id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-18,272 |
\dfrac{x}{(x + 7\cdot \left(-1\right))\cdot (x + 6)}\cdot (6 + x) = \frac{x^2 + x\cdot 6}{x^2 - x + 42\cdot (-1)}
|
-21,683 |
-\frac153 = -\frac{1}{5}3
|
-28,759 |
x^2 \cdot 2 - 2 \cdot x + 6 - \dfrac{23}{x + 3} = \frac{1}{3 + x} \cdot \left(2 \cdot x^3 + 4 \cdot x^2 + 5 \cdot (-1)\right)
|
32,611 |
t^{-l} = \frac{1}{t^l}
|
31,877 |
212/39 = \frac{17}{39} + 5
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-20,201 |
\frac17 \cdot 5 \cdot \tfrac{(-1) + a}{(-1) + a} = \frac{1}{7 \cdot (-1) + 7 \cdot a} \cdot (5 \cdot (-1) + 5 \cdot a)
|
-4,024 |
\tfrac{10}{3}\cdot t = t\cdot 10/3
|
-20,823 |
(80 (-1) - 60 p)/(30 p) = (8(-1) - p*6)/(3p) \frac{1}{10}10
|
-25,584 |
\frac{d}{dt} (-\frac3t) = \frac{3}{t^2}
|
15,233 |
\tfrac{1}{350} \cdot 1807 = 57/350 + 5
|
-27,710 |
\frac{d}{dz} (-\cos{z}\cdot 12) = \sin{z}\cdot 12
|
17,306 |
6\cdot (-1) + 2\cdot x^2 - 4\cdot x = -(9\cdot x - x^3\cdot 3 + 6\cdot x^2) - x^3\cdot 3 + x^2\cdot 8 + 5\cdot x + 6\cdot \left(-1\right)
|
-19,682 |
\frac45\cdot 10 = 40/5
|
54,286 |
\frac{1}{1 + 4 + 1}\cdot \left(1\cdot 2 + \frac{1}{2}\cdot 4 + 0\right) = \left(2 + 2\right)/6 = 4/6 = 2/3
|
-22,338 |
(y + 9\times (-1))\times (1 + y) = y^2 - 8\times y + 9\times (-1)
|
32,778 |
(n-2i)+(i) = (n-i)
|
18,055 |
\tfrac{1}{25}*25 = 1
|
31,082 |
1+\frac1{1+\frac1{\frac53}}=1+\frac1{1+\frac1{1+\frac23}}
|
21,880 |
1 - n + n\cdot 2 - 2\cdot n + (-1) = -n
|
4,778 |
4 + l^2 + l\cdot 4 = (l + 2) \cdot (l + 2)
|
-24,216 |
8 \times (10 + 5) = 8 \times 15 = 120
|
-5,970 |
\frac{4}{5 \cdot y + 40} = \frac{1}{(y + 8) \cdot 5} \cdot 4
|
-11,136 |
\left(x + 9\cdot (-1)\right)^2 + b = (x + 9\cdot (-1))\cdot (x + 9\cdot (-1)) + b = x^2 - 18\cdot x + 81 + b
|
7,349 |
det\left(k\cdot C\right) = k^{29}\cdot det\left(C\right) = k\cdot det\left(C\right)
|
5,146 |
\tfrac{1}{t + 1} = 1 - t + t^2 - \frac{1}{1 + t} t^3
|
5,663 |
\frac{1}{b\cdot R} = 1/(R\cdot b) \implies R\cdot b = R\cdot b
|
-3,070 |
3^{1 / 2} \cdot 8 = (1 + 5 + 2) \cdot 3^{\tfrac{1}{2}}
|
5,808 |
\binom{n}{2} \binom{n + 2 \left(-1\right)}{l}/(\binom{n}{l}) = \binom{-l + n}{2}
|
23,420 |
q = \frac{1}{3} + \frac{2}{3} (\dfrac{1}{3} + \dfrac{q}{3}) = 5/9 + \frac{2}{9} q
|
-1,600 |
2 \cdot \pi - 5/12 \cdot \pi = \pi \cdot 19/12
|
253 |
\sin(\frac{1}{12}) = \sin(-\frac{1}{4} + \frac{1}{3})
|
15,017 |
\frac{1}{1 + e^{-z}} = \dfrac{e^z}{e^z + 1}
|
13,258 |
17 = 563 + 546 \cdot (-1) = g - 4 \cdot a - 5 \cdot a - g = 2 \cdot g - 9 \cdot a
|
21,132 |
x\cdot y^2 + t\cdot y + s = (1 + 4\cdot k)\cdot \pi \Rightarrow -\pi\cdot (1 + k\cdot 4) + y \cdot y\cdot x + t\cdot y + s = 0
|
24,512 |
( z_k^1, z_k^2, z_k^3 \dotsm) = z_k
|
8,459 |
d/dx \sqrt{x} = 1/\left(\sqrt{x}*2\right)
|
7,805 |
\dfrac14*3*\int A^{-1/3}\,\text{d}A = (\int \tfrac{1}{A^{1/3}}\,\text{d}A)*\tfrac34
|
-5,456 |
\frac{2}{10 + 2 \cdot m} = \frac{2}{2 \cdot (5 + m)}
|
-1,650 |
\pi \dfrac{1}{12}11 + \pi \cdot 4/3 = 9/4 \pi
|
27,331 |
\left(a + d\right)^3 = a^3 + 3\cdot a^2\cdot d + a\cdot d \cdot d\cdot 3 + d \cdot d \cdot d
|
8,832 |
|\bar{y}^2/y| = |\bar{y}|^2/|y| = \frac{|y|^2}{|y|} = |y|
|
12,353 |
-3 \times y \times z + \left(-z + x\right)^2 + (x - 3 \times y)^2 + 2 \times x^2 = x^2 \times 4 + 9 \times y^2 + z^2 - 6 \times x \times y - 3 \times y \times z - 2 \times x \times z
|
35,442 |
\sum_{n=2}^\infty \frac{14^n}{3^{3n+4}(3n+7)}\leq\sum_{n=2}^\infty \frac{14^n}{7\cdot 3^{3n+4}}=\frac{1}{7}\sum_{n=2}^\infty \frac{14^n}{3^4\cdot 27^n}=\frac{1}{7\cdot 81}\sum_{n=2}^\infty \left(\frac{14}{27}\right)^n
|
-26,148 |
-4\cdot 25^{\frac12\cdot 3} - -4\cdot 0^{\frac32} = -500 + 0 = -500
|
32,420 |
2 \cdot (5 \cdot n + 11) + n + 2 = 24 + 11 \cdot n
|
-18,332 |
\frac{1}{(10 + y)\cdot (3 + y)}\cdot (y + 10)\cdot y = \frac{10\cdot y + y^2}{30 + y \cdot y + 13\cdot y}
|
28,659 |
2*\cos^2(Z) + (-1) = \cos\left(Z*2\right)
|
1,912 |
\binom{m}{r} = \dfrac{1}{r!*(m - r)!}*m!
|
-12,557 |
172 + 123 (-1) = 49
|
29,236 |
h^k \cdot h^x = h^{x + k}
|
-20,580 |
\frac{1}{10 \cdot n + 10 \cdot \left(-1\right)} \cdot (n \cdot 5 + 15 \cdot (-1)) = 5/5 \cdot \frac{3 \cdot (-1) + n}{2 \cdot \left(-1\right) + n \cdot 2}
|
9,494 |
z \cdot 3 + z + (-1) = z \cdot 4 + (-1)
|
28,779 |
1 + i_1 = 21 \implies 20 = i_1
|
2,301 |
j^2\cdot 32 = \dfrac{1}{2}\cdot \left(j\cdot 8\right)^2
|
28,535 |
d^{m + 1} = d^m\cdot d^1
|
11,426 |
\|X\| = \|X + F - F\| \leq \|X + F\| + \|F\|
|
27,878 |
g^{k_1}*g^{k_2} = g^{k_1 + k_2}
|
21,479 |
\frac12 \lt \dfrac{1}{y^2 + 1}y\Longrightarrow 0 \gt (y + (-1))^2
|
7,694 |
200 = (300 \cdot (-1) + 500 - 200 + 0)/2 + 200
|
-20,400 |
-\frac{1}{n*9 + 90*\left(-1\right)}*63 = -\frac{1}{10*\left(-1\right) + n}*7*9/9
|
32,787 |
R_b \cdot R_a = R_b \cdot R_a
|
-7,562 |
\frac{1}{41}(60 - 130 i + 48 i + 104) = \frac{1}{41}(164 - 82 i) = 4 - 2i
|
-4,026 |
x^2/3 = \frac13 \cdot x \cdot x
|
27,716 |
7^B = (1 + 6)^B
|
-12,686 |
40 = 112 \cdot (-1) + 152
|
4,684 |
\dfrac{1}{4} = (-1/2)^2
|
12,948 |
\left(\sqrt{T} \cdot 2 = T \implies T^2 = T \cdot 4\right) \implies -T \cdot 4 + T^2 = 0
|
10,433 |
-\dfrac12 = \cos(2\pi/5) + \cos(\pi\cdot 4/5)
|
-13,757 |
2 + \frac{1}{6} 24 = 2 + 4 = 2 + 4 = 6
|
32,371 |
bg + bh + gh = ((g + h + b)^2 - h \cdot h + b^2 + g^2)/2
|
6,375 |
\frac{1}{d}\cdot K\cdot A\cdot \epsilon_0 = C \Rightarrow \epsilon_0\cdot \frac{K}{d}\cdot A = C
|
-1,987 |
\pi = \pi*\frac{7}{12} + \pi*5/12
|
7,046 |
\frac{3^2\cdot 7\cdot 11\cdot 19}{13\cdot 17\cdot 50\cdot 49} = \tfrac{13167}{541450}
|
52,616 |
\sqrt{y^2-2y}-y=\left(\sqrt{y^2-2y}-y\right)\cdot\frac{\sqrt{y^2-2y}+y}{\sqrt{y^2-2y}+y}
|
-24,170 |
\tfrac{66}{7 + 4} = \frac{1}{11} \cdot 66 = 66/11 = 6
|
15,711 |
\sin(x+\pi)=-\sin x
|
-2,174 |
2/14 = -\frac{3}{14} + 5/14
|
39,604 |
65536 = 4096\times 2^4
|
-474 |
\pi\cdot 95/3 - 30\cdot \pi = \pi\cdot 5/3
|
20,693 |
g \cdot b = t \cdot f \Rightarrow t = g \cdot b/f
|
-5,462 |
\frac{2}{3\cdot r + 30} = \frac{1}{(10 + r)\cdot 3}\cdot 2
|
27,833 |
1/17 + \dfrac{1}{16} \cdot 2 = 1/16 + \frac{1}{16} + 1/17
|
3,223 |
\sum_{r=0}^n a^r \cdot b^{n - r} = \sum_{r=0}^n (\frac{a}{b})^r \cdot b^n = b^n \cdot \sum_{r=0}^n (a/b)^r
|
13,385 |
2\cdot \pi = 6\cdot \pi/3
|
-25,581 |
\frac{d}{dt} (2t^3 + 6) = 3 \cdot 2t^2 = 6t^2
|
-2,117 |
-\pi/3 = 19/12\cdot \pi - 23/12\cdot \pi
|
16,038 |
13*(3 * 3^2*5)^2 = 236925
|
29,211 |
y^d \cdot y^c = y^{c + d}
|
-22,277 |
x^2 - 13\cdot x + 30 = (x + 10\cdot (-1))\cdot (x + 3\cdot (-1))
|
4,138 |
y^2 + 2\cdot y + 3 = \frac{1}{(-1) + y}\cdot \left(3\cdot (-1) + y^3 + y \cdot y + y\right)
|
37,348 |
1 + \dfrac{17}{24} = 41/24
|
-503 |
-\pi\cdot 6 + \frac{1}{12}\cdot 77\cdot \pi = 5/12\cdot \pi
|
3,893 |
3\cdot c_1 + x\cdot 6 = 0 \implies -x\cdot 2 = c_1
|
24,921 |
\frac{1}{2 + 3 + (-1)}*(3 + \left(-1\right)) = 2/4 = 1/2
|
19,674 |
a^2 - 2xa + x \cdot x = (-x + a) \cdot (-x + a)
|
-11,500 |
12 + 8 - i \cdot 10 = -10 \cdot i + 20
|
19,240 |
(-1/3 + \frac{1}{2})\cdot 5 = \tfrac{1}{2}\cdot 3 - 2/3
|
31,451 |
x + |1|*c_2 = 0 \Rightarrow x = -c_2
|
4,458 |
\sigma\times g_2/\sigma\times g_1 = \dfrac{g_1}{\sigma}\times \sigma\times \sigma\times g_2/\sigma
|
21,152 |
62/132 = \tfrac{31}{66}
|
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