id int64 -30,985 55.9k | text stringlengths 5 437k |
|---|---|
8,241 | s \cdot q = q \cdot s |
-23,331 | \dfrac{1}{3} \cdot \dfrac{2}{7} = \dfrac{2}{21} |
-18,984 | \dfrac58 = B_q/(100 \pi)*100 \pi = B_q |
41,333 | b_{i_x} = b_{i_x} |
-9,117 | 146.6\% = \frac{1}{100}\cdot 146.6 |
-16,490 | 5\cdot \left(9\cdot 7\right)^{1 / 2} = 63^{\frac{1}{2}}\cdot 5 |
-3,605 | 40/32 \frac{n^2}{n} = \frac{40 n^2}{n*32} |
-26,056 | (h_1 - h_2) \cdot \left(h_1 + h_2\right) = h_1^2 - h_2^2 |
-29,486 | 10 \left(-9 - 6\right) = 10 \left(-15\right) = -150 |
17,222 | 1/2 + 1/4 + 1/8 + \cdots + \frac{1}{2^k} = \frac{1}{2^k}*\left((-1) + 2^k\right) |
27,123 | z^{\frac14}\cdot z^4 = z^{\frac14 + 4} = z^{17/4} |
-20,905 | -7/4 \cdot \frac{x + 3 \cdot (-1)}{3 \cdot (-1) + x} = \frac{21 - x \cdot 7}{x \cdot 4 + 12 \cdot (-1)} |
29,204 | (a + \left(-1\right)) (c + (-1)) + 1 = c a - a + c + 2 |
15,060 | 11 = 11 + 0\cdot 3^{1/2} |
28,695 | 32\cdot x - 2\cdot 0 + 255\cdot (-1) = 0 \Rightarrow \frac{255}{32} = x |
-205 | \binom{7}{4} = \frac{1}{4!\cdot (7 + 4\cdot (-1))!}\cdot 7! |
-15,842 | -4/10\cdot 10 + \frac{6}{10}\cdot 5 = -10/10 |
19,821 | 38304 = (\frac{4}{120} + 1/4 + \dfrac{1}{6} + 1/2)*8! |
19,970 | {x \choose x + 2 \cdot \left(-1\right)} = {x \choose 2} |
-1,336 | \dfrac{\frac{1}{8}*3}{(-3)*1/7} = \frac18*3*(-7/3) |
34,845 | a\cdot 8 - 7\cdot a = a |
4,652 | -\sqrt{h} + \sqrt{x} = \frac{x - h}{\sqrt{h} + \sqrt{x}} |
-20,953 | 8/5 x*8/\left(8x\right) = \dfrac{1}{x*40}64 x |
34,845 | -7 e + e*8 = e |
-10,299 | -\dfrac{1}{3*x + 3*\left(-1\right)}*\dfrac{5}{5} = -\frac{1}{x*15 + 15*\left(-1\right)}*5 |
7,445 | -2 + 24*\left(-1\right) = -26 = (-1)*26 |
23,986 | (\frac{z}{g} \cdot g)^i = g \cdot z^i/g |
30,139 | \left(1 = (\frac{1}{x^3} \cdot a + 1)/2 \implies x^3 = a\right) \implies x = a^{1/3} |
250 | i = \cos(\frac{\pi}{2}) + i \cdot \sin(\pi/2) |
-10,358 | 4 = -2 + 4\cdot m + 6\cdot (-1) = 4\cdot m + 8\cdot \left(-1\right) |
24,966 | v = 2 + e^x \Rightarrow \frac{\mathrm{d}v}{\mathrm{d}x} = e^x = v + 2\cdot \left(-1\right) |
39,097 | (f - x)^2 = -(\varphi - h)^2 \Rightarrow (\varphi - h) \cdot (\varphi - h) + (f - x)^2 = 0 |
44,731 | 2 = \dfrac{1}{1}\cdot 2 |
32,624 | 18 \times 6 = 108 |
23,908 | \sinh^2(x) = \frac{1}{4} \cdot \left(e^x - e^{-x}\right)^2 = \frac14 \cdot \left(e^{2 \cdot x} + e^{-2 \cdot x} - 2 \cdot e^0\right) |
18,333 | 1/\left(y\cdot y\right) = \dfrac{1}{y \cdot y} |
922 | |\frac{1}{1 + i\cdot y\cdot 2}\cdot (i\cdot 2 - 3\cdot y)| = \frac{|-3\cdot y + 2\cdot i|}{|i\cdot y\cdot 2 + 1|} |
19,194 | k^2 + m^4 - m^2 \cdot k \cdot 2 = (-k + m \cdot m)^2 |
-9,464 | -6\cdot p = -p\cdot 2\cdot 3 |
-2,316 | 8/15 - \frac{3}{15} = 5/15 |
16,118 | k \neq i \Rightarrow -i + k \neq 0 |
-5,201 | 0.2 \cdot 10^{(-5) \cdot (-1) + 2} = 10^7 \cdot 0.2 |
46,338 | \dfrac{1}{45} = 4/180 |
2,696 | \frac{\text{d}}{\text{d}x} \dfrac{1}{z} = -\frac{1}{z^2}\frac{\text{d}z}{\text{d}x} |
27,238 | (-\dfrac14)^j = (-1)^j*2^{-j*2} |
7,669 | 4\cdot (t - l) = -\left(l - t\right)\cdot 4 |
12,330 | \tfrac{9}{3} + 5 - 0 \cdot 3 = 9/3 + 5 - 0 \cdot 3 |
12,659 | |x - y| = y - x = \frac{y^2 - x^2}{x + y} < (y^2 - x^2)/(2\cdot x) |
25,931 | {12 \choose 2}*{4 \choose 1}^2*{4 \choose 3}*{13 \choose 1} = 54912 |
1,991 | u \cdot v = v^R \cdot u = u^R \cdot v |
30,782 | (\tfrac1y\left(y + 2\right))^{-1/2} = (\frac{1}{y}2 + 1)^{-\frac{1}{2}} |
6,341 | 2 = \frac{1}{3 - \frac{1}{3 - \frac{2}{3 - \frac{2}{3 + 2(-1)}}}2}2 |
8,782 | s = r\cdot x/r \implies x = s\cdot r^2 |
840 | 2 + \dfrac{1}{\frac15 + 3} = \frac{1}{16} \cdot 37 |
2,807 | \dfrac{1}{1 - y}\cdot (4\cdot y + 3\cdot (-1)) = -\frac{1}{y + (-1)}\cdot \left(4\cdot (y + (-1)) + 1\right) = -4 + \dfrac{1}{1 - y} |
-1,758 | \pi \cdot \frac{1}{12} \cdot 13 = \pi \cdot 23/12 - 5/6 \cdot \pi |
-10,848 | \dfrac{1}{5} \cdot 65 = 13 |
38,637 | \frac{\mathrm{d}}{\mathrm{d}y} (9\times e^{6\times y}) = 9\times 6\times e^{6\times y} = 54\times e^{6\times y} |
-26,686 | 10 = |10| |
-25,239 | d/dx \tfrac{1}{x^{12}} = -\frac{12}{x^{13}} |
587 | \cot{z} - 8 \cdot \cot{8 \cdot z} = \cot{z} - 8 \cdot \cot{8 \cdot z} = \cot{z} - 8 \cdot \frac{\cot^{24}{z} + \left(-1\right)}{2 \cdot \cot{4 \cdot z}} |
29,547 | H\cdot h = h\cdot \frac1h\cdot h\cdot H |
41,599 | \binom{k}{x + 1} = \tfrac{k!}{\left(k - x + (-1)\right)! \cdot (x + 1)!} = \frac{k! \cdot (k - x)}{(k - x)! \cdot \left(x + 1\right) \cdot x!} = \binom{k}{x} \cdot \frac{k - x}{x + 1} |
4,730 | \frac{1}{d b} (a d - c b) = a/b - \frac{c}{d} |
4,591 | 3 k\cdot 5 = 15 k |
8,630 | 86/100\cdot 114/100 x = x |
28,071 | \dfrac13 = \frac22\cdot 1/3 |
16,805 | f^{n + N} = f^n\cdot f^N |
-11,696 | \dfrac{1}{25} = \left(1/5\right)^2 |
49,491 | \sum_{k=1}^\infty \frac{4^k + k}{k + 6^k} = \sum_{k=1}^\infty \frac{\frac{4^k}{k} + 1}{\frac1k\cdot 6^k + 1} |
27,754 | qr^i r^k = qr^i r^k |
44,425 | 41 + 32\times (-1) = 9 |
20,741 | \mathbb{E}(X^2) = \mathbb{E}(X)^2 + \mathbb{E}(\left(X - \mathbb{E}(X)\right)^2) |
32,274 | 5 + n*2 = \left(-1\right) + 2*(n + 3) |
29,630 | H^2 - x \times x = \left(H - x\right)\times (x + H) |
-16,866 | 8 = 8 \cdot 4 \cdot q + 8 \cdot 3 = 32 \cdot q + 24 = 32 \cdot q + 24 |
1,340 | 21821 \times \left(3 \times 7 \times 11 \times 13\right) \times \left(3 \times 7 \times 11 \times 13\right) = 196781974389 |
24,224 | A_k^T \cdot A_{k + (-1)}^T \cdot ... \cdot A_2^T \cdot A_1^T = (A_1 \cdot A_2 \cdot ... \cdot A_{k + (-1)} \cdot A_k)^T |
-29,210 | 15 = (-1) + 0*3 + 4*4 |
10,913 | \cos(y)/(\sqrt{2}) + \dfrac{1}{\sqrt{2}} \cdot \sin(y) = \cos(y - \frac{\pi}{4}) |
12,399 | x^4 + 5 \times x + 1 = (x^2 + 1) \times (x \times x + (-1)) + 5 \times x + 5 \times \left(-1\right) = (x + (-1)) \times \left(x \times x \times x + x^2 + x + 6\right) |
23,260 | \cos(-v + π/2) = \sin\left(v\right) |
17,368 | \binom{l\times 2}{l}\times l!^2 = (l\times 2)! |
10,149 | \sin(\frac{13 \pi}{6}) = 1/2 |
2,925 | 540 = 3! \cdot \binom{3}{1} \cdot \binom{4}{2} \cdot \binom{5}{1} |
19,489 | E = E \cap (Y \cup c) = \left(E \cap Y\right) \cup \left(E \cap c\right) |
-3,732 | \frac{p^3}{p} = \frac{pp p}{p} = p^2 |
-6,632 | \frac{4}{(1 + z) \cdot (z + 8)} \cdot \frac99 = \frac{1}{\left(z + 1\right) \cdot (8 + z) \cdot 9} \cdot 36 |
40,946 | 3 \beta - 2 y + z + 3 = 0 = 4 \beta - 3 y + 4 z + 1 |
1,343 | \int_a^b 1/x\,\mathrm{d}x = \int\limits_a^b 1/x\,\mathrm{d}x |
2,966 | 180 - -X + 180 - Z = X + Z |
40,087 | (2^2*3*5)^{\dfrac{1}{2}} = 2 (3*5)^{\frac{1}{2}} = 2*15^{1 / 2} |
-10,662 | \frac{2}{2}\cdot \left(-5/\left(6\cdot t\right)\right) = -\frac{10}{t\cdot 12} |
-24,321 | 1 + 4 \cdot 8 = 1 + 32 = 1 + 32 = 33 |
4,215 | 5 = i - l + (-1) = i - l + 1 |
-9,022 | 131.8\% = \frac{1}{100}\cdot 131.8 |
9,176 | \frac{x}{(x + (-1))!} = \dfrac{1}{\left(x + (-1)\right)!} \cdot (x + \left(-1\right) + 1) = \dfrac{1}{(x + 2 \cdot (-1))!} + \frac{1}{\left(x + (-1)\right)!} |
25,096 | \cos{2*t} = \cos^2{t} - \sin^2{t} = 1 - 2*\sin^2{t} |
22,386 | (1 + 1) \cdot \left(1 + 2\right) \cdot (1 + 3)/4 = 24/4 = 6 |
5,504 | \dfrac{3 + m*4}{m*7 + 5*(-1)} = \frac{1}{7 - 5/m}*(4 + \dfrac3m) |
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