id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-19,707 |
6*9/(7) = \dfrac{54}{7}
|
27,869 |
x\cdot r/s = \tfrac11\cdot x\cdot r/s = \frac{x}{s}\cdot r
|
33,843 |
\frac{1}{36}11 = 1100/3600
|
6,706 |
-1/t + t = (-b + a)^2 \Rightarrow |-b + a| = \sqrt{t - 1/t}
|
26,541 |
1.001*2^{-6}=2^{-6}+2^{-9}=0.017578125
|
10,250 |
\left(l + (-1)\right) \cdot l! \cdot (\frac{1}{l!} + ... + \dfrac{1}{l} + 1) = \left((-1) + l\right) \cdot \left(1! + 2! + ... + l!\right)
|
8,675 |
\tfrac{1}{h \cdot b} = \frac{1}{h \cdot b} = \frac{1}{b \cdot h}
|
33,336 |
-\frac{256}{9 \cdot (r + 4)} + \frac{625}{9 \cdot (5 \cdot (-1) + r)} = \dfrac{41 \cdot r + 420}{r^2 - r + 20 \cdot (-1)}
|
51,002 |
(-1) + x^{10} = \left(x + (-1)\right) \cdot (1 + x^4 + x^3 + x^2 + x) \cdot \left(1 + x^4 - x \cdot x^2 + x^2 - x\right) \cdot (x + 1)
|
-22,399 |
6 + 10\cdot (-1) = -4
|
40,163 |
y' z + xy u + x' z = xy u + zx' + y' z + uz
|
-18,314 |
\tfrac{1}{(n + 1) (n + 7\left(-1\right))}(1 + n) (n + 3(-1)) = \frac{3(-1) + n^2 - 2n}{7(-1) + n^2 - 6n}
|
34,573 |
A^0\cdot B^k\cdot B^0\cdot A^l = A^l\cdot B^k
|
-5,180 |
0.6 \cdot 10^{12 + 5\left(-1\right)} = 10^7 \cdot 0.6
|
32,314 |
d\cdot d^{d + (-1)} = d^d
|
19,388 |
(i^2 + d^2) \left(f^2 + g * g\right) = (gi + fd)^2 + (gd - if)^2
|
23,841 |
\|x\|^4 = \|x\|^2 \cdot \|x\|^2
|
19,087 |
d = d + 0 \cdot 0
|
14,914 |
(c + g) \cdot (c + g)^k = (c + g)^{k + 1}
|
17,390 |
\dfrac{1}{5}\cdot 53 = 1 + \frac15\cdot 48
|
27,420 |
-(b \times 9 + g)^2 \times 80 + (80 \times b + 9 \times g)^2 = -b^2 \times 80 + g^2
|
12,526 |
(\frac{1}{2})^4 + (\frac{1}{2})^4 = \frac{2}{16} = \frac{1}{8}
|
10,669 |
e = e + 0*i
|
-22,213 |
18 + x^2 - x\cdot 11 = (x + 9(-1)) \left(x + 2(-1)\right)
|
36,556 |
2^{k + 1} = 2^1 \cdot 2^k
|
8,334 |
2 = 1^2 + 1 * 1 = (1 + i)*(1 - i)
|
15,360 |
4 + k \cdot 4 = 4 + k \cdot 4
|
33,186 |
\binom{n}{r + (-1)} \cdot (n - r + (-1))/r = \binom{n}{r + (-1)} \cdot \frac{1}{r} \cdot (n + 1 - r)
|
-26,648 |
81*p^8 + 100*(-1) = \left(9*p^4\right) * \left(9*p^4\right) - 10^2
|
14,791 |
( dg', xh) = ( g', x) ( d, h)
|
21,574 |
A Q = Q A
|
-18,138 |
48 + 30 \cdot (-1) = 18
|
-3,358 |
(1 + 2)\times 13^{\frac{1}{2}} = 13^{1 / 2}\times 3
|
-2,416 |
6^{1/2} \cdot (3 + 1) = 4 \cdot 6^{1/2}
|
11,949 |
\dfrac{38\cdot 2}{7} = \frac{76}{7}
|
24,851 |
{\left(-1\right) + 28 + 5 \choose 28} = {28 + 5 + (-1) \choose \left(-1\right) + 5}
|
41,450 |
Q^Q \leq (2^Q)^Q = 2^{Q\cdot Q} = 2^Q
|
5,951 |
(y + z)*x = x*y + z*x
|
9,415 |
1 = 1^{1/2} = (e^{2 \cdot \pi \cdot i})^{\dfrac12} = e^{\pi \cdot i} = -1
|
11,242 |
9/48 + 3/54 = \frac{3}{16} + 1/18 = \dotsm
|
5,646 |
(-7 + 89^{1/2})/4 = \tfrac{1}{4} \cdot 89^{1/2} - \dfrac{7}{4}
|
14,088 |
r = x \frac1r/(y*1/r) \frac{x}{r} = x^2/(y r)
|
-3,800 |
\dfrac{q \cdot 7}{4q^4}1 = \frac{q}{q^4} \cdot 7/4
|
9,442 |
\cos^2{\theta} = \frac{1}{2}\cdot \left(\cos{\theta\cdot 2} + 1\right)
|
-10,743 |
-\frac{21}{9\times p + 15\times (-1)} = -\dfrac{7}{p\times 3 + 5\times (-1)}\times \tfrac{3}{3}
|
12,613 |
1 + y = 1 + y^2/2 + y - \frac12 \times y^2
|
31,519 |
x\cdot f^Y\cdot c = x\cdot c\cdot f^Y
|
-12,015 |
4/5 = \frac{t}{8 \cdot π} \cdot 8 \cdot π = t
|
31,925 |
A - B \cup C = A \cap B \cup C^\complement = B^\complement \cap (A \cap C^\complement) = C^\complement \cap (A \cap B^\complement) = A - B - C
|
4,105 |
(\int\limits_0^{\pi/2} 1\,\mathrm{d}z)\cdot 3 = \int_0^{\frac32\cdot \pi} 1\,\mathrm{d}z
|
-17,636 |
54 + 22\times (-1) = 32
|
-19,459 |
\frac{1}{1/6} \cdot \dfrac{5}{3} = 5/3 \cdot \dfrac61
|
5,530 |
\frac{1}{\left(-1\right) + y}*(y + 1)*\left((-1) + y\right) = 1 + y
|
12,625 |
(b + a) \cdot (b + a) = a \cdot b \cdot 2 + a \cdot a + b^2
|
5,471 |
\frac12\cdot \left(-\sqrt{5} + 1\right) = -\tfrac{1}{2}\cdot \sqrt{5} + 1/2
|
-10,753 |
12/12\cdot \dfrac{8}{3\cdot y} = \frac{96}{36\cdot y}
|
32,359 |
\frac14 \cdot (20 + 30 + 10 + 5) \cdot \frac{1}{4} \cdot (5 + 6 + 100 + 4) = 16.25 \cdot 28.75 = 467.18
|
18,540 |
3^{2\cdot n} + (-1) = 9^n + \left(-1\right) = (8 + 1)^n + (-1)
|
7,608 |
(s\cdot t)^2 = s^2\cdot t^2
|
18,142 |
(\cos{I*2} + 1)/2 = \cos^2{I}
|
-20,250 |
\frac{10}{-5} = -\frac{5}{-5} \cdot (-2/1)
|
-16,488 |
7 \cdot 9^{1 / 2} \cdot 2^{1 / 2} = 7 \cdot 3 \cdot 2^{\frac{1}{2}} = 21 \cdot 2^{\frac{1}{2}}
|
-23,104 |
--\frac13 \times 4 \times 3 = 4
|
8,991 |
5 (3 (-1) + x^2) = 15 (-1) + x^2 \cdot 5
|
36,032 |
-\cos{\theta}*3 + 4\cos^3{\theta} = \cos{3\theta}
|
22,837 |
m + 2 \left(-1\right) + m + (-1) = 3 (-1) + 2 m
|
9,598 |
Y^l*Y^l = Y^{2*l}
|
-17,206 |
\dfrac{1}{\sec^2{\theta}}*\sec^2{\theta} = \dfrac{1}{\sec^2{\theta}}*(1 + \tan^2{\theta})
|
-30,264 |
\tfrac{1}{y + 3} \cdot \left(y \cdot y + 6 \cdot y + 9\right) = \frac{1}{y + 3} \cdot \left(y + 3\right)^2 = y + 3
|
-3,573 |
\frac{z}{z^4} = z/(z*z*z*z) = \frac{1}{z^3}
|
1,375 |
1/\left(x\times f\right) = 1/(f\times x)
|
-20,068 |
\tfrac{x\cdot (-45)}{x\cdot (-20)} = \frac{x\cdot (-5)}{\left(-1\right)\cdot 5\cdot x}\cdot \frac{9}{4}
|
-2,946 |
13^{1/2}\cdot (3 + 5) = 13^{1/2}\cdot 8
|
16,565 |
\frac{5}{2} \cdot \frac{1}{3} \cdot 2 = \frac53
|
-6,231 |
\frac{3 \cdot (p + 8)}{15 \cdot (p + 3 \cdot (-1)) \cdot (p + 8)} = \dfrac{\frac{1}{3 \cdot (8 + p)} \cdot 3 \cdot \left(8 + p\right)}{(p + 3 \cdot (-1)) \cdot 5} \cdot 1
|
37,803 |
Z \cdot X = Z \cdot X
|
77 |
a^4 + b^4\cdot 4 = (a^2 - 2 a b + b b\cdot 2) (a a + 2 a b + 2 b^2)
|
30,842 |
\frac{1}{2}\cdot a\cdot a=\frac{a^{2}}{2}
|
14,632 |
\left|{A Z}\right| = \left|{Z A}\right|
|
-22,346 |
Z^2 - 13 Z + 36 = (4 (-1) + Z) (Z + 9 (-1))
|
-5,768 |
\frac{z*2}{\left(z + 9\right) \left(z + 5\right)} = \frac{2z}{45 + z^2 + 14 z}
|
29,310 |
-\cot\left(\dfrac{\pi}{2} + x\right) = \tan{x}
|
3,230 |
\int d*d*|W|/(d*|W|)\,\mathrm{d}W = \int d\,\mathrm{d}W
|
6,866 |
-x + (-1) = (x^2 + x)/\left(x*\left(-1\right)\right)
|
-20,086 |
4/1 \cdot \frac122 = 8/2
|
22,456 |
E[U\cdot 2] = 2E[U]
|
15,685 |
(x + 1)\cdot \left(x + 2\right)\cdot (x + 3)\cdot (x + 4) = (x^2 + 5\cdot x + 5 + 1)\cdot \left(x^2 + 5\cdot x + 5 + (-1)\right) = (x^2 + 5\cdot x + 5)^2 - 1 \cdot 1
|
16,129 |
f = \frac{f!}{((-1) + f)!}
|
1,901 |
\frac{4}{\sqrt{2} + 2} = \frac{\sqrt{2} \cdot 2}{2 + \sqrt{2}} \cdot \sqrt{2}
|
-15,336 |
\frac{k*y}{(y^5*k^3)^2} = \frac{y*k}{k^6*y^{10}}
|
-20,250 |
10/(-5) = -\frac{5}{-5}*(-2/1)
|
-23,201 |
\frac12 \cdot 27 = \dfrac32 \cdot 9
|
-18,264 |
\dfrac{1}{m^2 + m \cdot 6} \cdot \left(54 \cdot (-1) + m^2 - 3 \cdot m\right) = \frac{(m + 6) \cdot (9 \cdot (-1) + m)}{m \cdot (m + 6)}
|
41,458 |
(-2)\cdot 10 + 21 = 1
|
4,058 |
k\cdot f\cdot d/d = \frac{f}{d}\cdot d\cdot k\cdot d/d
|
11,884 |
1 + \dfrac{x}{(-x + 1)^2} = 1 + x + 2*x^2 + 3*x * x * x + \dots
|
24,289 |
5 * 5*6^4 \binom{5}{3} \binom{9}{4}*4^3 = 2612736000
|
-28,939 |
2 = \frac12 \times 4
|
27,219 |
(n + 6 \cdot (-1)) \cdot 8/2 = 24 \cdot (-1) + n \cdot 4
|
22,409 |
2*s^2 - 2*s + 1 = d^2 - n^2 = (d + n)*\left(d - n\right) = \left(101 - 2*s\right)*(d - n)
|
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