id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
19,627 |
4^{2\cdot (1 + p)} + 4 = 4 + 4^{2 + p\cdot 2}
|
9,395 |
[a, b] = \left\{a\right\} = \left\{b\right\} = \left[b, a\right]
|
42,125 |
14 + 3 = 13 + 4
|
34,933 |
-(16*5)^{1/2} = -4*5^{1/2}
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-20,065 |
\frac{1}{(-1) \cdot 5 \cdot r} \cdot (r \cdot 5 + 7) \cdot \frac{4}{4} = \dfrac{1}{(-20) \cdot r} \cdot (r \cdot 20 + 28)
|
22,520 |
2*4*\sqrt{7} = \sqrt{7}*2*4
|
-8,004 |
\dfrac{1}{4 i + 4} \left(i \cdot 4 + 4\right) \frac{1}{-i \cdot 4 + 4} (-8 + 24 i) = \dfrac{-8 + i \cdot 24}{4 - i \cdot 4}
|
-18,407 |
\frac{((-1) + t)*t}{(t + 10*(-1))*(t + (-1))} = \frac{t^2 - t}{10 + t^2 - t*11}
|
272 |
9! - 3 \cdot 2! \cdot 8! + 3 \cdot 7! \cdot 2! = 151200
|
39,775 |
y = \tan(\arctan{y})
|
6,368 |
\frac{1}{X + \frac1X} = 1/\left(2*X\right) = \frac{2}{X} = 2*X
|
11,767 |
y^{g_2 + g_1} = y^{g_1} \cdot y^{g_2}
|
-17,886 |
15 = 37 \cdot \left(-1\right) + 52
|
477 |
e^m = 1 + m + m^2/2! + ... \gt m
|
-10,443 |
\frac{32}{4*x + 4*(-1)} = \frac{8}{x + \left(-1\right)}*4/4
|
-28,771 |
-\frac12 - \frac{1}{2 - 2\times y}\times 4 = -1/2 + \frac{2}{y + (-1)}
|
10,433 |
\cos{\dfrac{\pi}{5} \cdot 4} + \cos{\frac25 \cdot \pi} = -\frac12
|
17,933 |
\dfrac{5\cdot 10}{2} = 25
|
-4,898 |
4.69*10 = \frac{4.69*10}{1000} = \dfrac{1}{100}4.69
|
23,234 |
2g + H = (g + H) \left(g + H\right) = (g + H)^2
|
31,243 |
\left(3 + n\right)!/n! = \tfrac{\left(n + 3\right)!}{(n + 3 + 3\cdot (-1))!}
|
-19,304 |
\frac{3\cdot \tfrac14}{7\cdot \frac13} = 3/7\cdot 3/4
|
9,609 |
4/10 = \frac152
|
-25,847 |
\frac{f^6}{f^1} = f\cdot f\cdot f\cdot f\cdot f\cdot f/f
|
11,225 |
{m + r + 5\cdot (-1) \choose r + 2\cdot (-1)} = {m + 2\cdot (-1) + r + 2\cdot \left(-1\right) + (-1) \choose r + 2\cdot (-1)}
|
-7,814 |
\frac{1}{13} \cdot (-3 - 63 \cdot i - 2 \cdot i + 42) = \dfrac{1}{13} \cdot \left(39 - 65 \cdot i\right) = 3 - 5 \cdot i
|
13,632 |
i*4 + 4 = (i + 2)^2 - i^2
|
34,668 |
12 \left(-1\right) + 20 = 8
|
21,416 |
h\cdot \pi\cdot 2 = 2\cdot \pi/(\tfrac{1}{h})
|
21,772 |
da/(cb) = a\frac{1}{b}/(c\cdot 1/d)
|
23,067 |
\tfrac{1}{a\cdot b} = 1/\left(a\cdot b\right)
|
8,450 |
(-d + d_n)\cdot (d_n \cdot d_n + d\cdot d_n + d^2) = d_n^3 - d^3
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46,304 |
256 + 99\cdot (-1) = 157
|
7,001 |
12 \cdot g = 11 + \tfrac{24}{3 \cdot g} + 12 \cdot (-1) \implies (-1) + \frac8g = g \cdot 12
|
8,119 |
\tfrac{64}{3\cdot 3\cdot 3}\cdot 1 = (\frac13\cdot 4)^3
|
6,642 |
(a + b)*2 = a + b + a + b
|
-23,112 |
\dfrac{45}{16}*3/4 = 135/64
|
-488 |
19/4\cdot \pi - 4\cdot \pi = \frac14\cdot 3\cdot \pi
|
-20,714 |
-9/4 \cdot \frac{1}{(-7) \cdot r} \cdot (r \cdot \left(-7\right)) = \frac{r \cdot 63}{r \cdot (-28)}
|
-19,426 |
\dfrac83\cdot \frac19 8 = \frac{\frac{8}{3}}{9\cdot 1/8} 1
|
20,946 |
\sqrt{(\dfrac{1}{12}*5)^2*((12/5)^4 + 1)} = \frac{5}{12}*\sqrt{\left(12/5\right)^4 + 1} \approx 5/12*(12/5) * (12/5) = 12/5 = 2.4
|
-12,007 |
1/2 = x/(12\cdot \pi)\cdot 12\cdot \pi = x
|
-6,848 |
11 \cdot 11 \cdot 5 = 605
|
25,191 |
\left\{4, 3, \dotsm, 1, 2, 0\right\} = \mathbb{N}
|
12,318 |
|\xi| \gt \frac{\mathrm{d}x}{\mathrm{d}t} = 0 \implies x = \xi
|
-19,058 |
3/4 = \dfrac{G_t}{49 \cdot π} \cdot 49 \cdot π = G_t
|
8,301 |
0 = z^3 - 2z * z - 5z + 6 = (z + (-1)) (z + 2) (z + 3(-1))
|
-6,207 |
\tfrac{4 \times p}{p^2 + 5 \times p + 24 \times \left(-1\right)} \times 1 = \dfrac{4 \times p}{(p + 8) \times \left(3 \times (-1) + p\right)}
|
-5,273 |
5.3*10^4 = 5.3*10^{9 + 5*(-1)}
|
-3,330 |
4\sqrt{6} = (2(-1) + 5 + 1) \sqrt{6}
|
25,959 |
984390625 = \frac{1}{4} \cdot 3937562500
|
14,233 |
(p + t \cdot l^{\frac{1}{2}})^2 = 2 \cdot t \cdot l^{1 / 2} \cdot p + p^2 + l \cdot t \cdot t
|
10,616 |
f - x = (\sqrt{f} - \sqrt{x})*(\sqrt{f} + \sqrt{x}) \geq (\sqrt{f} - \sqrt{x}) * (\sqrt{f} - \sqrt{x})
|
10,768 |
d > a\Longrightarrow a \cdot a = a \cdot a \lt a \cdot d < d \cdot d = d^2
|
51,611 |
\left(x + z\right) \cdot (x^{2 \cdot l} - z \cdot x^{(-1) + 2 \cdot l} + z^2 \cdot x^{l \cdot 2 + 2 \cdot (-1)} - \ldots + x \cdot x \cdot z^{l \cdot 2 + 2 \cdot (-1)} - z^{2 \cdot l + \left(-1\right)} \cdot x + z^{l \cdot 2}) = x^{2 \cdot l + 1} + z^{2 \cdot l + 1}
|
-15,571 |
\frac{1}{y^{25}\cdot (\frac{y}{k^5})^3} = \frac{1}{y^{25}\cdot \frac{y^3}{k^{15}}}
|
22,765 |
\left(r^1\right)^2 = r \cdot r
|
35,508 |
f^2 + b^2 = f + b = (f + b) * (f + b)
|
18,866 |
(x + f) (-x + f) = f^2 - x^2\Longrightarrow f + x = \left(f + x\right) \frac{f - x}{f - x} = \frac{1}{f - x}(f^2 - x^2)
|
-18,282 |
\frac{1}{(r + 5 (-1)) (r + 5 (-1))} r*(r + 5 (-1)) = \tfrac{r^2 - 5 r}{25 + r^2 - 10 r}
|
17,140 |
(xb)^2 = x^2 b^2
|
9,802 |
\frac{1}{-t^j + 1}\cdot \left(-t^{2\cdot j} + 1\right) = 1 + t^j
|
-1,158 |
-45/72 = \tfrac{(-45) \frac19}{72*\frac19} = -\dfrac185
|
8,544 |
\left(z^2 - 2 \cdot z + (-1)\right) \cdot (z + (-1)) = 1 + z^3 - 3 \cdot z^2 + z
|
18,525 |
0 = 4 \cdot \sin^3(s) - 3 \cdot \sin\left(s\right) - \dfrac{37}{64} = -\sin\left(3 \cdot s\right) - 37/64
|
-20,070 |
-1/3 \cdot \frac{z \cdot (-8)}{z \cdot (-8)} = \dfrac{z \cdot 8}{\left(-24\right) \cdot z}
|
48,249 |
\frac{2^{k + 2}}{e^{k + 3 \cdot (-1)}} = \dfrac{2 \cdot 2}{e^k \cdot \frac{1}{e^3}} \cdot 2^k = \frac{2^k}{e^k} \cdot 4 \cdot e \cdot e \cdot e
|
-9,598 |
0.01\cdot (-37) = -37.5/100 = -\frac38
|
7,664 |
(1 - y^2/3 + y^4/5 - y^6/7 + \cdots)^{-1} = -\frac{1}{45}*4*y^4 + 1 + y^2/3
|
7,883 |
\dfrac{1 + n}{2^{1 + n}} = \dfrac{1}{2^{n + 1}} \left(3 \left(-1\right) + n*2 + 4 - n\right)
|
-20,134 |
\frac{1}{x + 10 \times (-1)} \times ((-2) \times x) \times 9/9 = \frac{x \times \left(-18\right)}{9 \times x + 90 \times (-1)}
|
34,613 |
105 = 28 \times 15 \times 6/4!
|
25,925 |
y^3 - y y - y*2 + 2 = (y^2 + 2 (-1)) \left((-1) + y\right)
|
12,859 |
a^{z + x} = a^z*a^x
|
-4,947 |
0.85*10^{\left(-1\right)*\left(-1\right) + 2} = 0.85*10^3
|
23,498 |
E[Y*X] = E[Y]*E[X]
|
-20,032 |
10/7 \frac{x*10 + 5(-1)}{5\left(-1\right) + 10 x} = \dfrac{1}{70 x + 35 (-1)}(50 (-1) + x*100)
|
9 |
\cos{m\times s\times 2} = 2\times \cos^2{m\times s} + (-1)
|
12,371 |
2^{k+1}+2^{k+1}-2 = 2(2^{k+1}-1)
|
11,663 |
z_1^2 - 3z_1 + a = 0 = (-z_1)^2 + 3(-z_1) - a
|
-3,349 |
(5 + 3 \cdot (-1) + 4) \cdot \sqrt{13} = \sqrt{13} \cdot 6
|
-19,459 |
\dfrac{1}{3}\cdot 5/\left(\tfrac{1}{6}\right) = \dfrac61\cdot 5/3
|
2,118 |
z \in C rightarrow z \in C
|
-10,755 |
\frac22 \frac{r*3 + 2(-1)}{r*2 + 4} = \frac{r*6 + 4(-1)}{4r + 8}
|
31,739 |
-\left(\sqrt{-2 \cdot n}\right)^2 = 2 \cdot n
|
23,629 |
v + w = (\frac{v}{2} + \tfrac{w}{2}) \cdot 2
|
-2,895 |
-5^{\tfrac{1}{2}} + 4^{1 / 2}\cdot 5^{1 / 2} = -5^{\tfrac{1}{2}} + 2\cdot 5^{\frac{1}{2}}
|
-206 |
\frac{1}{3! \cdot 2!}5! = 10
|
21,982 |
\dfrac{1}{\cos^2(z)} = 1 + \tan^2(z)
|
8,860 |
25 = c \cdot c \implies \sqrt{c^2} = \sqrt{25}
|
-4,582 |
\frac{27 \cdot (-1) + x \cdot 7}{x^2 - 8 \cdot x + 15} = \frac{1}{x + 5 \cdot \left(-1\right)} \cdot 4 + \dfrac{1}{3 \cdot (-1) + x} \cdot 3
|
29,796 |
\sin(z) = \frac{1}{2 i} (e^{i z} - e^{-i z}) = -i \sinh(i z)
|
6,678 |
1 + 9 z^2 + 6 z = \left(z*3 + 1\right) \left(z*3 + 1\right)
|
292 |
\sqrt{2 + y^2} + y = r \cdot r \implies \dfrac{1}{2\cdot r \cdot r}\cdot (2\cdot (-1) + r^4) = y
|
40,078 |
H_1 \cdot H_2 = H_1 \cdot H_2
|
19,243 |
|AB| = |AB|
|
5,038 |
A/A = \frac1AA
|
9,970 |
\binom{-k + N_2}{-k + N_1} = \dfrac{(N_2 - k)!}{(-N_1 + N_2)! \cdot (N_1 - k)!}
|
26,547 |
\sin(x) = \frac{\sin^2(x)}{\sin(x)} = \sin(x)
|
19,981 |
\dfrac{1}{2} \cdot (-Q_t^2 + (Q_t + V_t) \cdot (Q_t + V_t) - V_t^2) = V_t \cdot Q_t
|
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