id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
15,997 |
0 = -B + x \implies x^2 - B^2 = 0
|
16,915 |
\sin{x/2} = \cos{\frac12*(-x + \pi)}
|
13,239 |
2 + \mu \cdot \mu + y^2 + z^2\cdot 2 + 2\cdot \mu\cdot z - y\cdot 2 + z\cdot 2 = (z + \mu)^2 + (\left(-1\right) + y)^2 + \left(1 + z\right)^2
|
-4,594 |
9*(-1) + y^2 = \left(3*(-1) + y\right)*(y + 3)
|
16,085 |
h + b = b + h \Rightarrow [h,b]
|
18,837 |
80^4 = 5^4*2^{16}
|
11,840 |
(5^{1/2} - 1)/4 = \cos{\pi*2/5}
|
-16,340 |
6*80^{1/2} = (16*5)^{1/2}*6
|
40,327 |
\frac{\text{d}}{\text{d}x} |x| = \frac1x|x|
|
25,536 |
n + 2n + 3n + \cdots + n^2 \approx nn^2 = n^3
|
3,794 |
52!/(13!\cdot 39!) = 52!/(13!\cdot 39!)
|
3,407 |
(-a)^{2}-1=(a)^{2}-1
|
23,476 |
e^{\frac{3*\pi*i}{4}}*e^{\pi*i/4} = e^{\pi*i} = -1
|
-21,609 |
\sin\left(-π\cdot 5/6\right) = -0.5
|
28,124 |
2\cdot \cos(o)\cdot \sin(o) = \sin(o\cdot 2)
|
32,085 |
\left(\tan^2{x} = \dfrac{1}{\cos^2{x}} \times \sin^2{x}\Longrightarrow \frac{1}{\tan^2{x}} = \tfrac{1}{\sin^2{x}} \times \cos^2{x}\right)\Longrightarrow \frac{\sec^2{x}}{\tan^2{x}} = \frac{\cos^2{x}}{\sin^2{x}} \times \sec^2{x} = \dfrac{1}{\sin^2{x}}
|
-5,700 |
\dfrac{2}{(n + 9(-1)) \left(7(-1) + n\right)} = \dfrac{2}{n^2 - n \cdot 16 + 63}
|
14,111 |
A \cdot D \cdot v = D \cdot A \cdot v
|
34,841 |
1 = -377\cdot 1597 + 610\cdot 987
|
11,681 |
0\left(-1\right) + 0^5 = 0
|
18,824 |
A^{2\cdot l} = A^l\cdot A^l
|
-26,474 |
\left(-b + a\right)^2 = a^2 - b \cdot a \cdot 2 + b^2
|
20,834 |
\frac{1}{\dfrac{1}{X}} = X
|
9,085 |
\frac{4}{7} = \dfrac{4}{7}
|
-25,871 |
z^3 = z^5/(z z)
|
18,392 |
6\cdot x^2 + x\cdot z\cdot 11 - 35\cdot z \cdot z = (z\cdot 7 + x\cdot 2)\cdot \left(-5\cdot z + x\cdot 3\right)
|
4,160 |
k + 1 = \dfrac{1}{k!}\cdot (1 + k)!
|
3,240 |
\dfrac12 \cdot (21 + 7) = 14
|
9,627 |
3 = 3 + b \Rightarrow b = 0
|
-10,548 |
60 = 150 - 12*z + 60*(-1) = -12*z + 90
|
30,987 |
(c + b)^2 = c^2 + 2 \cdot c \cdot b + b^2 = c \cdot c + 0 \cdot c \cdot b + b^2 = c \cdot c + b^2
|
8,942 |
\dfrac12 (-\sqrt{3} i - 1) + \dfrac12 \left(\sqrt{3} i - 1\right) = -1
|
16,190 |
90000 + 27216 \cdot (-1) = 62784
|
-5,668 |
\frac{1}{3*(p + 2*(-1))}*5 = \frac{5}{p*3 + 6*(-1)}
|
33,030 |
0 = \tan^{-1}(0/\left(\sqrt{2}\right))
|
5,976 |
(9 + 1) \cdot \ln(9 + 1) + 9 \cdot (-1) = 10 \cdot \ln\left(10\right) + 9 \cdot (-1) = 10 + 9 \cdot \left(-1\right) = 1
|
36,311 |
a^n*a^m = a^{n + m}
|
28,364 |
-\frac{1}{(1 - z)^2} = -\frac{1}{(-z + 1)^2}
|
-9,208 |
20 a^3 = a*2*2*5 a a
|
1,846 |
\frac{h_2}{d \cdot h_1} = 1/(h_1) \cdot h_2/d
|
-6,712 |
\tfrac{3}{10} + \frac{2}{100} = \frac{2}{100} + \frac{30}{100}
|
23,084 |
\frac{5}{16} = \dfrac{1}{16} + 1/6 + \tfrac{1}{12}
|
-26,577 |
(8 + x) \cdot (x + 8 \cdot (-1)) = x^2 - 8^2
|
24,076 |
f^2 - g \cdot g = (f - g)\cdot (f + g)
|
31,700 |
6^3 = 210 + 6
|
4,622 |
\sum_{x=1}^\infty a*x*(5 + 2*(-1))^x = \sum_{x=1}^\infty a*x*3^x
|
20,305 |
36 = 3^4 - -1^4*3 + 2^4*3
|
47,225 |
15=3\cdot 5
|
17,176 |
{1 + k \choose k + \left(-1\right)} = {k + 1 \choose 2}
|
-10,607 |
4/4\cdot (-\frac{1}{l^2}\cdot (2 + 5\cdot l)) = -\frac{20\cdot l + 8}{4\cdot l^2}
|
-20,951 |
\dfrac{1}{k*14}(8\left(-1\right) + k*2) = 2/2 (k + 4(-1))/(7k)
|
-3,647 |
\frac{1}{s^2}\cdot s^4 = s\cdot s\cdot s\cdot s/\left(s\cdot s\right) = s^2
|
-18,458 |
x + 2 = 10\cdot \left(3\cdot x + 6\cdot \left(-1\right)\right) = 30\cdot x + 60\cdot \left(-1\right)
|
4,623 |
8 = -\left(4\cdot (-1) + 5\right) \cdot \left(4\cdot (-1) + 5\right) + 9
|
35,965 |
b+a=a+b
|
35,823 |
{100 \choose 48} = {100 \choose 52} = {100 \choose 50} \cdot \frac{2450}{51 \cdot 52} \cdot 1
|
18,135 |
(180 + z^2 + 20 z) (z^2 - z \cdot 2 + 18 \left(-1\right)) = z^4 + z^3 \cdot 18 + z^2 \cdot 122 - 720 z + 3240 (-1)
|
15,165 |
\dfrac{1}{(-D/x + 1)*x} = \frac{1}{-D + x}
|
15,888 |
2017 = 44^2 + 9^2 = (-44)^2 + 9^2 = \ldots
|
28,862 |
417*31/1000 = 31*0.417
|
7,135 |
1 > \frac13 \cdot p\Longrightarrow 3 > p
|
-9,200 |
-k \cdot 72 + 36 \cdot (-1) = -k \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 - 2 \cdot 2 \cdot 3 \cdot 3
|
-19,275 |
5\cdot 1/9/(6\cdot \dfrac15) = 5/9\cdot 5/6
|
16,211 |
(1 + z)^{1 + z} = 1 + (1 + z) z + \dotsm = 1 + z + z z + \dotsm
|
28,313 |
28/p = \tfrac7p\cdot 4/p = \frac7p
|
-6,687 |
4/10 + 4/100 = 4/100 + \frac{40}{100}
|
2,867 |
\frac{1/32}{\tfrac{1}{32}5 + 5/32}5 = \frac12
|
36,950 |
A \cdot T_2 + T_1 \cdot A = A \cdot (T_2 + T_1)
|
16,083 |
\tfrac1m*(m + 1) = \frac{1}{m} + 1
|
35,517 |
\left(1 + q + (-1)\right)^m = q^m
|
9,832 |
\frac{2!}{2^2} = 2*\frac12/2 = \dfrac12
|
3,002 |
2 \cdot \sqrt{11} = -(-\sqrt{11} + \sqrt{5} \cdot 2) + \sqrt{5} \cdot 2 + \sqrt{11}
|
4,835 |
\cos(x) \cdot x = \sin\left(x\right) \Rightarrow \tan(x) = x
|
31,753 |
R \cdot x \cdot y = x \cdot R \cdot y
|
31,103 |
a^{k + 1} = a^{k + 1}
|
32,343 |
(1 + 0\cdot (-1))\cdot (-a + b) = -a + b
|
-474 |
\frac{1}{3}\times 95\times π - π\times 30 = \frac53\times π
|
29,413 |
130 = 133 + 3\cdot (-1)
|
-1,716 |
\pi \cdot 23/12 - \frac{1}{12} \cdot \pi = 11/6 \cdot \pi
|
2,217 |
-1^5*{4 \choose 3} + 4^5 - {4 \choose 1}*3^5 + 2^5*{4 \choose 2} = \frac{4}{2!}*5!
|
-20,923 |
\frac22\cdot \frac{1}{-9}\cdot (-2\cdot n + 8) = \dfrac{1}{-18}\cdot (16 - 4\cdot n)
|
36,738 |
L \cdot A = A \cdot L
|
7,329 |
I_n\cdot b^2 + I_n\cdot a^2 = I_n\cdot (b \cdot b + a^2)
|
-20,424 |
\frac{1}{45}\cdot (5\cdot x + 25) = \tfrac15\cdot 5\cdot \frac{1}{9}\cdot (x + 5)
|
18,062 |
n^2 + n + 1 = (n + 1) \cdot (n + 1) - n
|
9,427 |
(3y)^{1/2} * (3y)^{1/2} = y*3
|
28,118 |
\frac{12!}{5!\cdot 4!\cdot 3!} = {12 \choose 5}\cdot {7 \choose 4}
|
576 |
x - g = (-g*4 + 4*x)/4
|
11,401 |
\tfrac{1}{31} + 1/31\cdot 30/30 = 2/31
|
-26,577 |
-8^2 + y^2 = \left(y + 8\right)\times (8\times (-1) + y)
|
8,021 |
4096 = 64*64
|
364 |
(r + 2\times r)\times \cot(\dfrac14\times \pi) = 3\times r
|
-435 |
(e^{7\cdot i\cdot π/4})^5 = e^{7\cdot i\cdot π/4\cdot 5}
|
-7,527 |
\frac{1}{-i + 1} \cdot \left(-1 + i \cdot 5\right) = \frac{1}{1 - i} \cdot (i \cdot 5 - 1) \cdot \dfrac{1 + i}{1 + i}
|
-389 |
\frac{4! \cdot \frac{1}{1!}}{\frac{1}{6!} \cdot 9!} = \dfrac{\frac{1}{3! \cdot \left(4 + 3 \cdot (-1)\right)!} \cdot 4!}{9! \cdot \frac{1}{\left(3 \cdot (-1) + 9\right)! \cdot 3!}}
|
13,525 |
2 \cdot i - 5 \cdot (2 + i) + 1 = -9 - i \cdot 3
|
16,676 |
\sqrt{x^2} + \sqrt{x} = x + \sqrt{x} = \sqrt{x} (\sqrt{x} + 1)
|
35,714 |
-X + z = z - X
|
14,983 |
\mathbb{E}(z_3 + z_1 + z_2) = \mathbb{E}(z_1) + \mathbb{E}(z_2) + \mathbb{E}(z_3)
|
4,318 |
2*\sin(1) = 1.683*\ldots \gt \frac85
|
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