id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
8,456 |
1 - 8 \cdot a \cdot a^2 - 15 \cdot a^2 - 6 \cdot a = \left(a + 1\right)^2 \cdot (-a \cdot 8 + 1)
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27,243 |
3! \cdot \frac16 \cdot 6 \cdot 5 = 5 \cdot 3!
|
1,692 |
\arctan(z) = \frac{1}{1 + z^2}
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-7,875 |
\frac{1}{1 + 2\cdot i}\cdot (i - 2)\cdot \frac{1 - 2\cdot i}{-i\cdot 2 + 1} = \frac{i - 2}{1 + 2\cdot i}
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-29,590 |
-x^3 \cdot 8 + x^2 \cdot 9 - x \cdot 2 = d/dx (-2 \cdot x^4 + x^3 \cdot 3 - x^2)
|
10,425 |
(-y^2 + \left(y + x\right)^2 - x^2)/2 = y\cdot x
|
12,592 |
(a + b)\cdot E = b\cdot E + E\cdot a
|
20,199 |
e^{C_2 + C_1} = e^{C_2} \cdot e^{C_1} \implies (C_2,C_1) = 0
|
32,235 |
(a + b)^2 = a^2 + b^2 + 2*b*a
|
1,294 |
\pi/4 = 1 - \dfrac13 + 1/5 - \dots
|
22,592 |
\sum_{n=1}^\infty \dfrac{1}{n \cdot n} = \sum_{n=1}^\infty \dfrac{1}{n^3} \cdot n
|
12,452 |
2 - x^2 - y^2 = x^2 \implies y \cdot y/2 + x^2 = 1
|
226 |
2k = i + k + k - i
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27,119 |
(x + 3 \cdot (-1)) \cdot \left(2 \cdot \left(-1\right) + x\right) = x^2 - x \cdot 5 + 6
|
26,707 |
128 = \left(1 + 1\right) \cdot (1 + 1) \cdot (1 + 1) \cdot \left(3 + 1\right) \cdot \left(3 + 1\right)
|
21,970 |
\frac{y}{(1 - y) \cdot (1 - y)} = y + y^2\cdot 2 + 3\cdot y^3 + \ldots
|
8,659 |
z + g = u\Longrightarrow u - g = z
|
4,689 |
(d + a) \cdot (a + d) = d^2 + a^2 + a \cdot 2 \cdot d
|
-3,117 |
\sqrt{13}*\left(1 + 3 + 2\right) = 6\sqrt{13}
|
12,435 |
hk = 1/(h_1 k_1) = 1/(k_1 h_1)
|
2,806 |
\sqrt{a} - b = (-b + \sqrt{a}) \frac{\sqrt{a} + b}{\sqrt{a} + b}
|
6,851 |
-x \times x + \dotsm = 1 - x^2/2 + \dotsm + (-1) - x^2/2
|
25,563 |
\frac{\mathrm{d}}{\mathrm{d}x} \sin^{-1}{x} = \dfrac{1}{\sqrt{-x^2 + 1}}
|
4,584 |
-x \cdot x - x^2 \cdot 22 = -x^2 \cdot 23
|
20,118 |
\tan^2{y} + \sin^2{y} + \cos^2{y} = \frac{\text{d}}{\text{d}y} \tan{y}
|
30,551 |
\binom{-1/2}{2} = \frac38
|
26,386 |
\dfrac{1}{128} = 1/(8\cdot 16)
|
8,637 |
(b - a)/(a\cdot b) = -1/b + 1/a
|
47,199 |
24 = 3 \times 8
|
-20,623 |
54/(-24) = -\frac{6}{-6} (-9/4)
|
-9,336 |
36\cdot q^3 - q \cdot q\cdot 36 = -q\cdot 2\cdot 2\cdot 3\cdot 3\cdot q + q\cdot 2\cdot 2\cdot 3\cdot 3\cdot q\cdot q
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28,390 |
(k + 2)*(k + 1)*k*... = (2 + k)!
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27,953 |
-m*(-m) = mm
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6,553 |
-\dfrac{8}{(-6)^3} = 1/27
|
8,274 |
\frac{9!}{4!\cdot 3!\cdot 2!} = \frac{362880}{24\cdot 6\cdot 2} = 1260
|
-1,297 |
\frac{1}{4*5/7} = \tfrac{7*\frac{1}{5}}{4}
|
4,738 |
e*(h + e) + h*(e + h) = (h + e)*(e + h)
|
41,013 |
1063 = 1024 + 32 + 8 + (-1)
|
14,583 |
-2 \cdot z \cdot e - \int (-2 \cdot e)\,\mathrm{d}z = -2 \cdot e \cdot z + 2 \cdot \int e\,\mathrm{d}z = -2 \cdot e \cdot z + 2 \cdot e
|
18,697 |
z^2 - z = z*((-1) + z)
|
-735 |
(e^{\frac16 \times i \times 5 \times \pi})^{19} = e^{19 \times \frac16 \times 5 \times i \times \pi}
|
4,388 |
1/h - \frac{1}{b} = b/(h*b) - h/(h*b) = \dfrac{1}{h*b}*(b - h)
|
3,508 |
21673*\left(3*7*11*13\right)^2 = 195447309057
|
7,221 |
x^3 + z^3 = (x + z) (z^2 + x \cdot x - zx)
|
27,637 |
1 + 2 + 3 + \dots + k \leq k + k + k + \dots + k = k\cdot k = k^2
|
29,788 |
f^2 \cdot a = |f^2 \cdot a| = 2/3 \cdot |f|^3 + \frac{|a|^3}{3}
|
35,584 |
0 + \left\lfloor{100/5}\right\rfloor + \left\lfloor{\dfrac{100}{25}}\right\rfloor = 24
|
21,467 |
l^2 + x * x + 2xl = \left(x + l\right)^2
|
10,764 |
\dfrac{2}{3} \cdot 5/18 = \frac{1}{54} \cdot 10 = \frac{5}{27}
|
-29,061 |
x^6\cdot x^0 = x^6
|
271 |
\frac{1}{(1 - z)^2} = d/dz \frac{1}{1 - z}
|
-20,520 |
-\tfrac15 \cdot 6 \cdot \frac{10}{10} = -60/50
|
15,886 |
1 + 3 \cdot (x \cdot 2 + (-1)) = x \cdot 6 + 2 \cdot (-1)
|
-3,332 |
\sqrt{11}*8 = \sqrt{11}*(5 + 3)
|
1,663 |
w_1 \times X = x \times w_1 rightarrow X^2 \times w_1 = x \times X \times w_1 = x \times x \times w_1
|
3,183 |
{\eta \choose j}^2 = {\eta \choose j}\cdot {\eta \choose j}
|
-9,980 |
\frac15 = \frac{5}{25}
|
27,187 |
\int \sqrt{x}\,\mathrm{d}x = \frac{2}{3} \times x \times \sqrt{x}
|
5,379 |
\Im{\left(2\cdot \sqrt{2}\cdot i\right)} = 2\cdot \sqrt{2} \gt -\dfrac{1}{2}
|
4,248 |
x_2\cdot x_1\cdot d = x_1\cdot d\cdot x_2
|
1,634 |
\mathbb{E}[B]\cdot \mathbb{E}[A] = \mathbb{E}[A\cdot B]
|
32,516 |
1 = \frac{1}{12} + 1/2 + 1/4 + \frac16
|
18,775 |
\sin(h + x) = \cos(h) \sin(x) + \cos(x) \sin(h)
|
876 |
z^4 - y^4 = 15 \Rightarrow 15 = (y^2 + z^2)*(z^2 - y * y)
|
-12,050 |
1/8 = \frac{p}{8 \cdot \pi} \cdot 8 \cdot \pi = p
|
-20,470 |
-\frac{10}{7}\cdot (-\frac{10}{-10}) = 100/\left(-70\right)
|
27,040 |
(i + x)\cdot (i - x) = i - x^2 = (i - x)\cdot (i + x)
|
13,078 |
(67^{1 / 2})^2 + 6 \cdot 6 = (103^{\dfrac{1}{2}})^2
|
-25,838 |
\dfrac{1}{x + 7}\cdot (30 + x \cdot x \cdot x + 5\cdot x \cdot x - 9\cdot x) = x^2 - 2\cdot x + 5 - \frac{1}{x + 7}\cdot 5
|
-29,356 |
z*(-7)*(z + 3*(-1)) = z^2 - 3*z - 7*z + 21 = z^2 - 10*z + 21
|
-3,511 |
6/10 = 3\cdot 2/(5\cdot 2)
|
-23,423 |
\frac{1}{3}\frac{4}{9} = \frac{4}{27}
|
-4,413 |
(4\cdot (-1) + x)\cdot (x + 2\cdot (-1)) = 8 + x^2 - 6\cdot x
|
36,293 |
4*(1 + t * t) = (1 + t^2 - t*y)^2 + y^2 = (1 + t^2)*(1 + (y - t)^2)
|
2,588 |
\frac{y_l}{1 + y_l} = y_l - \frac{1}{1 + y_l}y_l^2
|
42,929 |
15\cdot 5 = 75
|
1,688 |
6 \cdot (-1) + x \cdot x^2 - x^2 \cdot 6 + 11 \cdot x = \left((-1) + x\right) \cdot (2 \cdot (-1) + x) \cdot (x + 3 \cdot (-1))
|
9,986 |
(-1) + (\left(-1\right) + 6)\cdot 5^j = 5^j\cdot 6 + 6\cdot (-1) - 5^j + 5
|
18,257 |
1 + (-1) + 1 + (-1) + 1 - \cdots = 1/2
|
2,973 |
-2\cdot \sin^2{\frac{1}{2}\cdot \theta} + 1 = \cos{\theta}
|
17,416 |
49 * 49 * 49 + 84^3 + 102^3 = 121 * 121 * 121
|
-20,495 |
-\frac{9}{4 + x*10}*7/7 = -\dfrac{1}{x*70 + 28}63
|
37,079 |
1 + 1 + 6 = 8 = 2 \times 2^2
|
10,417 |
(z + H)*(x + y) = (x + y)*(H + z)*(x + z)
|
14,142 |
\left(X + x\right)*(X - x) = -x * x + X^2
|
39,507 |
-2 = 0^3 - 3*0 + 2(-1)
|
-5,744 |
\frac{1}{36*(-1) + q*4}*3 = \frac{3}{4*(9*(-1) + q)}
|
-9,293 |
12 - y \cdot 30 = -y \cdot 2 \cdot 3 \cdot 5 + 2 \cdot 2 \cdot 3
|
-20,755 |
\tfrac{2 + 5z}{-z*15 + 6(-1)} = \frac{1}{-5z + 2(-1)}\left(2(-1) - 5z\right) (-1/3)
|
29,071 |
(U^2 + (-1)) \cdot (1 + U^4 + U^2) = (-1) + U^6
|
39,462 |
\delta \cos{\delta x} = \frac{\partial}{\partial x} \sin{\delta x}
|
29,100 |
{(-1) + 6 + 6 \choose 6} = {11 \choose 6}
|
16,660 |
-101 = (-13) \cdot 7 + 10 \cdot \left(-1\right) = \left(-8\right) \cdot 13 + 3
|
20,303 |
\operatorname{E}[(-\operatorname{E}[X] + X) \cdot \left(-\operatorname{E}[Y] + Y\right)] = \operatorname{E}[X \cdot Y] - \operatorname{E}[X] \cdot \operatorname{E}[Y]
|
25,441 |
E\left[E\left[x\right] X\right] = E\left[X\right] E\left[x\right]
|
-20,492 |
\frac{s*3 + 30*(-1)}{3*s + 18*\left(-1\right)} = \frac{1}{6*(-1) + s}*(10*\left(-1\right) + s)*3/3
|
21,367 |
\epsilon = 4/3 x \implies x = \epsilon\cdot 3/4
|
34,708 |
3 \cdot \left(-70\right) = -210
|
-20,877 |
\frac{1}{x \cdot (-60)} \cdot ((-54) \cdot x) = \dfrac{x \cdot (-6)}{x \cdot (-6)} \cdot \frac{9}{10}
|
6,582 |
0 = -a \cdot 16 + 8 \cdot c \implies c = 2 \cdot a
|
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