id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
8,241 |
s \cdot q = q \cdot s
|
-23,331 |
\dfrac{1}{3} \cdot \dfrac{2}{7} = \dfrac{2}{21}
|
-18,984 |
\dfrac58 = B_q/(100 \pi)*100 \pi = B_q
|
41,333 |
b_{i_x} = b_{i_x}
|
-9,117 |
146.6\% = \frac{1}{100}\cdot 146.6
|
-16,490 |
5\cdot \left(9\cdot 7\right)^{1 / 2} = 63^{\frac{1}{2}}\cdot 5
|
-3,605 |
40/32 \frac{n^2}{n} = \frac{40 n^2}{n*32}
|
-26,056 |
(h_1 - h_2) \cdot \left(h_1 + h_2\right) = h_1^2 - h_2^2
|
-29,486 |
10 \left(-9 - 6\right) = 10 \left(-15\right) = -150
|
17,222 |
1/2 + 1/4 + 1/8 + \cdots + \frac{1}{2^k} = \frac{1}{2^k}*\left((-1) + 2^k\right)
|
27,123 |
z^{\frac14}\cdot z^4 = z^{\frac14 + 4} = z^{17/4}
|
-20,905 |
-7/4 \cdot \frac{x + 3 \cdot (-1)}{3 \cdot (-1) + x} = \frac{21 - x \cdot 7}{x \cdot 4 + 12 \cdot (-1)}
|
29,204 |
(a + \left(-1\right)) (c + (-1)) + 1 = c a - a + c + 2
|
15,060 |
11 = 11 + 0\cdot 3^{1/2}
|
28,695 |
32\cdot x - 2\cdot 0 + 255\cdot (-1) = 0 \Rightarrow \frac{255}{32} = x
|
-205 |
\binom{7}{4} = \frac{1}{4!\cdot (7 + 4\cdot (-1))!}\cdot 7!
|
-15,842 |
-4/10\cdot 10 + \frac{6}{10}\cdot 5 = -10/10
|
19,821 |
38304 = (\frac{4}{120} + 1/4 + \dfrac{1}{6} + 1/2)*8!
|
19,970 |
{x \choose x + 2 \cdot \left(-1\right)} = {x \choose 2}
|
-1,336 |
\dfrac{\frac{1}{8}*3}{(-3)*1/7} = \frac18*3*(-7/3)
|
34,845 |
a\cdot 8 - 7\cdot a = a
|
4,652 |
-\sqrt{h} + \sqrt{x} = \frac{x - h}{\sqrt{h} + \sqrt{x}}
|
-20,953 |
8/5 x*8/\left(8x\right) = \dfrac{1}{x*40}64 x
|
34,845 |
-7 e + e*8 = e
|
-10,299 |
-\dfrac{1}{3*x + 3*\left(-1\right)}*\dfrac{5}{5} = -\frac{1}{x*15 + 15*\left(-1\right)}*5
|
7,445 |
-2 + 24*\left(-1\right) = -26 = (-1)*26
|
23,986 |
(\frac{z}{g} \cdot g)^i = g \cdot z^i/g
|
30,139 |
\left(1 = (\frac{1}{x^3} \cdot a + 1)/2 \implies x^3 = a\right) \implies x = a^{1/3}
|
250 |
i = \cos(\frac{\pi}{2}) + i \cdot \sin(\pi/2)
|
-10,358 |
4 = -2 + 4\cdot m + 6\cdot (-1) = 4\cdot m + 8\cdot \left(-1\right)
|
24,966 |
v = 2 + e^x \Rightarrow \frac{\mathrm{d}v}{\mathrm{d}x} = e^x = v + 2\cdot \left(-1\right)
|
39,097 |
(f - x)^2 = -(\varphi - h)^2 \Rightarrow (\varphi - h) \cdot (\varphi - h) + (f - x)^2 = 0
|
44,731 |
2 = \dfrac{1}{1}\cdot 2
|
32,624 |
18 \times 6 = 108
|
23,908 |
\sinh^2(x) = \frac{1}{4} \cdot \left(e^x - e^{-x}\right)^2 = \frac14 \cdot \left(e^{2 \cdot x} + e^{-2 \cdot x} - 2 \cdot e^0\right)
|
18,333 |
1/\left(y\cdot y\right) = \dfrac{1}{y \cdot y}
|
922 |
|\frac{1}{1 + i\cdot y\cdot 2}\cdot (i\cdot 2 - 3\cdot y)| = \frac{|-3\cdot y + 2\cdot i|}{|i\cdot y\cdot 2 + 1|}
|
19,194 |
k^2 + m^4 - m^2 \cdot k \cdot 2 = (-k + m \cdot m)^2
|
-9,464 |
-6\cdot p = -p\cdot 2\cdot 3
|
-2,316 |
8/15 - \frac{3}{15} = 5/15
|
16,118 |
k \neq i \Rightarrow -i + k \neq 0
|
-5,201 |
0.2 \cdot 10^{(-5) \cdot (-1) + 2} = 10^7 \cdot 0.2
|
46,338 |
\dfrac{1}{45} = 4/180
|
2,696 |
\frac{\text{d}}{\text{d}x} \dfrac{1}{z} = -\frac{1}{z^2}\frac{\text{d}z}{\text{d}x}
|
27,238 |
(-\dfrac14)^j = (-1)^j*2^{-j*2}
|
7,669 |
4\cdot (t - l) = -\left(l - t\right)\cdot 4
|
12,330 |
\tfrac{9}{3} + 5 - 0 \cdot 3 = 9/3 + 5 - 0 \cdot 3
|
12,659 |
|x - y| = y - x = \frac{y^2 - x^2}{x + y} < (y^2 - x^2)/(2\cdot x)
|
25,931 |
{12 \choose 2}*{4 \choose 1}^2*{4 \choose 3}*{13 \choose 1} = 54912
|
1,991 |
u \cdot v = v^R \cdot u = u^R \cdot v
|
30,782 |
(\tfrac1y\left(y + 2\right))^{-1/2} = (\frac{1}{y}2 + 1)^{-\frac{1}{2}}
|
6,341 |
2 = \frac{1}{3 - \frac{1}{3 - \frac{2}{3 - \frac{2}{3 + 2(-1)}}}2}2
|
8,782 |
s = r\cdot x/r \implies x = s\cdot r^2
|
840 |
2 + \dfrac{1}{\frac15 + 3} = \frac{1}{16} \cdot 37
|
2,807 |
\dfrac{1}{1 - y}\cdot (4\cdot y + 3\cdot (-1)) = -\frac{1}{y + (-1)}\cdot \left(4\cdot (y + (-1)) + 1\right) = -4 + \dfrac{1}{1 - y}
|
-1,758 |
\pi \cdot \frac{1}{12} \cdot 13 = \pi \cdot 23/12 - 5/6 \cdot \pi
|
-10,848 |
\dfrac{1}{5} \cdot 65 = 13
|
38,637 |
\frac{\mathrm{d}}{\mathrm{d}y} (9\times e^{6\times y}) = 9\times 6\times e^{6\times y} = 54\times e^{6\times y}
|
-26,686 |
10 = |10|
|
-25,239 |
d/dx \tfrac{1}{x^{12}} = -\frac{12}{x^{13}}
|
587 |
\cot{z} - 8 \cdot \cot{8 \cdot z} = \cot{z} - 8 \cdot \cot{8 \cdot z} = \cot{z} - 8 \cdot \frac{\cot^{24}{z} + \left(-1\right)}{2 \cdot \cot{4 \cdot z}}
|
29,547 |
H\cdot h = h\cdot \frac1h\cdot h\cdot H
|
41,599 |
\binom{k}{x + 1} = \tfrac{k!}{\left(k - x + (-1)\right)! \cdot (x + 1)!} = \frac{k! \cdot (k - x)}{(k - x)! \cdot \left(x + 1\right) \cdot x!} = \binom{k}{x} \cdot \frac{k - x}{x + 1}
|
4,730 |
\frac{1}{d b} (a d - c b) = a/b - \frac{c}{d}
|
4,591 |
3 k\cdot 5 = 15 k
|
8,630 |
86/100\cdot 114/100 x = x
|
28,071 |
\dfrac13 = \frac22\cdot 1/3
|
16,805 |
f^{n + N} = f^n\cdot f^N
|
-11,696 |
\dfrac{1}{25} = \left(1/5\right)^2
|
49,491 |
\sum_{k=1}^\infty \frac{4^k + k}{k + 6^k} = \sum_{k=1}^\infty \frac{\frac{4^k}{k} + 1}{\frac1k\cdot 6^k + 1}
|
27,754 |
qr^i r^k = qr^i r^k
|
44,425 |
41 + 32\times (-1) = 9
|
20,741 |
\mathbb{E}(X^2) = \mathbb{E}(X)^2 + \mathbb{E}(\left(X - \mathbb{E}(X)\right)^2)
|
32,274 |
5 + n*2 = \left(-1\right) + 2*(n + 3)
|
29,630 |
H^2 - x \times x = \left(H - x\right)\times (x + H)
|
-16,866 |
8 = 8 \cdot 4 \cdot q + 8 \cdot 3 = 32 \cdot q + 24 = 32 \cdot q + 24
|
1,340 |
21821 \times \left(3 \times 7 \times 11 \times 13\right) \times \left(3 \times 7 \times 11 \times 13\right) = 196781974389
|
24,224 |
A_k^T \cdot A_{k + (-1)}^T \cdot ... \cdot A_2^T \cdot A_1^T = (A_1 \cdot A_2 \cdot ... \cdot A_{k + (-1)} \cdot A_k)^T
|
-29,210 |
15 = (-1) + 0*3 + 4*4
|
10,913 |
\cos(y)/(\sqrt{2}) + \dfrac{1}{\sqrt{2}} \cdot \sin(y) = \cos(y - \frac{\pi}{4})
|
12,399 |
x^4 + 5 \times x + 1 = (x^2 + 1) \times (x \times x + (-1)) + 5 \times x + 5 \times \left(-1\right) = (x + (-1)) \times \left(x \times x \times x + x^2 + x + 6\right)
|
23,260 |
\cos(-v + π/2) = \sin\left(v\right)
|
17,368 |
\binom{l\times 2}{l}\times l!^2 = (l\times 2)!
|
10,149 |
\sin(\frac{13 \pi}{6}) = 1/2
|
2,925 |
540 = 3! \cdot \binom{3}{1} \cdot \binom{4}{2} \cdot \binom{5}{1}
|
19,489 |
E = E \cap (Y \cup c) = \left(E \cap Y\right) \cup \left(E \cap c\right)
|
-3,732 |
\frac{p^3}{p} = \frac{pp p}{p} = p^2
|
-6,632 |
\frac{4}{(1 + z) \cdot (z + 8)} \cdot \frac99 = \frac{1}{\left(z + 1\right) \cdot (8 + z) \cdot 9} \cdot 36
|
40,946 |
3 \beta - 2 y + z + 3 = 0 = 4 \beta - 3 y + 4 z + 1
|
1,343 |
\int_a^b 1/x\,\mathrm{d}x = \int\limits_a^b 1/x\,\mathrm{d}x
|
2,966 |
180 - -X + 180 - Z = X + Z
|
40,087 |
(2^2*3*5)^{\dfrac{1}{2}} = 2 (3*5)^{\frac{1}{2}} = 2*15^{1 / 2}
|
-10,662 |
\frac{2}{2}\cdot \left(-5/\left(6\cdot t\right)\right) = -\frac{10}{t\cdot 12}
|
-24,321 |
1 + 4 \cdot 8 = 1 + 32 = 1 + 32 = 33
|
4,215 |
5 = i - l + (-1) = i - l + 1
|
-9,022 |
131.8\% = \frac{1}{100}\cdot 131.8
|
9,176 |
\frac{x}{(x + (-1))!} = \dfrac{1}{\left(x + (-1)\right)!} \cdot (x + \left(-1\right) + 1) = \dfrac{1}{(x + 2 \cdot (-1))!} + \frac{1}{\left(x + (-1)\right)!}
|
25,096 |
\cos{2*t} = \cos^2{t} - \sin^2{t} = 1 - 2*\sin^2{t}
|
22,386 |
(1 + 1) \cdot \left(1 + 2\right) \cdot (1 + 3)/4 = 24/4 = 6
|
5,504 |
\dfrac{3 + m*4}{m*7 + 5*(-1)} = \frac{1}{7 - 5/m}*(4 + \dfrac3m)
|
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