id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
16,035 |
-6/5 + \tfrac43 = \dfrac{1}{15}\cdot 2
|
11,392 |
(c - f) (f + c) = -f f + c c
|
-26,459 |
\left(3 \cdot z\right)^2 = z \cdot z \cdot 9
|
10,386 |
(a + f)/6 = (f + c)/7 = \frac{1}{8}\cdot (c + a) = \dfrac{1}{6 + 7 + 8}\cdot (a + f + f + c + c + a) = (a + f + c)/10.5
|
23,427 |
4\cdot 3/2 = 1 + 2 + 3
|
32,468 |
\sin{x} \lt 0 rightarrow \sin{x} = -\frac{3}{\sqrt{13}}
|
29,822 |
\sin{w} = 2\cdot \cos{w/2}\cdot \sin{\frac{w}{2}}
|
8,616 |
\frac{x}{g} = \tfrac{x}{g}
|
9,774 |
1 = y \cdot \frac{1}{z} \cdot y^2 \cdot z^2 = y \cdot z \cdot y^4 \cdot z \cdot y/z = y \cdot \frac{z}{z} \cdot z \cdot y^{16} \cdot y = z \cdot y^{21}
|
12,953 |
11\cdot (10 + z) = z + 160 \Rightarrow 160 + z = 110 + z\cdot 11
|
-5,309 |
0.45\cdot 10^{\left(-1\right)\cdot (-1) + 5} = 0.45\cdot 10^6
|
30,968 |
\operatorname{asec}(2) = \pi/3
|
33,988 |
10 + 140 - 50 + 30 \implies 70 = 10 + 60
|
33,912 |
-\cos{Z}*\sin{C} + \cos{C}*\sin{Z} = \sin(-C + Z)
|
19,339 |
1/6 = 1/6\cdot 2/2
|
19,671 |
\sum_{k=1}^n (-k! + (k + 1)!) = \sum_{k=1}^n (1 + k)! - \sum_{k=1}^n k!
|
22,161 |
0 = (1 - \tfrac{1}{a\cdot c})\cdot \left(c - a\right) = \dfrac{1}{a\cdot c}\cdot (c - a)\cdot \left(a\cdot c + \left(-1\right)\right)
|
-20,896 |
\frac{1}{10}\times 3\times \left(-2/(-2)\right) = -6/(-20)
|
22,600 |
(L + 1)/3 = L \implies \tfrac12 = L
|
6,234 |
(2/l + 1)^{3l} = ((1 + 2/l)^l)^3
|
7,508 |
\left(x + Y\right)\cdot v = x\cdot v + Y\cdot v
|
20,059 |
-\sin{x} = \cos(\pi/2 + x)
|
-16,498 |
\sqrt{175}*2 = \sqrt{25*7}*2
|
-24,443 |
9 + 6\cdot 8 = 9 + 48 = 9 + 48 = 57
|
34,432 |
\dfrac{1}{1 - \frac{b}{y}} \cdot (\frac{1}{y} \cdot b + 1) = \frac{1}{y - b} \cdot (y + b)
|
10,643 |
|b_n a_n - LM| = |b_n a_n - a_n M + a_n M - LM|
|
-7,532 |
\frac{1}{3}\cdot (-12\cdot i + 6) = -i\cdot 12/3 + \frac13\cdot 6
|
31,375 |
0 = \frac{4}{a^3} + \tfrac{2}{a} - \frac{1}{a^2} \cdot b = \frac{1}{a^3} \cdot \left(4 + 2 \cdot a^2 - b \cdot a\right)
|
28,900 |
3^{n + 1} + (-1) = 3\cdot 3^n + (-1) = 2\cdot 3^n + 3^n + \left(-1\right)
|
8,570 |
-3^{1/2}/3 + 1 = 1 - \frac{1}{3^{1/2}}
|
51,853 |
6 \Rightarrow 1
|
6,661 |
v \cdot 2 \cdot 3 \cdot u = u \cdot v \cdot 6
|
1,445 |
j^2 + j + 1 = 0 \Rightarrow -j = 1 + j^2
|
27,754 |
r^i\cdot q\cdot r^j = q\cdot r^i\cdot r^j
|
4,313 |
26*1/9/(13*1/9) = 2 = Y \Rightarrow 2 = Y
|
-2,110 |
-\frac{5}{3} \pi + \pi*17/12 = -\frac{\pi}{4}
|
17,186 |
1 - u^2 = \left(1 - u\right) \left(u + 1\right)
|
-18,369 |
\frac{1}{t^2 + 10 t}\left(t^2 + t + 90 \left(-1\right)\right) = \frac{1}{(10 + t) t}(9(-1) + t) (t + 10)
|
14,025 |
(7 + n) \cdot \binom{n + 6}{n} = \binom{7 + n}{n} \cdot 7
|
-22,283 |
y^2 - 3y - 70 = (y + 7)(y - 10)
|
-25,510 |
\frac{d}{dx} (\dfrac{4}{x + 2}) = -\dfrac{4}{(2 + x)^2}
|
2,272 |
s_n - s \lt \epsilon \Rightarrow s_n < \epsilon + s
|
-9,211 |
2\cdot 5\cdot 11 - 3\cdot 3\cdot 11 l = -99 l + 110
|
44,392 |
\cos(\pi - \theta) = -\cos\left(-\theta\right) = -\cos\left(\theta\right)
|
14,466 |
\frac{f_1}{f_1 - f_2} = \tfrac{0(-1) + f_1}{f_1 - f_2}
|
10,364 |
0 = y^p + (-1) = (y + \left(-1\right))^p
|
19,674 |
a^2 - b*a*2 + b * b = (-b + a)^2
|
-28,950 |
(3 + n)*(3*\left(-1\right) + n) = 9*(-1) + n^2
|
-6,023 |
\frac{2}{(5 \cdot \left(-1\right) + n) \cdot (10 + n)} = \dfrac{2}{n^2 + 5 \cdot n + 50 \cdot (-1)}
|
547 |
-\frac{1}{5}2 = -\frac{2}{5}
|
32,606 |
x\cdot \tau = x\cdot \tau
|
6,836 |
\tfrac{1}{\beta \cdot x} = \frac{1}{x \cdot \beta}
|
30,036 |
\frac{1}{d^2} \cdot x^2 = r rightarrow x^2 = d^2 \cdot r
|
18,920 |
(e/2)^n = e^n\cdot (\frac12)^n
|
16,601 |
a^{g + c} = a^c*a^g
|
12,637 |
6\cdot 5^m + 6\cdot (-1) - 5^m + 5 = \left(-1\right) + (6 + \left(-1\right))\cdot 5^m
|
-20,614 |
\frac{-q \times 21 + 49 \times (-1)}{28 \times (-1) - q \times 12} = \frac{1}{-3 \times q + 7 \times (-1)} \times (-q \times 3 + 7 \times \left(-1\right)) \times 7/4
|
39,091 |
800 = 6400*13\%
|
-764 |
0 + \dfrac{6}{10} + 5/100 + 9/1000 + \frac{1}{10000}\cdot 0 = 6590/10000
|
-20,157 |
\dfrac{z + 8}{z + 8}\cdot (-\tfrac{1}{10}\cdot 7) = \frac{56\cdot (-1) - 7\cdot z}{80 + 10\cdot z}
|
40,729 |
-(x - y) = -x + y
|
-5,098 |
\frac{6.5}{10000} = 6.5/10000
|
-10,277 |
30 = 10 t + 16 + 50 (-1) = 10 t + 34 (-1)
|
30,362 |
(-t + 1) \cdot (1 + t) = 1 - t^2
|
-29,363 |
(y + 4) \cdot (y + 6) = y^2 + 6 \cdot y + 4 \cdot y + 24 = y^2 + 10 \cdot y + 24
|
10,592 |
\frac{717}{999} - 71/99 = (717\cdot ((-1) + 100) - (1000 + (-1))\cdot 71)/(99\cdot 999)
|
22,530 |
E(Q - \theta) = E(Q) - E(\theta) = E(Q) - \theta
|
27,807 |
\dfrac{x^2 + (-1)}{x + (-1)} = \frac{\left(x + (-1)\right) (x + 1)}{x + (-1)} = x + 1
|
28,520 |
1 + z + z^2 + \dotsm*z^{m + (-1)} = \dfrac{1}{1 - z}*(1 - z^m) = \dfrac{1}{1 - z} - \frac{1}{1 - z}*z^m
|
19,168 |
\frac{n \cdot n}{(1 + n - l)^2} - \dfrac{1}{1 + n - l}\cdot n = \frac{n}{(n - l + 1)^2}\cdot \left(l + (-1)\right)
|
5,365 |
x = 16\cdot x_1^4\cdot x_2^4\cdot \ldots\cdot x_r^4 + 1 = (2\cdot x_1\cdot x_2\cdot \ldots\cdot x_r)^4 + 1
|
-5,889 |
\frac{1}{4\cdot (y + 9\cdot (-1))}\cdot 3 = \frac{3}{36\cdot \left(-1\right) + 4\cdot y}
|
24,908 |
v\cdot w^3 = v \Rightarrow 0 = (w^3 + \left(-1\right))\cdot v
|
4,824 |
-(-\dfrac138 + 5)^2 + 9 = \frac1932
|
129 |
\cos(13*\pi/7) = \cos\left(\pi/7\right)
|
21,472 |
Cov(y_1,y_2) = \mathbb{E}(y_1 \cdot y_2) - \mathbb{E}(y_1) \cdot \mathbb{E}(y_2) = \mathbb{E}(y_1 \cdot y_2)
|
-2,679 |
\sqrt{12} + \sqrt{75} = \sqrt{4 \cdot 3} + \sqrt{25 \cdot 3}
|
31,127 |
\dfrac{1}{4 \cdot n} \cdot \operatorname{Var}\left(B^2\right) = \frac{-E\left(B^2\right)^2 + E\left(B^4\right)}{n \cdot 4}
|
11,841 |
(-f + g) \left(g + f\right) = -f^2 + g^2
|
16,343 |
10 \cdot 10 \cdot 8 \cdot 8 \cdot 8 = 51200
|
-15,997 |
5/10 \cdot 9 - \tfrac{1}{10} \cdot 5 \cdot 7 = 10/10
|
15,199 |
-\dfrac{1}{5 \cdot (\dfrac45 + (-1))} = -1/(5(-1/5)) = 1
|
-8,907 |
(-3) (-3) (-3) = -3^2 * 3
|
1,234 |
\alpha,x,x \geq \alpha\Longrightarrow x*\alpha = x
|
32,276 |
2 \cdot 1 - 1^3 = 1
|
23,834 |
16 \cdot (z^2 + 16) = 100 \cdot z^2 \Rightarrow 256 = 84 \cdot z^2
|
18,083 |
-3*(1 + 2 + 3 + 4 + 5 + \cdots) = 1/4
|
21,898 |
y + (-1) = (y + (-1))\times (y + 1) \Rightarrow 1 = 1 + y
|
15,324 |
2^x\times 5^y\times 6^z = 2^x\times 5^y\times 2^z\times 3^z = 2^{x + z}\times 3^z\times 5^y
|
24,780 |
(4^n + 2)*3 = 3*4^n + 6
|
12,782 |
\frac{1}{4}(9 + 1) + \frac{1}{9}(4 + 1) = 5/2 + 5/9 \neq \mathbb{N}
|
-17,274 |
-\frac{48}{13} = -\frac{48}{13}
|
-20,054 |
\frac{81 + x\times 18}{9\times x + 9\times (-1)} = 9/9\times \tfrac{1}{x + (-1)}\times (9 + x\times 2)
|
39,418 |
100 = 50 \cdot (-1) + 150
|
20,743 |
\dfrac{1}{2}\cdot 6 = 3
|
10,440 |
{x + 3 + (-1) \choose 3 + (-1)} = {x + 2 \choose 2} = (x + 2) (x + 1)/2
|
2,854 |
(7^2)^{10*m} = (50 + (-1))^{10*m} = (1 + 50*(-1))^{10*m}
|
8,275 |
\dfrac{1}{i + 2} \cdot (2 \cdot i^4 + 1) = 1 = i^2
|
-20,576 |
\frac{-16*n + 16}{n*10 + 10*(-1)} = \dfrac{1}{n*2 + 2*\left(-1\right)}*(2*n + 2*(-1))*(-8/5)
|
15,894 |
m\times g\times k'\times x = m\times g\times x\times k'
|
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