id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
8,016
|
\binom{4}{1}\cdot \binom{4}{1}\cdot \binom{2}{1}\cdot \binom{10}{1} + 8 = 328
|
-10,609
|
\frac{1}{12 \cdot x + 8} \cdot 12 = \frac{3}{x \cdot 3 + 2} \cdot \frac{4}{4}
|
-24,673
|
21 i - 92 = -5 + 20 i - 87 + i
|
5,556
|
\binom{6 + 4 + \left(-1\right)}{4 + (-1)} = 84
|
22,888
|
\left(6 = 2*(z + y) \Rightarrow 3 = z + y\right) \Rightarrow -z + 3 = y
|
18,012
|
bx^k/b = (b\frac{x}{b})^k
|
4,634
|
\int\limits_0^∞ y^2 \cdot e^{(\left(-1\right) \cdot y^2)/2}\,\mathrm{d}y = \int\limits_0^∞ (-e^{\dfrac12 \cdot \left(\left(-1\right) \cdot y \cdot y\right)})\,\mathrm{d}y
|
-16,378
|
3 \sqrt{25*7} = \sqrt{175}*3
|
11,876
|
(\pi \cdot \left(-3\right))/4 = \frac{\pi}{4}5 - \pi \cdot 2
|
-9,378
|
-2*5*11 - t*2*5*7 = -t*70 + 110*(-1)
|
18,669
|
\left(x + 3*(-1)\right)*\left(x + 5\right) - (x + 4)*(x + 5*(-1)) = x^2 + 2*x + 15*(-1) - x * x - x + 20*(-1) = 3*x + 5
|
26,303
|
(4 - \sqrt{15})^{1/3} (4 + \sqrt{15})^{\frac{1}{3}} = 1
|
34,595
|
A^x \cdot B = B \cdot A^x
|
10,926
|
64 = x \cdot x - y^2 = (x + y) \cdot \left(x - y\right)
|
18,163
|
\sin{z}*\cos{z} = \frac12*\sin{z*2}
|
26,102
|
a_m + a_{m + (-1)} + \dots + a_2 + a_1 = a_1 + a_2 + \dots + a_{m + (-1)} + a_m
|
-1,505
|
7/8 \cdot \frac18 \cdot 7 = \tfrac{7 \cdot 1/8}{\frac17 \cdot 8}
|
30,805
|
66 = 12!/(10!*2!)
|
4,547
|
20\cdot x^3 + 17\cdot (-1) = 77\cdot (-1) + (3 + x^3)\cdot 20
|
29,226
|
\frac{2}{3} \cdot x = (x + 1)/3 + \frac13 \cdot (x + (-1))
|
-26,406
|
\frac{1}{729*9^{12}} = 9^{-3 + 12 (-1)} = \frac{1}{205891132094649}
|
32,976
|
z^{t + s} = z^t z^s
|
-26,739
|
\sum_{n=1}^\infty \frac{\left(n + 5\right)*(-5)^n}{n * n*5^n} = \sum_{n=1}^\infty \frac{\left(-1\right)^n*5^n}{n^2*5^n}*(n + 5) = \sum_{n=1}^\infty (-1)^n*\frac{1}{n^2}*\left(n + 5\right)
|
17,140
|
(g \cdot f)^2 = g^2 \cdot f^2
|
20,326
|
f \cdot x^3 = f \cdot x^3
|
22,299
|
\cos(x\cdot 2) = 1 - 2 \sin^2(x)
|
5,318
|
w_2^3 = (3 + 2^{1/3})^3 = 29 - 27 \cdot w_2 + 9 \cdot w_2^2 \cdot w_2
|
41,512
|
\frac{1}{1!*1!*1!}3! = 6
|
17,843
|
\dfrac{1}{9^2 + 11 \left(-1\right)}9\cdot 8/9 = 4/35 \approx 0.114285714285714
|
-27,335
|
\frac{\cos^2(x) \cdot 3}{-\sin(x) \cdot 2 + 2} = \left(1 + \sin(x)\right) \cdot 3/2
|
-23,252
|
4/5\cdot \dfrac{2}{7} = 8/35
|
-20,078
|
\dfrac{4}{4} (-r*5 + 4(-1))/\left(\left(-4\right) r\right) = \tfrac{16 (-1) - r*20}{(-16) r}
|
21,830
|
3 - \frac12 = \frac{6}{2} - \dfrac12 = 5/2
|
25,536
|
k + 2 \cdot k + 3 \cdot k + \dotsm + k^2 \approx k \cdot k \cdot k = k^3
|
19,475
|
2240 + 1876 \cdot (-1) + 324 + 240 + 96 \cdot (-1) + 4 + 4 \cdot (-1) = 832
|
22,117
|
2 \times n^2 + 4 \times n + 1 = (1 + n) \times (n + 1) + n \times \left(2 + n\right)
|
33,814
|
t r = t r
|
17,276
|
Y\cdot L\cdot b + a\cdot L\cdot V = \left(b\cdot Y + V\cdot a\right)\cdot L
|
-20,889
|
\frac{4 - 10\cdot k}{-k\cdot 2 + 20} = 2/2\cdot \frac{1}{-k + 10}\cdot (-k\cdot 5 + 2)
|
17,054
|
(w \cdot w + 3(-1)) (2(-1) + w^2) = w^4 - w^2 \cdot 5 + 6
|
-3,399
|
\sqrt{7}*\left(5 + 3 + (-1)\right) = 7\sqrt{7}
|
-18,360
|
\frac{x^2 + x*8 + 9 (-1)}{x^2 - x} = \frac{(x + (-1)) (9 + x)}{x*(x + (-1))}
|
-3,757
|
\dfrac{96}{120\cdot z^3}\cdot z^3 = 96/120\cdot \dfrac{1}{z^3}\cdot z^3
|
8,607
|
(n^2 - n + 1) \times (n + 1) = n \times n \times n + 1
|
24,648
|
\frac{\pi\cdot 7}{8} = -\pi/8 + \pi
|
40,574
|
0(-1) + 1 = 1
|
17,683
|
3^{1 / 2} - 2^{\frac{1}{2}} + 2^{1 / 2} + 3^{1 / 2} = 3^{\frac{1}{2}}*2
|
22,833
|
xb d = xbd
|
-5,540
|
\frac{5}{3 \cdot (q + 2)} = \frac{5}{3 \cdot q + 6}
|
-22,760
|
\frac{1}{56}*84 = 28*3/(28*2)
|
5,250
|
1 + 2^0 + 2^1*\dotsm*2^{n + \left(-1\right)} + 2^n = 2*2^n = 2^{n + 1}
|
-22,231
|
(4 + n)\times \left(6\times (-1) + n\right) = 24\times (-1) + n^2 - 2\times n
|
8,111
|
{k \choose g} + {k \choose g + 1} = {k + 1 \choose g + 1}
|
17,695
|
((-1) + z^2) \cdot ((-1) + z^2) = (1 + z) \cdot ((-1) + z) \cdot (z + 1) \cdot (z + (-1))
|
1,374
|
a\cdot b\cdot d = (a\cdot b + 1)\cdot d = (a\cdot b + 1)\cdot d + 1 = a\cdot b\cdot d + d + 1
|
2,388
|
a^{k_1 + k_2} = a^{k_1} a^{k_2}
|
26,544
|
{8 \choose 2} = \dfrac{8*7}{2} = 28
|
19,626
|
|1/y - 1/3| = \frac{1}{3y}|y + 3(-1)| < \dfrac{1}{6}|y + 3(-1)|
|
-10,899
|
88/4 = 22
|
19,453
|
-\sin{x}\cdot i + \cos{x} = \sin{-x}\cdot i + \cos{-x}
|
-16,700
|
-3 = -3 (-2 x) - 21 = 6 x - 21 = 6 x + 21 \left(-1\right)
|
22,126
|
\frac{1}{1 + l} + 1 = \frac{2 + l}{1 + l}
|
-22,328
|
(9 + q) \cdot \left(q + 7\right) = 63 + q^2 + 16 \cdot q
|
26,084
|
-1 = 0/8 - 1 + 0 + 0/2 + 0/4
|
6,717
|
1 - \cos{4*x} = 2*\sin^{22}{x} = 8*\sin^2{x}*\cos^2{x} = 8*\left(1 - \cos{x}\right)*\left(1 + \cos{x}\right)*\cos^2{x}
|
13,220
|
\left(4 \lt \sqrt{17} \Rightarrow -\sqrt{17} - 1 < -5\right) \Rightarrow -1 > (-1 - \sqrt{17})/4
|
-13,351
|
\frac{1}{1 + 4}*50 = 50/5 = 50/5 = 10
|
-2,090
|
\frac{1}{6}\pi - \frac{4}{3}\pi = -\frac{7}{6}\pi
|
14,655
|
1/6 = \tfrac{1}{6^2} \cdot 6
|
19,847
|
135.966 = 2.666\times 51
|
7,229
|
1 = \lim_{n \to \infty}(1 + \frac1n) = \lim_{n \to \infty}\left(1 + \frac{1}{n}\cdot 2\right)
|
43,298
|
110334 = 2\times 3\times 7\times 2627
|
-27,832
|
d/dx (-3\cot(x)) = -3d/dx \cot(x) = 3\csc^2(x)
|
-20,867
|
\frac{80}{8 \cdot x + 80} \cdot x = \frac{1}{8} \cdot 8 \cdot \frac{10 \cdot x}{10 + x}
|
-1,897
|
\pi\cdot \dfrac{1}{6}\cdot 7 + \frac{\pi}{12} = 5/4\cdot \pi
|
17,922
|
\frac{14}{9} + 4\sqrt{10}/9 = \frac19(\sqrt{10}\cdot 4 + 14)
|
38,663
|
\|z\| = \|z*z\| = |z|*\|1\|
|
45,493
|
2 + 2 * 2 + 2 * 2 * 2 + \ldots + 2^x = 2*\left(1 + 2 + 2 * 2 + \ldots + 2^{x + (-1)}\right) = 2*\frac{2^x + (-1)}{2 + (-1)} = 2^{x + 1} + 2*\left(-1\right)
|
-22,961
|
8\cdot 10/(7\cdot 10) = 80/70
|
-3,565
|
\tfrac1m \frac{10}{3} = \frac{10}{3 m}
|
27,298
|
( g_1 g_2, e_2 e_1) = ( g_1 g_2, e_1 e_2)
|
6,279
|
\sin^2{y} = \frac{1}{5}\cdot 4 + \frac{1}{5}\cdot (\sin{y} - \cos{y}\cdot 2)\cdot (\cos{y}\cdot 2 + \sin{y})
|
21,155
|
\dfrac{1 - x^2}{1 - x} = x^0 + x^1
|
11,918
|
(x^{\dfrac{1}{2}} \cdot W^{1/2})^2 = W \cdot x
|
47,729
|
2*\operatorname{atan}(\frac{1}{\phi^{\dfrac{3}{2}}}) = \operatorname{atan}(\tfrac{2*\phi^{\frac12*3}}{\phi^3 + \left(-1\right)}) = \operatorname{atan}\left(\phi^{\frac{1}{2}}\right)
|
29,837
|
c_1 \left( 1, 0\right) + c_2 ( 1, 1) = ( c_1 + c_2, c_2) = \left\{0\right\} \Rightarrow c_1 = c_2 = 0
|
16,121
|
-\frac{108}{2^7} + 1 = \dfrac{20}{2^7}
|
20,998
|
-a^2 + b^2 = (-a + b)*\left(b + a\right)
|
-1,809
|
\pi*\frac{2}{3} - \pi/12 = 7/12*\pi
|
27,159
|
\left(x + \frac1x = 1 \Leftrightarrow 0 = 1 + x^2 - x\right) rightarrow x^2 \cdot x + 1 = (x + 1)\cdot (x^2 - x + 1) = 0
|
9,242
|
\frac{1}{1 + 2\cdot q}\cdot (q + 3\cdot (-1)) = \frac{-3/q + 1}{2 + 1/q}
|
33,222
|
b \cdot b + a^2 - a \cdot b \cdot 2 = (a - b)^2
|
-25,483
|
-3 \cdot \sin{y} + 8 \cdot y = d/dy (4 \cdot y^2 + 3 \cdot \cos{y})
|
18,590
|
\sin{\frac{1}{2}\left(\pi*(-3)\right)} = 1
|
51,377
|
1 + 1/2 + 1/4 + 1/4 + \dfrac18 + \frac{1}{8} + \frac18 + 1/8 + \dotsm = 1/2 + 1 + \frac12 + 1/2
|
18,665
|
3 \cdot 37 = (10^{\dfrac{1}{2}} + 11) (11 - 10^{\frac{1}{2}})
|
-22,987
|
\frac{32}{24} = \dfrac{32}{3 \cdot 8}1
|
16,004
|
{x \choose m} = \frac{x!}{m! \cdot (-m + x)!}
|
-4,148
|
96\cdot x^3/(12\cdot x) = x^3/x\cdot \dfrac{1}{12}\cdot 96
|
-3,341
|
\sqrt{3} \cdot (4 + 2 \cdot (-1)) = 2 \cdot \sqrt{3}
|
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