id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
25,013
|
\sqrt{h_2^2 + h_1^2} = \left(h_2^2 + h_1^2\right)^{1/2}
|
22,270
|
1 = [h,f] \Rightarrow ( f h, f^2) = f
|
-16,412
|
3\sqrt{48} = 3\sqrt{16 \cdot 3}
|
15,659
|
\dfrac{2}{45} = \dfrac{4}{90}
|
29,925
|
k \cdot 625 + 125 = (k \cdot 5 + 1) \cdot 5^3
|
-17,917
|
18 = 25 (-1) + 43
|
32,727
|
\left(c \cdot 14 + c \cdot 2 + c \cdot 2 + 4c + 8c = 1 \Rightarrow 1 = 30 c\right) \Rightarrow 1/30 = c
|
-2,594
|
275^{\tfrac{1}{2}} - 99^{\frac{1}{2}} = (25\cdot 11)^{1 / 2} - (9\cdot 11)^{1 / 2}
|
19,276
|
π \cdot r \cdot r \cdot π \cdot X \cdot 2 = 2 \cdot π^2 \cdot X \cdot r \cdot r
|
36,175
|
\alpha \cdot \left(y + z\right) = \alpha \cdot z + \alpha \cdot y
|
19,455
|
\frac{40}{120} = \frac13 = \frac26
|
2,358
|
( x, y, t)\cdot ( x', y', t') = ( x, y, t)\cdot ( x', y', t')
|
8,415
|
n*0.25*(b*2)^2 = b^2*n
|
4,988
|
\left(2017 + 1\right)/2 = 1009
|
13,537
|
4\cdot x = 2\cdot x + 1 + 2\cdot x + (-1)
|
10,732
|
\frac{1}{28}3 = -\frac{1}{28}25 + 1
|
32,957
|
f^{b + c} = f^b f^c
|
30,740
|
\frac{1}{y - a} = \frac{1}{y\cdot (1 - a/y)}
|
39,166
|
y^x + (-1) = (\left(-1\right) + y) \cdot \left(1 + y + \ldots + y^{(-1) + x}\right)
|
2,972
|
((-1) + 26^2)^{1 / 2} + 26 = 26 + 3^{1 / 2}\cdot 15
|
-22,270
|
(r + 5) \cdot (r + 10) = r^2 + r \cdot 15 + 50
|
15,140
|
(t^{2 \cdot f})^{1/2} = (t^f \cdot t^f)^{1/2} = |t^f|
|
26,600
|
AB=A'B' \Rightarrow (A')^{-1}AB=B'
|
21,420
|
1.75 = \frac{1}{4}*3 + 1/2 + \dfrac14*2
|
-3,198
|
\sqrt{6}*\sqrt{25} + \sqrt{6}*\sqrt{4} = \sqrt{6}*5 + 2*\sqrt{6}
|
9,349
|
\frac{8}{3} + 2 + 4 = \frac{1}{3} \cdot 26
|
-13,047
|
9/13 = \dfrac{18}{26}
|
47,882
|
324 = 314 + 10
|
-3,129
|
9\cdot 3^{\dfrac{1}{2}} = (4 + 5)\cdot 3^{1 / 2}
|
20,909
|
8*(\sin(-\pi)*i + \cos\left(-\pi\right)) = -8
|
-10,114
|
1 = 10/10 = \frac{0*0.01}{1} = 10/100 = 10^{-1}
|
-29,451
|
(-10.74)*(-11) = v - \left(-11\right)*(-11) = v
|
-1,412
|
-24/15 = \frac{\left(-24\right) \cdot \frac{1}{3}}{15 \cdot \dfrac{1}{3}} = -8/5
|
4,827
|
\lim_{y \to 0^+} 1/y - 1 + (-1) = \int\limits_0^1 \dfrac{1}{y \cdot y}\,dy + (-1)
|
-4,147
|
t\cdot \frac{6}{11} = \frac{t\cdot 6}{11}
|
-10,322
|
\dfrac{5}{p*10 + 6}*5/5 = \frac{25}{p*50 + 30}
|
23,282
|
A/B + C/D = (C\cdot B + D\cdot A)/(B\cdot D)
|
7,011
|
\frac{{8 \choose 5} \cdot 1024}{{32 \choose 5}} \cdot 1 = 256/899
|
21,959
|
\dfrac{1}{\left(-1\right) + 98} \times ((-1) + 98^4) \times 52 = 9944 \times 9945/2
|
19,880
|
\dfrac14*(1 + 1 + 1 + 0) = 3/4
|
-10,267
|
-\frac{1}{4\cdot (-1) + y}\cdot \left(y\cdot 3 + 3\cdot \left(-1\right)\right)\cdot 15/15 = -\frac{1}{60\cdot (-1) + y\cdot 15}\cdot \left(45\cdot (-1) + 45\cdot y\right)
|
-21,018
|
-\frac72*\frac{3*(-1) + p}{3*\left(-1\right) + p} = \frac{1}{2*p + 6*(-1)}*(21 - p*7)
|
8,805
|
-(W_{2\cdot s} - W_s) + W_{2\cdot t} - W_t = -(-W_s + W_t) + W_{t\cdot 2} - W_{2\cdot s}
|
12,030
|
\frac13*2/3 = \dfrac29
|
5,294
|
y^4 - 6y^2 \cdot y + 12 y^2 - 12 y + 4 = (y^2 - 3y + 2)^2 - y^2 = (y^2 - 4y + 2) (y \cdot y - 2y + 2)
|
14,258
|
(2 \cdot n + 3) \cdot n + 1 = 2 \cdot n^2 + 3 \cdot n + 1 = \left(2 \cdot n + 1\right) \cdot \left(n + 1\right)
|
31,533
|
48 = \dfrac15 (3 (-1) + 3^5)
|
13,731
|
{l + t + (-1) \choose t + (-1)} = {l + t + (-1) \choose l}
|
29,246
|
(-b + d) \cdot (b + d) = -b \cdot b + d^2
|
31,642
|
n\cdot \cos(n\cdot y + A) = \frac{\partial}{\partial y} \sin\left(y\cdot n + A\right)
|
10,021
|
h^2 - d^2 = (-d + h)\cdot (h + d)
|
20,072
|
x - a = -(a - x)
|
-15,276
|
\frac{b}{\frac{1}{p^{10}}\cdot b^8} = \frac{1}{(\dfrac{b^4}{p^5})^2\cdot 1/b}
|
2,370
|
\varepsilon^{-2/3} = \varepsilon^{2 \cdot (-1) + \frac{1}{3} \cdot 4}
|
4,285
|
(\frac1K + 1)/n = \frac{1}{n} + 1/(n\cdot K)
|
20,081
|
m^2 + 2 \cdot m + 3 \cdot \left(-1\right) = 0 = m^2 + m + 6 \cdot (-1)
|
35,009
|
1 + z^8 + z = z^8 - z^5 + z^5 + z + 1
|
12,091
|
25 \cdot π = 45 \cdot π/2 + 10 \cdot \frac14 \cdot π
|
-22,418
|
2 + 10\cdot (-1) = -8
|
5,294
|
z^4 - 6\cdot z^3 + 12\cdot z^2 - 12\cdot z + 4 = \left(z \cdot z - 3\cdot z + 2\right)^2 - z^2 = (z^2 - 4\cdot z + 2)\cdot (z \cdot z - 2\cdot z + 2)
|
-22,367
|
(8\cdot (-1) + x)\cdot (x + 6) = x \cdot x - 2\cdot x + 48\cdot \left(-1\right)
|
17,248
|
\left(z_1 = \arcsin\left(3 - z_2 \cdot z_2\right) \Rightarrow 3 - z_2^2 = \sin{z_1}\right) \Rightarrow (-\sin{z_1} + 3)^{1/2} = z_2
|
19,134
|
280 = 20 (-1) + (120 + 20 (-1))*3
|
17,448
|
1 + (x^2 + 1) (x^4 + x * x + (-1)) = x^6 + x^4*2
|
-22,996
|
\frac{110}{33} = 10*11/(3*11)
|
2,259
|
\frac{6}{1 + 6/2} = \frac{3}{2}
|
24,031
|
n n n = {n \choose 1} + {1 + n \choose 3}*6
|
1,287
|
\frac{1}{-61^3 + 1049^2 \cdot 1049}\cdot (1823^3 - 1699^3) = 1
|
18,824
|
B^{n*2} = B^n B^n
|
27,650
|
\frac{6^2\cdot 2}{6^3} = \dfrac{1}{3}
|
-10,451
|
-25 = 35 + q + 1 = q + 36
|
17,626
|
T\cdot U = T\cdot U\cdot (Z + x) = T\cdot U\cdot Z + T\cdot U\cdot x
|
-25,716
|
\frac{d}{dr} (-2\cdot \sin\left(r + 1\right)) = -2\cdot \cos(1 + r)
|
-13,120
|
424 = \tfrac{1}{0.7} \cdot 296.8
|
8,805
|
-(Q_{q*2} - Q_q) + Q_{2x} - Q_x = Q_{x*2} - Q_{q*2} - Q_x - Q_q
|
19,213
|
\frac{\mathrm{d}}{\mathrm{d}z} \arctan(\tanh{z}) = \frac{\frac{\mathrm{d}}{\mathrm{d}z} \tanh{z}}{1 + \tanh^2{z}}
|
8,973
|
L' - \frac{1}{\sin{L'} + 1}\times (L' - \cos{L'}) = L'
|
-30,848
|
\frac{y^2}{y + 4} = \frac{y^3 - 4 \cdot y^2}{16 \cdot (-1) + y^2}
|
21,046
|
(-l, l) = \left(-l,l\right)
|
1,167
|
\frac{x}{(-1) + l} \cdot \frac1l \cdot \left(l - x\right) = \frac{1}{l \cdot l - l} \cdot \left(-x^2 + x \cdot l\right)
|
36,744
|
1.75 + 0\left(-1\right) = 1.75
|
37,545
|
0.00046 = \dfrac{1}{1000}\cdot 0.46
|
15,315
|
(-\alpha)^{1 / 2}\cdot i = i\cdot i\cdot \alpha^{1 / 2}\cdot \dots
|
41
|
-2^2 + 4^2 = h^2 \Rightarrow h = \sqrt{12}
|
-639
|
(e^{\frac{\pi\cdot i}{6}\cdot 7})^5 = e^{5\cdot i\cdot \pi\cdot 7/6}
|
12,535
|
\tfrac{a^x}{a^n} = a^{x - n}
|
11,363
|
22 = 1 + 7 + 7 + 7
|
-17,456
|
1 = 16 + 15 \cdot \left(-1\right)
|
2,123
|
Hb f = bHf
|
-2,478
|
3\cdot \sqrt{7} + 4\cdot \sqrt{7} + \sqrt{7}\cdot 2 = \sqrt{7}\cdot \sqrt{9} + \sqrt{16}\cdot \sqrt{7} + \sqrt{7}\cdot \sqrt{4}
|
15,372
|
a_2 + a_1 = (a_2/2 + \frac{a_1}{2})\cdot 2
|
37,508
|
\sqrt{g} \cdot \sqrt{g} = g
|
41,085
|
10 = \dfrac12\cdot 4\cdot 5
|
27,731
|
\left((-1) + n\right)^2 = n \cdot n - n \cdot 2 + 1
|
-1,896
|
\frac{\pi}{6} + \pi \cdot 5/12 = \frac{7}{12} \cdot \pi
|
-20,902
|
\frac{12 \cdot z}{4 \cdot z + 12 \cdot (-1)} = 4/4 \cdot \frac{3 \cdot z}{z + 3 \cdot (-1)}
|
-13,014
|
\frac{3}{4} = 12/16
|
26,839
|
e^{a + x} = e^a\times e^x
|
14,417
|
\frac{1}{\ln(1 + z)} = \frac{1}{z\cdot (1 - \dfrac{1}{2}\cdot z - \frac13\cdot z^2 + z^3/4 + ...)}
|
12,379
|
n^2 + 3 \cdot n = n^2 + n + 2 \cdot n = 2 \cdot {n + 1 \choose 2} + 2 \cdot n
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.