id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
18,064
|
2*x + 4 + x^2 + 3*(-1) = x * x + 2*x + 1
|
-23,013
|
\dfrac{50}{40} = \dfrac{5 \cdot 10}{ 4\cdot 10}
|
6,828
|
x\cdot \pi = \frac{\pi}{3}\cdot r \Rightarrow x\cdot 3 = r
|
10,799
|
\dfrac{1}{1 - t} + \frac{1}{-t/2 + 1} (1/2 (-1)) = \dfrac{1}{-2 + t} - \frac{1}{-1 + t}
|
-1,811
|
7/4 \pi - \pi*0 = \pi*7/4
|
-2,827
|
\sqrt{5}\cdot \sqrt{16} + \sqrt{25}\cdot \sqrt{5} = \sqrt{5}\cdot 4 + \sqrt{5}\cdot 5
|
-22,208
|
p^2 - 9p + 18 = (p + 3\left(-1\right)) (p + 6(-1))
|
-20,012
|
\frac{5}{8}\cdot \dfrac{5 + 3\cdot k}{5 + k\cdot 3} = \frac{1}{24\cdot k + 40}\cdot (25 + k\cdot 15)
|
34,930
|
f\cdot g = \frac{1}{2}\cdot \left(\left(g + f\right)^2 - f^2 - g^2\right)
|
14,753
|
\frac{1}{p_j \cdot p_k} \cdot (p_k + p_j) = 1/(p_j) + \frac{1}{p_k}
|
13,183
|
1 > \tfrac49
|
8,961
|
B \cdot A + D \cdot B - D \cdot A = -D \cdot A + A \cdot B + D \cdot B
|
-4,332
|
\frac{x}{x^4}\cdot 28/70 = \dfrac{28\cdot x}{70\cdot x^4}\cdot 1
|
36,300
|
\frac{1}{2}18 = 9 = 3^2
|
13,837
|
\frac{1}{(n + 2\cdot (-1))!}\cdot n! = n\cdot ((-1) + n)
|
-3,786
|
\frac3p = \tfrac{1}{p} \cdot 3
|
26,624
|
\left(-1\right) + z \cdot 2 = \left(z - 1/2\right) \cdot 2
|
12,311
|
\sin(z + r) = \sin(z) \cos(r) + \sin(r) \cos\left(z\right)
|
24,166
|
\cos(y) = \cos\left(y + \pi\times 2\right)
|
-20,914
|
5/5*\frac{1}{\left(-5\right)*z}*(-6*z + 9) = \dfrac{1}{z*(-25)}*(-z*30 + 45)
|
32,637
|
0 = c^7 + 1 = \left(c + 1\right) \cdot \left(c^6 - c^5 + c^4 - c^3 + c^2 - c + 1\right)
|
-5,457
|
\frac{1}{(r + 3)\cdot \left(r + 3\right)}\cdot r = \dfrac{1}{r^2 + 6\cdot r + 9}\cdot r
|
7,102
|
(16^3)^{\frac14} = 16^{3/4}
|
27,867
|
z^4 + z + 1 = (z + b)\cdot (z + b^2)\cdot (z + b^4)\cdot (z + b^8) = (z + b)\cdot (z + b^2)\cdot \left(z + b + 1\right)\cdot (z + b^2 + 1)
|
34,233
|
30 = (2 \cdot 2 + 2 \cdot 3) \cdot 3
|
1,433
|
5/7\cdot 1/(9\cdot 10)\cdot 6/8\cdot 24\cdot 3 = 3/7
|
25,984
|
{6 \choose 3} + 7*7*6 + 2{7 \choose 3} = 384
|
3,539
|
y^2 + (-1) = \left(y + 1\right)\times (y + (-1))
|
9,596
|
1/16 = \frac{\frac{1}{2}}{2}\cdot \dfrac12\cdot \frac12
|
10,527
|
4 \cdot h \cdot b = -\left(h - b\right)^2 + (h + b) \cdot (h + b)
|
-6,590
|
\frac{2\cdot a}{(a + 5\cdot (-1))\cdot (4\cdot (-1) + a)} = \frac{2\cdot a}{a^2 - 9\cdot a + 20}
|
-20,573
|
\frac{1}{-3}\cdot (x + 1)\cdot \dfrac18\cdot 8 = (x\cdot 8 + 8)/(-24)
|
31,567
|
\left(252 + 8 + 30\right)/20 = 14.5
|
-10,149
|
0.01 \cdot (-64) = -\tfrac{64}{100} = -16/25
|
35,179
|
\frac{1}{54}*25 = \frac{3600}{7776}
|
-4,651
|
\frac{4}{x + 2 \cdot (-1)} - \frac{1}{x + 5 \cdot \left(-1\right)} = \tfrac{3 \cdot x + 18 \cdot (-1)}{10 + x \cdot x - 7 \cdot x}
|
641
|
250 = e + 2*e + 3*e + 10 \Rightarrow e = 40
|
39,230
|
1 - \sin{2*A}*\tan{A} = 1 - 2*\sin^2{A} = \cos{2*A}
|
20,732
|
(Y*t^{1/3})^3 = t*Y^3
|
15,023
|
\dfrac{1}{z + y} = \frac{1}{z^2 - y^2}(z - y)
|
8,529
|
\tan(\operatorname{acot}(x)) = 1/\cot(\operatorname{acot}(x)) = \dfrac{1}{x}
|
-17,307
|
0.433 = \frac{1}{100}\cdot 43.3
|
9,240
|
6 = \dfrac14 \cdot 4!
|
-3,050
|
160^{1/2} - 40^{1/2} = (16*10)^{1/2} - (4*10)^{1/2}
|
25,398
|
z^{11/2} = z^{1 / 2} z^5
|
18,053
|
\mathbb{E}[C_F] \mathbb{E}[C_G] = \mathbb{E}[C_F C_G]
|
20,341
|
2 \cdot 2 \cdot 53 = 212
|
-22,453
|
100^{-3/2} = (1/100)^{3/2} = ((1/100)^{1/2})^2 \cdot (1/100)^{1/2}
|
13,026
|
R*\psi = R*\psi
|
-10,714
|
-\frac{1}{z\cdot 100 + 100}(z\cdot 40 + 140 (-1)) = 20/20 (-\frac{2z + 7(-1)}{5 + z\cdot 5})
|
-2,520
|
\sqrt{9\cdot 5} + \sqrt{5} = \sqrt{45} + \sqrt{5}
|
-19,309
|
\frac{\frac{1}{2}*9}{1/7} = 9/2*7/1
|
5,605
|
(-\dfrac{1}{e} + e^1)/2 = \sinh{1}
|
18,568
|
36 = (\alpha x + \alpha z + xz)*2 + x^2 + \alpha^2 + z^2 \Rightarrow \alpha x + \alpha z + xz = 9
|
34,840
|
E[X\cdot \chi_G] = E[\chi_G\cdot X]
|
5,968
|
\frac{1}{x + 2}\cdot (x \cdot x + 4) + 2\cdot (-1) = \frac{1}{x + 2}\cdot (x^2 + 4 - 2\cdot x + 4\cdot (-1)) = \frac{1}{x + 2}\cdot \left(x^2 - 2\cdot x\right)
|
6,764
|
x^2 - 6\cdot x + 2 = (x + 3\cdot (-1))^2 + 7\cdot (-1)
|
6,230
|
(2/3)^3 = q^3 r^2 \cdot r \Rightarrow \frac{8}{27 r^3} = q^3
|
29,128
|
6^2 = 2*2*9
|
18,726
|
8 = (\sqrt{a a + b^2})^3\Longrightarrow \left(a^2 + b^2\right)^3 = 8^2 = (2^3)^2 = 2^6
|
1,529
|
\sin(\frac{\pi}{2} + t) = \cos{\pi/2} \cdot \sin{t} + \cos{t} \cdot \sin{\dfrac{\pi}{2}}
|
12,172
|
-\cos{J} = \sin{J \cdot 0} - \cos{J}
|
37,948
|
10^l = 2^l \cdot 5^l
|
16,923
|
-y^5 + 2 \cdot y + 3 = -y^5 + 5 \cdot y^4 \cdot y + 3 = 4 \cdot y^5 + 3 = 0 \Rightarrow y^5 = -3/4
|
7,868
|
x = e*x/e
|
26,693
|
\varnothing = \left( 1, 0\right) \cdot ( 1, 0) = ( 1, 1) \cdot ( 1, 0)
|
-15,636
|
\frac{(\dfrac{1}{x^4})^5}{\frac{1}{p \cdot p \cdot p} \cdot 1/x} = \dfrac{1}{x^{20} \cdot \dfrac{1}{x \cdot p^3}}
|
-23,120
|
7 \cdot 1/4/2 = 7/8
|
-5,176
|
10^3*0.69 = 0.69*10^{7 + 4*(-1)}
|
22,165
|
h_2^h h_2^{h_1} = h_2^{h_1 + h}
|
-15,100
|
\frac{k^4}{\frac{1}{\frac{1}{q^4}*k^{16}}} = \frac{1}{\frac{1}{k^{16}}*q^4}*k^4
|
13,854
|
R_j \cdot R_k = R_j \cdot R_k
|
27,354
|
t^0 \cdot t = t
|
14,278
|
{l_2 \choose l_1} + {l_2 \choose (-1) + l_1} = {l_2 + 1 \choose l_1}
|
17,771
|
25 \cdot \frac15 \cdot 4 \cdot \frac45 = 16
|
5,257
|
\dfrac12(f + a) = f_1 \Rightarrow a < f_1 \lt f
|
11,824
|
x \cdot w_2 \cdot w_1 = x \cdot w_2 \cdot w_1
|
3,922
|
(y + x\times 3)\times (x\times 2 + y) = x^2\times 6 + 5\times y\times x + y \times y
|
-6,422
|
\dfrac{1}{x \cdot 5 + 50} = \frac{1}{5 \cdot (10 + x)}
|
4,743
|
1 + 2\cdot (-1) + 3 + 4\cdot \left(-1\right) + 5\cdot \dotsm = \dfrac{1}{4}
|
-20,152
|
\tfrac{3}{7}\cdot \frac{l + 8\cdot (-1)}{l + 8\cdot (-1)} = \frac{3\cdot l + 24\cdot \left(-1\right)}{56\cdot (-1) + 7\cdot l}
|
15,678
|
d_n = \left(d_{n + \left(-1\right)} + a\right)/2 \Rightarrow a < d_n < d_{n + \left(-1\right)}
|
19,825
|
l^2 = \left(l + 3\right) (l + 2) - 5\left(l + 2\right) + 4
|
29,486
|
\left(x \cdot 3 + c \cdot 2\right) \cdot (-2 \cdot x + c) = -x^2 \cdot 6 + 2 \cdot c^2 - x \cdot c
|
7,571
|
1024 + 4\cdot (-1) + 60\cdot \left(-1\right) = 960
|
2,939
|
5 = |7\times (-1) + 2|
|
17,696
|
\operatorname{atan}(-2) = \operatorname{atan}\left(\frac{2}{-1}\right)
|
9,394
|
6\cdot K + z\cdot 15 = 3\cdot (2\cdot K + 5\cdot z)
|
28,461
|
26 = 5^2 + 1 * 1 = 4^2 + 3^2 + 1^2 = 3^2 + 3^2 + 2^2 + 2^2
|
9,557
|
(\frac29)^{\left(-1\right) + 1} \cdot b_1 = b_1
|
-1,694
|
\frac54 π - π/4 = π
|
10,687
|
0 = \frac1z \implies 1 = 0 \cdot z
|
20,099
|
\left(z_1 + z_2\right) \cdot \left(z_1 + z_2\right) - 2 \cdot z_2 \cdot z_1 = z_1^2 + z_2^2
|
14,394
|
z \cdot z = \frac{z^{12}}{z^{10}}
|
31,921
|
\sum_{n=1}^\infty \frac{n}{n + 1}*t^n = \sum_{n=1}^\infty t^n - \sum_{n=1}^\infty \frac{t^n}{n + 1} = \frac{1}{1 - t} - \sum_{n=1}^\infty \frac{t^n}{n + 1}
|
24,518
|
\dfrac{1}{1 + 1/z} = \frac{z}{z + 1}
|
7,407
|
-\frac1d\times c + \frac{a}{x} = \frac{1}{d\times x}\times (d\times a - x\times c)
|
5,147
|
\left(3 \cdot y + 1\right)^4 \cdot (15 \cdot y + 1 + 3 \cdot y) = \left(y \cdot 3 + 1\right)^4 \cdot \left(1 + 18 \cdot y\right)
|
-1,708
|
\frac23 π - π\tfrac{1}{3}2 = 0
|
39,735
|
\sqrt{2} + 1 = \sqrt{2} + 1
|
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