id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
2,910 |
7^l + 7^m = 7^l \cdot (1 + 7^{-l + m})
|
11,768 |
{4 \choose 2} \cdot 3 = 18
|
-29,357 |
(2 + z)\times (2 - z) = 2^2 - z^2 = 4 - z^2
|
36,551 |
\binom{12 + 4 + (-1)}{12} \binom{4}{1} = 1820
|
11,073 |
B \cdot A = 50, C \cdot B = \frac{299}{2}, \frac12 \cdot 291 = A \cdot C \Rightarrow B \cdot A + C \cdot B + A \cdot C = 345
|
11,706 |
\cos(-m \times \phi) = \cos\left(m \times \phi\right)
|
14,943 |
2 (\frac12 \left((-1) + p\right) + 1) = p + 1
|
19,366 |
|y| > 1 \Rightarrow 1 > 1/|y|
|
25,370 |
(s + 2) \cdot (s + 2) + 1^2 = 5 + s^2 + 4\cdot s
|
-25,177 |
d/dx (3 \cdot x^2 \cdot (3 + 5 \cdot x)^{1/2}) = \frac{75 \cdot x \cdot x + 36 \cdot x}{2 \cdot (5 \cdot x + 3)^{1/2}}
|
450 |
y^6 + 1 = \left(y^2 + 1\right)*\left(y^4 - y^2 + 1\right) = \left(y * y + 1\right)*(\left(y + 1\right)^2 - y^2)
|
15,230 |
\left(-1\right)^3 + \left(-2\right)^3 + 3^3 = -1 + 8\cdot (-1) + 27 = 18 = 3\cdot (-\left(-2\right)\cdot 3)
|
37,913 |
(x + y)^2 - 4\cdot x\cdot y = \dotsm = (x - y) \cdot (x - y)
|
26,255 |
\sin\left(\frac12 \cdot \pi + y\right) = \cos{y}
|
23,131 |
N^2 + (5 \cdot (-1) + N/2)^2 = (N + 4 \cdot (-1))^2 + (N/2 + 3)^2
|
-20,497 |
8/8\cdot (-2\cdot t + 4)/2 = \frac{1}{16}\cdot (-16\cdot t + 32)
|
21,596 |
\dfrac{1}{x + (-1)} \cdot (1 + x + (-1))^2 \cdot \frac{1}{2 + x + (-1)} = \dfrac{x^2}{x^2 + (-1)}
|
26,883 |
-\cos(z) = \cos(z - \pi)
|
16,168 |
y*3/4 = \frac{3}{4} y
|
-17,808 |
41 = 56 + 15 \left(-1\right)
|
6,449 |
E\cdot \left(-F + B\right) = E\cdot B - E\cdot F
|
16,215 |
S^2 + S + 1 = 3/4 + (\frac12 + S)^2
|
16,981 |
e\sin{z} + c\sin{2z} = e\sin{z} + 2c\sin{z} \cos{z} = (e + 2c\cos{z}) \sin{z}
|
25,415 |
(\frac{7}{8})^3 = \dfrac{1}{512}\cdot 343
|
18,806 |
\left(p \times 2\right)^2 = 4 \times p^2
|
11,452 |
-1/16 + 2/3 = \tfrac{1}{48}*32 - 3/48
|
-3,923 |
\frac{80 t^3}{t^2 \cdot t\cdot 96} = 80/96 \frac{t^3}{t^3}
|
35,771 |
V^0\cdot V^k = V^{0 + k} = V^k
|
4,118 |
\frac12 = \frac{1}{2^{1 / 2}}*\frac{2}{2^{1 / 2}}/2
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-2,776 |
2 \cdot \sqrt{5} + \sqrt{5} \cdot 4 - 5 \cdot \sqrt{5} = \sqrt{4} \cdot \sqrt{5} + \sqrt{16} \cdot \sqrt{5} - \sqrt{5} \cdot \sqrt{25}
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-19,497 |
\frac54*2/3 = 5*1/4/(\frac12*3)
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-16,345 |
75^{\tfrac{1}{2}}\cdot 6 = \left(25\cdot 3\right)^{\frac{1}{2}}\cdot 6
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-20,108 |
7/7 \cdot \frac{10 - 2 \cdot x}{x \cdot (-5)} = \dfrac{1}{(-35) \cdot x} \cdot (-x \cdot 14 + 70)
|
6,324 |
0 = (-1)^6 - (-1) \cdot (-1)^2\cdot 7 + 8\cdot (-1)
|
-6,992 |
2/13 = \frac{1}{13} \cdot 4 \cdot \frac{1}{12} \cdot 6
|
-10,493 |
-\dfrac{1}{q*15 + 5*(-1)}*(25 + 20*q) = -\frac{1}{(-1) + q*3}*(5 + 4*q)*\frac55
|
8,710 |
-k^6 + (k + 1)^6 = 1 + k^5 \cdot 6 + k^4 \cdot 15 + k^3 \cdot 20 + 15 \cdot k^2 + k \cdot 6
|
18,444 |
{3 \choose 1}\cdot {2 \choose 1}\cdot {3 \choose 2}\cdot 2!\cdot {5 \choose 3} = 360
|
39,720 |
e^{i\cdot \pi/3} = \dfrac{B_1 + i\cdot B_2}{C_1 + i\cdot C_2} = \frac{1}{C_1^2 + C_2 \cdot C_2}\cdot (B_1 + i\cdot B_2)\cdot \left(C_1 - i\cdot C_2\right)
|
-5,395 |
2.8 \cdot 10 = \dfrac{28}{10^6}1 = \dfrac{2.8}{10^5}
|
7,155 |
1/4 + 1/6 + \dfrac{1}{13} = 77/156 = 0.49
|
-30,620 |
r^2\cdot 4 + 12 = 4(r^2 + 3)
|
22,325 |
3/2 \cdot z \cdot x - \frac{5}{4} = -\frac12 + 3/2 \cdot x \cdot z - 3/4
|
-25,857 |
\frac{1}{z \cdot z} \cdot z^7 = z^5
|
4,668 |
7^2 + 4 \cdot 4 = 65 = 5 \cdot 13
|
-30,553 |
-72/(-36) = -36/(-18) = -\tfrac{18}{-9} = 2
|
23,555 |
\left(n + 1\right)^4 - (n + 1)^2 = (n + 1) \cdot (n + 1)\cdot ((n + 1)^2 + (-1)) = (n + 1)^2\cdot (n + 1 + (-1))\cdot \left(n + 1 + 1\right)
|
12,544 |
{n + (-1) \choose i + (-1)}*n = {n \choose i}*i
|
16,645 |
\pi \frac73 = \tfrac{\pi*7}{3}
|
7,796 |
2*(-1) + Z^3 - Z*3 = (1 + Z)^2*\left(Z + 2*(-1)\right)
|
21,067 |
p + r' + x = p + x + r' + x
|
13,129 |
\frac{1}{8} \cdot (24 \cdot (-1) + 36) = 3/2
|
39,837 |
100 = \frac{1}{4} 20^2
|
30,183 |
-\arctan{z} + \arctan{z} (z^2 + 1) = \arctan{z} z^2
|
-20,426 |
\frac{5 \cdot 1/5}{z + 5} = \frac{5}{5 \cdot z + 25}
|
23,938 |
1 = (-1) (-1) = (z + \frac{1}{z}) (z^2 + \frac{1}{z^2}) = z^3 + z + \frac{1}{z} + \frac{1}{z^3} = z^3 + (-1) + \frac{1}{z^3}
|
-20,957 |
\frac{12*(-1) + f*42}{10 - f*35} = -6/5*\dfrac{-7*f + 2}{-7*f + 2}
|
2,002 |
1 + \frac{1}{n} = \frac1n*\left(1 + n\right)
|
28,315 |
(1 + \cos{2z})^2 = (1 + 2\cos^2{z} + (-1))^2 = 4\cos^4{z}
|
708 |
f \cdot \frac{\mathrm{d}y}{\mathrm{d}x} + b \cdot \frac{\mathrm{d}y}{\mathrm{d}x} = (b + f) \cdot \frac{\mathrm{d}y}{\mathrm{d}x}
|
19,839 |
0.52 = 0.01 + \frac{102}{2} \cdot 0.01
|
20,771 |
0 = z\cdot 2 + (-1) \Rightarrow z = \frac12
|
6,271 |
(5 + 2\cdot z)^2 = 4\cdot z^2 + 20\cdot z + 25
|
28,585 |
E[(-x + V)^2] = (-x + E[V])^2 + \mathbb{Var}[V]
|
29,450 |
\sin(A)\cdot \sin(D) + \cos(A)\cdot \cos\left(D\right) = \cos(A - D)
|
11,547 |
\left(1 - z\right)^2 = 2 \frac12 ((-1) + 2 - z) ((-1) + 2 - z)
|
-20,644 |
(90 \times x + 50)/(-20) = \frac{1}{-2} \times (5 + 9 \times x) \times 10/10
|
12,834 |
((-1) + y) (y + 1) = y^2 + (-1)
|
27,370 |
x^2 + x + 2 \cdot (-1) = (x + 2) \cdot \left(x + (-1)\right)
|
15,266 |
-14 = 3 \cdot (-1) + (-11)
|
16,864 |
\sqrt{3}/2 = \cos\left(\pi/6\right)
|
-2,075 |
\frac132 \pi = -\pi*2 + \frac83 \pi
|
-1,694 |
-\dfrac{\pi}{4} + 5/4 \pi = \pi
|
14,728 |
|2\cdot e^{i\cdot x} + (-1)|^2 = |2\cdot \cos{x} + 2\cdot i\cdot \sin{x} + (-1)|^2 = \left(2\cdot \cos{x} + (-1)\right)^2 + (2\cdot \sin{x})^2
|
13,386 |
\left(-b + a\right)^2 = (-a + b)^2
|
2,795 |
\sin(\alpha + W) = \cos(\alpha) \sin(W) + \cos(W) \sin(\alpha)
|
7,439 |
\frac{1}{52} = 51*1/52/51
|
6,062 |
x^2 - x \cdot 4 = (x + 2 \cdot (-1))^2 + 4 \cdot (-1)
|
243 |
y + (y^2 + 1)^{1/2} = \sqrt{y^2 + 1} + y
|
-19,789 |
0.01*(-130) = -\dfrac{130}{100} = -1.3
|
4,858 |
\frac{i + 1}{(-1) + i} = 1 + \frac{1}{i + (-1)}2
|
-30,540 |
\frac{dz}{dF} = Fe^{-z} + 10 e^{-z} = \tfrac{1}{e^z}\left(F + 10\right)
|
40,480 |
Y*Y^0 = Y^1
|
32,470 |
\frac{1}{4} + p \cdot 3/4 = (-p + 1)/4 + p
|
19,355 |
2 \cdot \left(y \cdot \alpha + n \cdot \alpha + \alpha \cdot w + n \cdot y + y \cdot w + w \cdot n\right) + \alpha^2 + y^2 + n^2 + w \cdot w = (\alpha + y + n + w)^2
|
29,387 |
(x + 1)! = x!\cdot \left(x + 1\right) = (x + \left(-1\right))!\cdot (x + 1)\cdot x
|
11,039 |
2^{2*x} = \left(2^x\right)^2
|
-7,085 |
\dfrac{1}{7} = \dfrac{1}{7}
|
8,806 |
q \cdot (z \cdot 2 + (-1)) = 3 \cdot (z^2 + 1)\Longrightarrow q + z^2 \cdot 3 - z \cdot q \cdot 2 + 3 = 0
|
21,143 |
217 = (20 \cdot z + 3) \cdot r + (20 \cdot z + 3 + 3 \cdot (-1))/20 = (20 \cdot z + 3) \cdot (r + 1/20) - 3/20
|
17,349 |
4^{1 + j} + \frac{4^2}{3}\cdot (4^{\left(-1\right) + j} + (-1)) = \frac{1}{3}\cdot (16\cdot 4^j - 16)
|
20,330 |
1 - r^m = r^0 - r^m
|
-11,545 |
i*12 - 15 = 0 + 15*(-1) + 12*i
|
-11,769 |
27^{-1/3} = (\dfrac{1}{27})^{1/3} = \frac13
|
23,437 |
(((-1) + 2*n)!)! = \left((-1) + 2*n\right)*(3*(-1) + 2*n)*\left(5*(-1) + 2*n\right)*\dotsm
|
-24,877 |
\frac{1}{15}*2 = s/12*12 = s
|
5,524 |
{n \choose 2} - 2 \cdot \left(-1\right) + n = {n + (-1) \choose 2} + 1
|
-3,045 |
4 \cdot \sqrt{2} - 2 \cdot \sqrt{2} = \sqrt{16} \cdot \sqrt{2} - \sqrt{4} \cdot \sqrt{2}
|
21,618 |
\frac{z}{z + \left(-1\right)} = \dfrac{1}{z + (-1)} \cdot (z + (-1) + 1) = 1 + \frac{1}{z + (-1)}
|
-16,974 |
1 = -9 \cdot r \cdot r + 15 \cdot r + (-3 \cdot r) + 5 = -9 \cdot r^2 + 15 \cdot r - 3 \cdot r + 5
|
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