id int64 -30,985 55.9k | text stringlengths 5 437k |
|---|---|
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} |
-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 |
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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