id int64 -30,985 55.9k | text stringlengths 5 437k |
|---|---|
6,127 | A^{b c} = A^{c b} |
667 | p + 1 = \frac{1}{(-1) + p}\cdot (p^2 + (-1)) |
-29,572 | (3 \cdot \gamma^2 + 10 \cdot (-1))/\gamma = \tfrac{3}{\gamma} \cdot \gamma^2 - \frac{1}{\gamma} \cdot 10 |
1,936 | 1 + x = 3 \pi/2 + \cos\left(\frac{\pi}{2} 3\right)\Longrightarrow 2 (-1) + 3 \pi/2 = x |
-22,138 | \frac{1}{2} = \frac{1}{24} 12 |
625 | |z + w| = |z - w| \implies |-w + z|^2 = |w + z|^2 |
-18,952 | \frac45 = \dfrac{A_s}{9 \cdot \pi} \cdot 9 \cdot \pi = A_s |
-4,614 | \frac{4}{(-1) + x} + \dfrac{5}{2 \cdot (-1) + x} = \frac{9 \cdot x + 13 \cdot \left(-1\right)}{x^2 - 3 \cdot x + 2} |
-3,798 | \frac{r^4}{r \cdot r} = \dfrac{r^4}{r\cdot r}\cdot 1 = r^2 |
39,869 | z/\left(\dfrac{1}{y}\right) = y \cdot z |
1,667 | 27 + y^6 = (y^2 + y\cdot 3 + 3)\cdot (y \cdot y - 3\cdot y + 3)\cdot (3 + y^2) |
9,949 | k/x + l/x = (l + k)/x |
-873 | \frac{3}{10000} + 0 + 0/10 + \frac{1}{100} + \frac{7}{1000} = 173/10000 |
16,263 | 1 = \frac{1}{d_2} + \frac{1}{d_2 + b} + \frac{1}{d_2 + b + d_1} \geq \frac{1}{d_2 + b + d_1}3 |
-16,493 | 10 \times \sqrt{9 \times 7} = 10 \times \sqrt{63} |
-1,874 | \pi/6 = 7/4 \cdot \pi - 19/12 \cdot \pi |
-30,543 | \frac{dy}{dx} = \frac{\left(xy\right)^2}{8} + y^2 = y \cdot y/8 (x \cdot x + 8) |
33,657 | x^3 - x^2 + x^2 - x = -x + x^2 \cdot x |
31,170 | \frac{16}{3} = \sqrt{64}/3\cdot 2 |
24,993 | x^R\cdot D^R\cdot D\cdot x = \|D\cdot x\|^2 \leq \|D\|^2\cdot x^R\cdot x |
-2,989 | \sqrt{11} = (4 + 3*\left(-1\right))*\sqrt{11} |
-22,297 | 3\cdot (-1) + k^2 + k\cdot 2 = \left((-1) + k\right)\cdot \left(3 + k\right) |
-26,490 | x^2*49 + 100 - 140*x = \left(10 - 7*x\right)^2 |
40,867 | 1 - 1 + 1 - 1 + 5 = (-1) \left(-1\right) \cdot 5 = 5 |
-2 | -15 = -11 + 4 \cdot (-1) |
-23,065 | --4/3 \times 5 = 20/3 |
-18,506 | 5*x + 10 = 6*\left(2*x + 2\right) = 12*x + 12 |
6,101 | \tfrac{1}{3}\cdot 2/3 = \frac19\cdot 2 |
22,416 | q^p\cdot s\cdot q^i = q^i\cdot s\cdot q^p |
38,825 | 3 \cdot 5^2 = 75 |
21,064 | \dfrac{1}{1 - x * x} = \frac{1}{\left(-1\right)*\left(x + (-1)\right)*(x + 1)} = -\dfrac{1}{(x + (-1))*(x + 1)} |
-20,600 | \frac{1}{-18}\cdot \left(-9\cdot y + 12\right) = 3/3\cdot \tfrac{1}{-6}\cdot (-3\cdot y + 4) |
-15,146 | \tfrac{y^5}{\dfrac{1}{\frac{1}{s^{25}} \frac{1}{y^{10}}}} = \frac{y^5}{y^{10} s^{25}} |
35,002 | -n^2 + m^2 = 0 rightarrow m^2 = n * n |
-1,700 | \frac{3}{4}\cdot \pi = \pi/2 + \pi/4 |
-2,546 | 275^{\dfrac{1}{2}} + 11^{1 / 2} = 11^{\frac{1}{2}} + (25\times 11)^{\dfrac{1}{2}} |
20,217 | \sqrt{0.5 \cdot ((-1) \cdot 0.5 + 1) \cdot 900} = 15 |
-20,496 | \frac{1}{16} \times 2 = \frac18 \times 1 |
19,415 | 3 \cdot \left(-1\right) + z \cdot 2 = z\Longrightarrow 3 = z |
32,548 | \left(-1 - \frac13\right)^2\cdot \frac59 + 4/9\cdot (2 - 1/3)^2 = 20/9 |
46,119 | 3^{9 + (-1)} = 3^8 = 6561 |
-16,341 | \sqrt{80} \cdot 10 = 10 \cdot \sqrt{16 \cdot 5} |
25,446 | (1 + x)^2 = 1 + x^2 = 1 - x \cdot x |
-14,605 | 83 = \dfrac{1}{4}*332 |
16,966 | d^2 - c \times c = (-c + d) \times (d + c) |
-27,693 | \frac{\mathrm{d}}{\mathrm{d}z} (-\sin\left(z\right) \cdot 9) = -\cos\left(z\right) \cdot 9 |
-17,009 | 3 = 3*(-u) + 3*(-5) = -3*u - 15 = -3*u + 15*(-1) |
-2,725 | (25 \cdot 6)^{1/2} - (4 \cdot 6)^{1/2} = -24^{1/2} + 150^{1/2} |
47,520 | |z_1 \cdot y_1 - z_2 \cdot y_2| = |z_1 \cdot y_1 - z_1 \cdot y_2 + z_1 \cdot y_2 - z_2 \cdot y_2| \leq |z_1 \cdot y_1 - z_1 \cdot y_2| + |z_1 \cdot y_2 - z_2 \cdot y_2| |
18,257 | 1 + (-1) + 1 + (-1) + 1 - \cdots = \frac12 |
26,709 | (y + x)^2 - (-x + y)^2 = 4yx |
24,190 | \frac{4\times 13^3}{26\times 17\times 50} = \dfrac{4\times 13^2}{2\times 17\times 50} = 169/425 |
4,559 | \sin(y_2 + y_1) = \sin{y_2} \cdot \cos{y_1} + \cos{y_2} \cdot \sin{y_1} |
7,454 | W_g x = W_g x |
8,704 | \cos(x - y) = \cos(x)*\cos(y) + \sin(x)*\sin\left(y\right) |
20,499 | \sin(x) < 0 \Rightarrow x = -2\pi/3 |
4,797 | ((-1) + e^x)\cdot \dfrac{x}{e^x + (-1)} = x |
-12,290 | \frac{1}{12} = s/(12 \pi)\cdot 12 \pi = s |
45,141 | \frac{x + (-1)}{x^2 - 5\cdot x + 6} = \dfrac{\frac{1}{2}\cdot (2\cdot x + 2\cdot (-1))}{x \cdot x - 5\cdot x + 6} = \dfrac{1}{x^2 - 5\cdot x + 6}\cdot (\frac{3}{2} + \frac12\cdot \left(2\cdot x + 5\cdot (-1)\right)) = \frac{2\cdot x + 5\cdot (-1)}{2\cdot (x^2 - 5\cdot x + 6)} + \frac{3}{2\cdot (x^2 - 5\cdot x + 6)} |
25,682 | p = (z - u)/2 \Rightarrow p^2 + 1 = (z \cdot z - u\cdot z\cdot 2 + u^2)/4 + 1 |
34,938 | det\left(t\cdot I - A\cdot D\right) = det\left(I\cdot t - D\cdot A\right) |
5,622 | \left(f - t\right) \cdot \left(t + f\right) = f^2 - t^2 |
18,567 | 2^2 \times x^2 = x^2 \times 4 |
31,500 | \left(-\sqrt{4^2 + 12 \times (-1)} + 2 = 0 \implies 2 - \sqrt{16 + 12 \times (-1)} = 0\right) \implies 0 = 0 |
35,241 | \overline{w}\cdot \overline{z} = \overline{z\cdot w} |
1,027 | a + \tfrac{1}{(-1) b} = a + (-1) + \frac{1}{1 + \frac{1}{b + (-1)}} |
-9,629 | 0.01 \cdot (-20) = -\frac{20}{100} = -0.2 |
-16,418 | 5 \cdot \left(16 \cdot 13\right)^{1/2} = 5 \cdot 208^{1/2} |
34,560 | \frac{2}{2} \cdot x = \frac12 \cdot 2 \cdot x = x |
6,782 | 10^{-(m + s)} = 10^{-m - s} |
-6,103 | \dfrac{5}{5(m + 10)} = \frac{5}{5m + 50} |
14,272 | \log_e\left(d\right)\cdot d^x = \frac{\partial}{\partial x} d^x |
-9,615 | -\frac{1}{5}4 = -0.8 |
-26,577 | (y + 8) \cdot (y + 8 \cdot (-1)) = y^2 - 8^2 |
139 | 4/27 = 2/3/3*2/3 |
-5,924 | \frac{1}{k \cdot k + 36 \cdot (-1)} \cdot \left(k + 6 + k \cdot 3 + 18 \cdot \left(-1\right) + 3 \cdot k\right) = \dfrac{12 \cdot (-1) + 7 \cdot k}{k \cdot k + 36 \cdot \left(-1\right)} |
33,321 | e \cdot 0 = e \cdot (0 + 0) = e \cdot 0 + e \cdot 0 |
21,327 | \sum_{m=1}^l h_m = \sum_{m=1}^l h_m |
-1,890 | \pi\cdot 2 - \dfrac13\cdot 4\cdot \pi = 2/3\cdot \pi |
1,062 | (2^p f)^3 = 2^{3 p} f^3 |
19,011 | 20 - 5 \times \sqrt{-2} = -5 \times \sqrt{2} \times i + 20 |
31,627 | \dfrac{x^2}{z}\cdot t = (t\cdot x)^2/(z\cdot t) |
-20,471 | 2/2 \frac{-2x + 8}{-x + 1} = \frac{-4x + 16}{-2x + 2} |
31,424 | \frac{1}{1 - x^2} = \sum_{k=0}^∞ (x^2)^k = \sum_{k=0}^∞ x^{2k} |
4,040 | (-1) + \left(q + (-1)\right) \cdot ((-1) + p) = p \cdot q - p - q |
-22,228 | \left(y + 8\right) \cdot (y + 6) = y^2 + y \cdot 14 + 48 |
21,725 | d^2 - b \times b = \left(-b + d\right)\times (b + d) |
28,122 | x_l\cdot x_{l + 1} = x_{l + 1}\cdot x_l |
19,107 | \sin(\frac12 \cdot π + x) = \cos(x) |
14,196 | \cos(\pi + i) = -\cos{i} = -\frac12\cdot (e^{i^2} + e^{-i \cdot i}) = -\left(e + 1/e\right)/2 |
25,263 | \dfrac{1}{1 + 1/4} \cdot (1 + \dfrac{1}{2}) = 1.2 < 1 + 1/4 |
20,333 | 24/72 = \tfrac13 |
6,835 | 1 - 80*x * x - 120*x + 45*(-1) = -5*(x^2*16 + 24*x + 9) + 1 |
1,409 | -n^{\tfrac{1}{2}} + (n + 1)^{1 / 2} = \frac{1}{(n + 1)^{\frac{1}{2}} + n^{\frac{1}{2}}} |
-18,492 | -\dfrac{1}{11}\cdot 13 = -\tfrac{13}{11} |
-12,940 | 5\left(-1\right) + 21 = 16 |
1,045 | \dfrac19(2^{3^m}*2^{3^m}*2^{3^m} + 1) = (2^{3^{m + 1}} + 1)/9 |
5,489 | -\pi/20 + \pi/2 = \pi\cdot 9/20 |
1,637 | \alpha + \beta + \alpha + \alpha = 3 \alpha + \beta |
7,204 | (-1) + R^2 = (R + 1) \cdot (R + (-1)) |
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