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int64 -30,985
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29,728 | 9^9 \frac{1}{e^9}/9! = 9^8 \dfrac{1}{e^9}/8! |
17,809 | \nu_x^1 = \nu_x |
-20,697 | \frac{4 + r}{r \cdot 9 + 4(-1)} \frac{5}{5} = \dfrac{5r + 20}{45 r + 20 \left(-1\right)} |
48,010 | \left(x^{1/2}\right)^2 = x |
21,571 | a = a \cdot b = b \implies b = a |
3,457 | (4 + x)\cdot \left(1 + x\right) = (-1) + x^2 + x\cdot 5 + 5 |
31,753 | z\cdot R\cdot x = x\cdot R\cdot z |
-4,055 | 9\cdot a^2/5 = 9/5\cdot a^2 |
-1,987 | \pi \dfrac{7}{12} + 5/12 \pi = \pi |
23,392 | \alpha - \beta = \frac{1}{\alpha + \beta} (-\beta \beta + \alpha^2) |
-26,658 | 3 + 2\cdot x \cdot x + 7\cdot x = (2\cdot x + 1)\cdot (x + 3) |
12,625 | x^2 + g * g + gx*2 = \left(x + g\right)^2 |
-15,309 | \frac{1}{1/m \frac{1}{p^5}}m^3 = \frac{m^3\cdot \frac{1}{1/m}}{\frac{1}{p^5}} = m^{3 - -1} p^5 = m^4 p^5 |
11,068 | 15 = (60\cdot (-1) + 90)\cdot \frac{1}{2} |
34,521 | a^{x + l} = a^l a^x |
6,322 | \frac{1/3*2}{3}*1 = \dfrac29 |
1,452 | (-y + x) * (-y + x) = y^2 + x^2 - 2*x*y |
23,880 | (L - c)*(b - d) = L*b + c*d - L*d - b*c = L*b + c*d - L*d + b*c |
12,380 | 2\cdot x = \pi \Rightarrow x = \pi/2 |
21,503 | \chi \gt -R + 1 \Rightarrow -\chi + 1 \lt R |
1,768 | [a, b] = \left[f,d\right] rightarrow a = b,f = d |
26,907 | 6/6 + 6/5 + \frac{6}{4} + 6/3 + \frac{6}{2} + \frac{6}{1} = 14.7 |
15,252 | \lim_{m \to \infty}(-b_m + c_m) = 0 \implies 1 = \lim_{m \to \infty} c_m/(b_m) |
-25,510 | \frac{d}{dt} (\frac{4}{2 + t}) = -\frac{4}{(t + 2)^2} |
-1,650 | \frac{11}{12}\cdot π + 4/3\cdot π = \frac14\cdot 9\cdot π |
-16,552 | 5 \cdot (9 \cdot 5)^{\frac{1}{2}} = 5 \cdot 45^{\frac{1}{2}} |
24,236 | X \backslash C + y = X \cap \overline{C + y} = X \cap \overline{C} + y |
5,479 | \tfrac{1}{2!} 4!*3!/2! = 3!*3! = 36 |
-11,540 | 4 + 6\times i = 4 + 0\times (-1) + i\times 6 |
51,267 | \frac{14}{95^{\frac{1}{2}} + 9 \cdot (-1)} = \left(95^{1 / 2} + 9\right)/1 = 18 + \frac{1}{1} \cdot (95^{\tfrac{1}{2}} + 9 \cdot (-1)) |
21,873 | \left(0 = 1 + 1 + 2n - n \cdot 6 + 10 \left(-1\right) \implies 8(-1) - 4n = 0\right) \implies n = -2 |
-26,554 | -(3 \times y)^2 + 10^2 = (10 + 3 \times y) \times (-y \times 3 + 10) |
11,029 | -b + ba - a = a\cdot \left(b + (-1)\right) + b\cdot (-1) |
-9,160 | -a\cdot 2\cdot 3\cdot 3 a - 2\cdot 13 a = -18 a \cdot a - 26 a |
6,642 | (b + f)\cdot 2 = f + b + f + b |
5,060 | \dfrac{1}{-1} \cdot \sqrt{|-1| \cdot 2 - (-1)^2} = -1 |
1,008 | (k + 1) \cdot \pi/3 = \pi/3 + \tfrac{\pi}{3} \cdot k |
31,802 | \frac{1}{12}\cdot \left(1 + \sqrt{6}\right) = \sqrt{6}/12 + \frac{1}{12} |
20,856 | A \cdot A^T \cdot A^T \cdot A \cdot A^T \cdot A = A \cdot A \cdot A^T \cdot A \cdot A^T \cdot A^T |
-20,533 | \tfrac{5 + 7 \cdot z}{7 \cdot z + 5} \cdot 4/1 = \frac{20 + 28 \cdot z}{7 \cdot z + 5} |
8,087 | -s\cdot t = -x \implies x = s\cdot t |
6,723 | (1 + \alpha)^3 = (1 + \alpha) (\alpha + 1) (1 + \alpha) |
-24,017 | 10 + 6*16/2 = 10 + 6*8 = 10 + 6*8 = 10 + 48 = 58 |
29,948 | 1 = \frac{1}{-\tfrac{2}{3 + (-1)} + 3} \cdot 2 |
-22,307 | 2 + r \cdot r + r\cdot 3 = (r + 1)\cdot (2 + r) |
27,255 | h\cdot e\cdot h = e = h\cdot e\cdot h |
10,430 | 19 + q^4 - q^2\cdot 20 = (19\cdot (-1) + q \cdot q)\cdot \left(q^2 + (-1)\right) |
-5,713 | \frac{3}{10 + 5 \cdot m} = \frac{1}{5 \cdot (m + 2)} \cdot 3 |
-22,835 | \frac{108}{120} = \frac{9\cdot 12}{10\cdot 12} |
23,394 | \left(1 + 6 + 3\right)^n = 10^n |
527 | 1 = \frac{1}{2} \cdot \left(v - u + 2\right) + u + v + 4 \cdot (-1) \Rightarrow v \cdot 3 + u = 8 |
13,055 | l\cdot 2\cdot 2 = 4\cdot l |
28,142 | -z^3 + z = \frac{1}{X^2}\cdot L\cdot M rightarrow (1 - z^2)\cdot z = \tfrac{L}{X \cdot X}\cdot M |
30,520 | \frac{x}{\sqrt{\frac{xy}{n}}}=x\sqrt{\frac{n}{xy}}=\sqrt{\frac{nx}y} |
-17,708 | 80 = 18*\left(-1\right) + 98 |
34,849 | 3952*253 - 255*3921 = 1 |
30,900 | (z_2 - z_1)\cdot (z_2^2 + z_2\cdot z_1 + z_1^2) = z_2^3 - z_1^3 |
47,341 | 39 = 14 + 1\cdot 25 |
884 | 1 = \left|{\dfrac{A}{A}}\right| = \left|{A}\right|\cdot \left|{\tfrac{1}{A}}\right| |
36,115 | |v\cdot x| = |v|\cdot |x| |
32,698 | 1431 = 1 + 2\times 26^2 + 3\times 26 |
22,814 | -1/2\cdot x_4 + x_1 = 0 \Rightarrow x_1 = 1/2\cdot x_4 |
15,252 | \lim_{n\to\infty}(a_n-b_n)=0\Rightarrow \lim_{n\to\infty}\frac{a_n}{b_n}=1 |
-18,069 | 4 = 73 (-1) + 77 |
-18,787 | 2 = \frac63 |
13,495 | (x + 4\cdot (-1))/2\cdot 2 = x + 4\cdot (-1) |
-12,038 | \frac{2}{3} = s/(16\times \pi)\times 16\times \pi = s |
24,855 | \left(1423 \cdot D\right) \cdot \left(1423 \cdot D\right) = 1423^2 \cdot D = 12 \cdot 34 \cdot D = D |
-26,622 | (9\cdot (-1) + 4\cdot x^3)\cdot (x \cdot x \cdot x\cdot 4 + 9) = -9^2 + \left(4\cdot x^3\right) \cdot \left(4\cdot x^3\right) |
-18,779 | \dfrac{8x}{4} = 2x |
-20,323 | (2 + x \cdot 2)/\left(-10\right) \cdot \frac{1}{4} \cdot 4 = \dfrac{1}{-40} \cdot (x \cdot 8 + 8) |
2,675 | \tan{x} = \frac{1}{\cos{x}} \cdot \sin{x} = 1/\cot{x} |
-23,374 | \frac{1}{6} = \frac{1}{3*2} |
-10,962 | 48 = \dfrac14 \cdot 192 |
3,971 | (4^3 - 4^2 + 4*(-1) + 1)*4^{2013} = 4^{2016} - 4^{2015} - 4^{2014} + 4^{2013} |
33,438 | \pi \cdot \frac13 \cdot 2 = 2 \cdot \pi/3 |
23,846 | \dfrac{1}{n + k}*n = \frac{1}{n + k}*(n + k - k) = 1 - \frac{k}{n + k} |
-543 | (e^{19 \pi i/12})^{10} = e^{10 \frac{1}{12}\pi*19 i} |
44,882 | \sum_{l=i}^n l = \sum_{l=0}^{n - i} (i + l) = \sum_{l=0}^{n - i} i + \sum_{l=0}^{n - i} l |
-22,429 | 8^{\frac{7}{3}}=\left(8^{\frac{1}{3}}\right)^{7}=2^{7} = 2\cdot2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2 = 4\cdot2\cdot 2\cdot 2\cdot 2\cdot 2 = 8\cdot2\cdot 2\cdot 2\cdot 2 = 16\cdot2\cdot 2\cdot 2 = 32\cdot2\cdot 2 = 64\cdot2 = 128 |
4,760 | 4\cdot y + 4\cdot \left(-1\right) = 4\cdot \left(y + 2\cdot (-1)\right) + 8 + 4\cdot (-1) = 4\cdot \left(y + 2\cdot \left(-1\right)\right) + 4 |
14,422 | \frac{3}{50} = \frac{8}{4 + 8} \cdot \frac{3}{5 + 3} \cdot (\left(-1\right) \cdot 0.4 + 1) \cdot 0.4 |
550 | 1 - 8/y^3 = 0 \implies y=2 |
29,596 | \left(\left(-1\right) + y\right)^3 + y^3 + \left(1 + y\right)^3 = y*6 + 3 y^3 |
33,657 | l^3 - l^2 + l^2 - l = l \cdot l^2 - l |
8,301 | 0 = x^2 * x - 2*x^2 - 5*x + 6 = (x + \left(-1\right))*(x + 2)*\left(x + 3*(-1)\right) |
-1,664 | -2 \cdot \pi + \pi \cdot 13/6 = \frac{\pi}{6} |
7,513 | \dfrac{y}{1} = \left(1 - z\right)/3 = r rightarrow y = r\wedge z = 1 - r\cdot 3 |
39,382 | 12 \left(-1\right) + 22 = 10 |
-3,695 | \frac{132\cdot q}{99\cdot q^2} = \frac{1}{q^2}\cdot q\cdot 132/99 |
23,692 | n^{j \cdot 2} + (-1) = (\left(-1\right) + n^j) \cdot \left(n^j + 1\right) |
25,363 | \frac{1}{2}\cdot \sqrt{X\cdot 4} = \sqrt{X} |
24,366 | b^{s/q} = (b^{\frac{1}{q}})^s = (b^s)^{\dfrac{1}{q}} |
48,475 | F_2 = F_2 |
-28,894 | 20!=20\cdot19\cdot18\cdot...\cdot3\cdot2\cdot1 |
48,842 | (-1)^{2/2} = (-1)^1 = -1 |
46,887 | 52 = \dfrac{1}{1/52} |
21,528 | b^{y + x} = b^x b^y |
26,216 | -z_2 * z_2 + z_1 * z_1 = (z_1 - z_2)*\left(z_2 + z_1\right) |
-26,543 | 9 - 25 z^2 = \left(-z*5 + 3\right) (z*5 + 3) |
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