id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
9,756 |
s*A^Y = \left(s*A\right)^Y = (s*I*A)^Y = A^Y*s*I
|
-1,060 |
-\dfrac{4}{5} \cdot \frac{1}{5}2 = \frac{2}{\frac{1}{4} (-5)}\frac{1}{5}
|
7,501 |
x^{2^l} = (x^2)^{2^{l + (-1)}} = \left(x + 1\right)^{2^{l + (-1)}} = x^{2^{l + \left(-1\right)}} + 1
|
5,710 |
\frac{1}{1 + n^2 + n} = \frac{1}{1 + (1 + n)^2 - 1 + n}
|
1,827 |
(n + 1)^3 + 2\cdot (n + 1) = n^3 + 3\cdot n^2 + 5\cdot n + 3 = n^3 + 2\cdot n + 3\cdot \left(n \cdot n + n + 1\right)
|
-26,992 |
\sum_{n=1}^\infty \frac{\left(0 + 4\right)^n}{n \cdot 4^n} = \sum_{n=1}^\infty \dfrac{1}{n \cdot 4^n} 4^n = \sum_{n=1}^\infty \frac{1}{n}
|
20,817 |
(q + \left(-1\right)) (1 + q) = q * q + \left(-1\right)
|
8,190 |
\psi\cdot n = N \Rightarrow N/n = \psi
|
5,999 |
\left(y^2 + 1\right) (y^2 + 4(-1)) = 4(-1) + y^4 - y * y*3
|
12,302 |
2*l*2 + (-1) = (-1) + 4*l
|
-22,019 |
1/12 - 4/5 = \frac{5}{12*5} - \tfrac{4*12}{5*12} = 5/60 - 48/60 = (5 + 48*(-1))/60 = -\frac{1}{60}*43
|
31,786 |
6 + (3\times \left(-1\right) + p)/2 + \frac12\times (p + (-1)) = p + 4
|
-25,973 |
8/0.01 = 800
|
1,294 |
1 - \frac{1}{3} + 1/5 - \cdots = \frac14 \cdot \pi
|
-23,821 |
\dfrac{20}{2 + 8} = \frac{20}{10} = 20/10 = 2
|
-19,474 |
\frac{1/5}{9} \cdot 8 = \dfrac{1}{9 \cdot 5/8}
|
49,050 |
102 = 17*6
|
23,381 |
\tfrac{1}{x^2 + 1} = d/dx \operatorname{atan}\left(x\right)
|
29,937 |
49 = ( x + f, x + f) = 16 + 2( x, f) + 25
|
30,964 |
\cos\left(g\right)\cdot \cos(a) + \sin\left(a\right)\cdot \sin\left(g\right) = \cos(a - g)
|
-11,542 |
i \cdot 20 + 4 + 16 (-1) = i \cdot 20 - 12
|
18,493 |
1 + n^3 = \left(1 + n\right) \cdot (n^2 - n + 1)
|
3,913 |
x\cdot \frac{3}{2} = n + 2/3 \Rightarrow n\cdot 2/3 + (2/3) \cdot (2/3) = x
|
9,499 |
\frac79 = 7 \cdot \dfrac{1}{36}/\left(\dfrac14\right)
|
-20,333 |
\frac{1}{t\cdot 18 + 16}\cdot (24\cdot (-1) - t\cdot 27) = -3/2\cdot \frac{t\cdot 9 + 8}{t\cdot 9 + 8}
|
11,947 |
5*V + 3*(-1) = 16*V + 5*V + 3*(-1) - 16*V = 16*x - 16*V = 16*(x - V)
|
20,722 |
2^{(2 + y) \cdot 2} = 4^{2 + y}
|
-20,271 |
\dfrac44\cdot \frac{-7\cdot x + 6\cdot \left(-1\right)}{6 - 2\cdot x} = \frac{-28\cdot x + 24\cdot \left(-1\right)}{-x\cdot 8 + 24}
|
42,910 |
\Im{(\overline{z})} = -\Im{(z)}
|
607 |
1/(C\times B)\times C = 1/(C\times B/C)
|
31,838 |
w \cdot 5 \cdot x = 5 \cdot w \cdot x = -5 \cdot x \cdot w
|
34,550 |
\sec(\arctan x)=\sqrt{x^2+1}
|
-26,481 |
5 \cdot x^2 - 20 \cdot x + 20 = 5 \cdot (x^2 - 4 \cdot x + 4) = 5 \cdot (x + 2 \cdot (-1))^2
|
-2,946 |
8\sqrt{13} = \sqrt{13} \cdot \left(5 + 3\right)
|
7,384 |
-n*t = -n*t
|
10,570 |
\cos{2\cdot z} = 2\cdot \cos^2{z} + \left(-1\right)
|
18,472 |
m^2 - 0 \cdot 0 = 0.5 = 1^2 - m^2
|
5,110 |
4\frac12(p + 3) \frac{1}{2}(p + 7\left(-1\right)) = \left(7(-1) + p\right) (3 + p)
|
-18,920 |
4x = \dfrac{8x}{2}
|
15,874 |
{45 \choose 2} = \frac{45!}{2!*(45 + 2*(-1))!} = 990
|
33,773 |
\left(-1 + 1\right)\cdot g - g = 0\cdot g - g = 0 - g = -g
|
-7,261 |
6 \cdot \dfrac17/2 = \frac37
|
-1,077 |
\frac{\frac{1}{7}}{1/5\cdot 8}\cdot 2 = \dfrac{1}{8}\cdot 5\cdot \frac27
|
10,727 |
\frac{l!^2}{2*l*2}*2 = l!^2/(l*2)
|
-10,505 |
\frac{1}{25\cdot n + 5\cdot \left(-1\right)}\cdot 15 = 5/5\cdot \tfrac{3}{5\cdot n + (-1)}
|
24,752 |
-\tfrac3g + \frac8b = 1\Longrightarrow b \cdot g = -b \cdot 3 + g \cdot 8
|
2,686 |
-(k + (-1)) + l - k = l - 2\cdot k + 1
|
49,277 |
\binom{5}{2} = \frac{1}{3!*2!}5! = \dfrac{5*4*3*2}{3*2*2}1 = \dfrac{1}{12}120 = 10
|
25,726 |
\sqrt{1} = \sqrt{(-1) \cdot (-1)} = \sqrt{-1} \cdot \sqrt{-1} = i \cdot i = -1
|
-30,270 |
Z^2 + 9*(-1) = (Z + 3)*(Z + 3*(-1))
|
-2,321 |
2/14 = -\tfrac{1}{14}*2 + 4/14
|
28,459 |
\sqrt{i} + \sqrt{i*2} + \sqrt{3*i} = (1 + \sqrt{2} + \sqrt{3})*\sqrt{i}
|
35,468 |
d/1 + h/1 = (d + h)/1 = (d + h)/1
|
-23,805 |
\dfrac{6}{1 + 2} = 6/3 = \frac{1}{3}6 = 2
|
28,527 |
t = z + (-1) \Rightarrow z = t + 1
|
8,490 |
(3*x) * (3*x) = 9*x^2
|
22,850 |
10/19 = 1 - \tfrac{9}{19}
|
14,797 |
x^2 - 2 x + 5 = x^2 - 2 x + 1 + 4 = (x + \left(-1\right))^2 + 4
|
688 |
e^{\nu + z} = e^z\cdot e^\nu
|
20,797 |
\cos{n \theta} = \sin\left(\pi/2 - n \theta\right)
|
-20,369 |
\frac{1}{30 + r\cdot 45}\cdot (15\cdot (-1) - r\cdot 10) = \frac{1}{9\cdot r + 6}\cdot (3\cdot \left(-1\right) - 2\cdot r)\cdot \frac{5}{5}
|
-4,583 |
y^2 + 9 \cdot y + 20 = \left(y + 4\right) \cdot (5 + y)
|
33,630 |
t^9 = (t \cdot t \cdot t)^3 = (t + 1) \cdot (t + 1) \cdot (t + 1) = t^3 + 1 = t + 2 = t + (-1)
|
-20,076 |
-\frac16*\frac{9*(-1) + x}{9*(-1) + x} = \tfrac{-x + 9}{x*6 + 54*(-1)}
|
-11,588 |
i\cdot 3 - 5 + 2\cdot (-1) = -7 + 3\cdot i
|
12,947 |
30 \cdot 7!/9! = 30/72 = \tfrac{1}{12} \cdot 5
|
-11,690 |
\dfrac{16}{9} = (\frac{1}{3}\cdot 4)^2
|
35,212 |
(a - b)^2 = (a - b) \cdot (a - b) = a \cdot a - a \cdot b - a \cdot b + b^2 = a^2 - 2 \cdot a \cdot b + b^2
|
19,073 |
(-c + f) \cdot (-c + f) = f^2 - 2 \cdot c \cdot f + c \cdot c
|
28,040 |
(\frac84)^2 = 4 = \dfrac{16}{4}
|
26,453 |
i + i + \left(-1\right) = 2\cdot i + \left(-1\right)
|
-25,363 |
\dfrac{\cos{x}}{\sin{x}} = \cot{x}
|
6,087 |
\dfrac{3 - 1.8}{5 + 2(-1)} = 1.2/3 = 2/5
|
28,388 |
( c, x, d) = ( 1, 78, 23) \implies 4121\times 67\times 1608 = ( c^3, x^2, d^3)
|
9,553 |
w = 4 + x \implies w + 4\cdot (-1) = x
|
2,968 |
\left(\tfrac{1}{10}\right)^2 + (1/10)^2 + ... + (1/10)^2 = 1/10 \gt 0.01
|
-20,832 |
-\dfrac{1}{-5} \cdot 5 \cdot \tfrac17 \cdot 10 = -\frac{50}{-35}
|
-8,677 |
5/2 - 2/4 = 5*2/\left(2*2\right) - 2/(4) = \frac{10}{4} - \frac{2}{4} = (10 + 2*\left(-1\right))/4 = 8/4
|
-18,953 |
\frac{1}{3}*2 = B_s/(100*\pi)*100*\pi = B_s
|
44,809 |
7\cdot ((-1) + 2^{21}) = 14680057
|
35,046 |
-\frac{8}{3} = -\frac13\cdot 8
|
-2,849 |
\sqrt{9} \sqrt{2} + \sqrt{2} = 3\sqrt{2} + \sqrt{2}
|
-3,790 |
\frac{1}{12} \cdot 20 \cdot \dfrac{x^4}{x} = \frac{x^4}{x \cdot 12} \cdot 20
|
-19,681 |
18/4 = 3*6/\left(4\right)
|
14,229 |
(A \cdot x - b)^Q \cdot \left(A \cdot x - b\right) = (x^Q \cdot A^Q - b^Q) \cdot (A \cdot x - b) = x^Q \cdot A^Q \cdot A \cdot x - x^Q \cdot A^Q \cdot b - b^Q \cdot A \cdot x + b^Q \cdot b
|
-26,357 |
25/4 = -5/2\cdot \left(-5/2\right)
|
-5,615 |
\frac{5}{t\cdot 5 + 40\cdot \left(-1\right)} = \dfrac{5}{5\cdot (t + 8\cdot (-1))}
|
8,228 |
\cos(x) \cdot g^2 \cdot 2 + \cos^2(x) \cdot g \cdot g + g^2 \cdot \sin^2(x) = g^2 - 2 \cdot g \cdot g \cdot \cos(-x + \pi)
|
3,089 |
m d_2 - m d_1 = (-d_1 + d_2) m
|
-2,297 |
9/11 = \frac{10}{11} - \frac{1}{11}
|
8,351 |
\dfrac{1}{c}\cdot (a + g) = \tfrac{g}{c} + \frac{a}{c}
|
37,573 |
\mathbb{P}(X = W) = 1 \Rightarrow E(W) = E(X)
|
8,857 |
(-e^{-y} + 1)^{k + (-1)} \cdot e^{-y} = \frac{\partial}{\partial y} (\frac1k \cdot \left(1 - e^{-y}\right)^k)
|
9,841 |
\binom{2\cdot l}{l} = \binom{2\cdot l}{l}
|
17,677 |
z^3 - 3 \cdot z^2 + 4 = z \cdot z \cdot z + 1 - 3 \cdot z^2 + 3 = (z + 1) \cdot \ldots - 3 \cdot (z^2 + (-1))
|
-404 |
\pi \frac123 = \dfrac{51}{2} \pi - 24 \pi
|
3,331 |
b \cdot a/d = \frac{b}{d} \cdot a
|
19,683 |
\int \sum_{l=1}^\infty e_l\,\text{d}\mu = \sum_{l=1}^\infty \int e_l\,\text{d}\mu
|
4,566 |
\frac{1}{n} \cdot z = \frac{z}{n}
|
-642 |
\left(e^{\pi\cdot i/3}\right)^8 = e^{\pi\cdot i/3\cdot 8}
|
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