E\left(Y\right)\cdot E\left(U\right)
|
-19,502 |
\frac{1}{7}\cdot 8/(7\cdot 1/8) = \dfrac87\cdot 8/7
|
-7,075 |
\frac17 \cdot 2 = 2/7
|
-4,285 |
\frac{6}{5} = \dfrac{6}{5}
|
-20,715 |
\frac{6 + 27 \cdot n}{n \cdot 24} = 3/3 \cdot \frac{2 + 9 \cdot n}{8 \cdot n}
|
-20,279 |
\frac{7*\tfrac{1}{7}}{9} = \frac{1}{63} 7
|
21,947 |
\dfrac{n}{m} + m/n = \frac{m^2 + n^2}{m\cdot n}
|
16,415 |
\frac{\pi\cdot 3}{8} = -\pi/8 + \frac{\pi}{2}
|
16,097 |
\epsilon z w^X = \epsilon w^X z
|
36,791 |
1/(m*j)*R/m = \frac{R}{m^2*j}
|
-3,732 |
q^3/q = qq q/q = q^2
|
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