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16,376 | y^2 = (y + 2)^2 - (y + 7*(-1))^2 = \left(y + 2 + y + 7*\left(-1\right)\right)*(y + 2 - y + 7) = 9*\left(2*y + 5*(-1)\right) = 18*y + 45*(-1) |
-20,701 | -7/1 \frac{k + 8(-1)}{k + 8\left(-1\right)} = \frac{-k*7 + 56}{8(-1) + k} |
10,786 | -2 \cdot 4 \cdot \frac92 + 16 = 25 - 9/2 \cdot 2 \cdot 5 |
10,297 | y \cdot y + z \cdot z^2 = 1 \implies z^2 \cdot z = 1 - y^2 |
15,533 | e^z = (e^\dfrac{z}{2})^2 |
26,940 | (g^2 + g\cdot z + z \cdot z)\cdot (g - z) = g^3 - z \cdot z^2 |
20,163 | 0 \times 0 - 1/2 \times 1/2 = -1/4 \lt 0 |
-1,824 | \dfrac43\times \pi + 11/6\times \pi = \tfrac{1}{6}\times 19\times \pi |
14,633 | 11^2 - 10^2 = -2^2 + 5^2 |
-10,270 | \dfrac44*(-\frac{1}{25*k^3}*(k + 1)) = -\frac{1}{100*k^3}*(4*k + 4) |
31,506 | (x + \left(-1\right))/(2*x) = \tfrac{1}{2}*(1 - \frac{1}{x}) = \dfrac{1}{2} - \frac{1}{2*x} |
8,562 | \left(\frac{1 + t}{1 - t}\right)^{1 / 2} = \frac{1 + t}{(1 - t^2)^{1 / 2}} = (1 + t) \mathbb{E}\left[t\right] |
-23,072 | -1/3*2 = -2/3 |
12,085 | 4000\cdot o + 48^2 = 4\cdot q^2 \implies q^2 = 1000\cdot o + 24^2 |
26,585 | (1 + z)^2 \cdot (z + (-1)) = (1 + z) \cdot ((-1) + z^2) |
-8,016 | \frac{6}{3}\cdot i + 12/3 = \frac13\cdot \left(12 + i\cdot 6\right) |
6,537 | x \times x \times x + 1 = x \times x^2 + 1 |
32,280 | XXX = X^2 * X |
36,958 | 2^{n + 1} = 2.2^n \gt n^2 + n^2 |
-23,448 | 3/5\times 5/9 = 1/3 |
36,503 | \frac{1}{1 - t} = 1 + \frac{t}{1 - t} |
20,042 | h = h^1 = h^{p \cdot m + R \cdot k} = \left(h^m\right)^p \cdot (h^k)^R |
633 | \left(h^n + z^n \Leftrightarrow h + z = 0\right) \Rightarrow h^n + z^n = 0 |
20,284 | D\cdot G = G\cdot D |
-7,917 | \dfrac{(7+17i) \cdot (2-3i)}{(2+3i) \cdot (2-3i)} = \dfrac{(7+17i) \cdot (2-3i)}{2^2 - (3i)^2} |
24,643 | \frac{1}{1 + l_2} = \frac{1}{1 + l_1}\Longrightarrow l_1 = l_2 |
-5,776 | \frac{5*m}{\left(3 + m\right)*(5*(-1) + m)}*1 = \frac{5*m}{m^2 - 2*m + 15*(-1)} |
-13,922 | \tfrac{42}{8 + 6} = \frac{42}{14} = \frac{1}{14}*42 = 3 |
18,697 | -y + y \cdot y = y\cdot (y + (-1)) |
-16,613 | -8 = -8*\left(-2*y\right) - 56 = 16*y - 56 = 16*y + 56*(-1) |
1,426 | (2*b + c)^1 = c + 2*b |
17,272 | \frac12(-i*4 - 2) = -i*2 - 1 |
-12,517 | \dfrac{26}{2} = 13 |
23,026 | x^3 + x + 2 = (x + 1)\cdot (x^2 + 2\cdot x + 2) = (x + 1)\cdot (\left(x + 1\right)^2 + 1) |
-9,370 | 20 + 4\cdot n = 2\cdot 2\cdot n + 2\cdot 2\cdot 5 |
571 | \binom{2^l}{2} + (-1) = \frac{2^l}{2}\times (2^l + \left(-1\right)) + (-1) = \frac12\times (2^{2\times l} - 2^l + 2\times \left(-1\right)) |
-18,930 | \frac{1}{30} \cdot 7 = \frac{A_s}{100 \cdot \pi} \cdot 100 \cdot \pi = A_s |
16,042 | \frac{1}{b\cdot n}\cdot (-b + a\cdot n) = \dfrac{a}{b} - \dfrac{1}{n} |
-28,873 | 72 = 2^3 \cdot 3 \cdot 3 |
-2,010 | -\pi \times 2/3 = -3/4 \times \pi + \dfrac{\pi}{12} |
2,101 | s^4 - s^3 \cdot 4 + 9 \cdot s^2 - s \cdot 10 + 6 = (s^2 - 2 \cdot s + 2) \cdot (3 + s^2 - 2 \cdot s) |
8,487 | x^3 + 1729 = x^3 + 12^3 + 1^3 = x^3 + 10 \cdot 10 \cdot 10 + 9^3 |
12,080 | |a_n - L|\cdot |f| = |f\cdot a_n - L\cdot f| |
50,440 | 4\times 28 = 112 |
-25,475 | -\frac{24}{x^5} - \tfrac{1}{x^3}*2 = \frac{\mathrm{d}}{\mathrm{d}x} (\frac{1}{x^2} + \frac{6}{x^4}) |
4,938 | \left(6*5 + 6*9 + 9*10\right)*8*2*5*6*7 = 584640 |
3,379 | (\sin^3(y))^{1/3} = \left(\cos^3\left(y\right)\right)^{\frac{1}{3}}\Longrightarrow \cos\left(y\right) = \sin(y) |
10,331 | f_m - x = (\sqrt{x} + \sqrt{f_m})*\left(\sqrt{f_m} - \sqrt{x}\right) |
34,321 | \left(x + I\right) (x + 1 + I) = x * x + x + I = x^2 + 1 + x + (-1) + I = x + 1 + I |
14,578 | \left(h + 4\cdot (-1)\right)^2 + b^2 = h \cdot h - 8\cdot h + 16 + b^2 = h^2 + b^2 |
4,451 | q \neq 1\wedge \frac1q*p = \sqrt{m} \Rightarrow m = \frac{1}{q^2}*p * p |
27,780 | \dfrac{\binom{14}{9}}{2^{15}} = 1001/16384 |
24,536 | 2\cdot (2\cdot \left(-1\right) + (\left(-1\right) + 2\cdot i)\cdot (\left(-1\right) + 2\cdot j)\cdot 2 + 2\cdot i + j\cdot 2) = 4\cdot (-i + 4\cdot i\cdot j - j) |
24,398 | \frac {2n+1}{(2n+1)!}=\frac {1}{(2n)!} |
-10,599 | \frac{3}{9 \cdot (-1) + 3 \cdot t} = \dfrac{1}{t + 3 \cdot \left(-1\right)} \cdot 1 |
41,820 | 7^2 + 7 \times 11 + 11^2 = 13 \times (2 \times 2 + 2 \times 3 + 3^2) = 13 \times 19 |
35,305 | 3^2 + 4^2 + 12^2 + 84^2 + 132^2 = 157 * 157 |
46,923 | 3^3*5 = 135 |
13,597 | \frac{6 \cdot 4 \cdot 2}{{8 \choose 3}} = 6/7 |
23,259 | 5^2 + 5*25 + 25^2 = 25*(1 1 + 5 + 5^2) = 25*31 |
12,061 | E_{(-1) + x - i} = E_{x - i + (-1)} |
-5,735 | \frac{4}{\left(4 \left(-1\right) + y\right) \cdot 3} = \frac{4}{12 (-1) + y \cdot 3} |
8,344 | r\frac{1}{y}/z = r\frac1z/y = r/(yz) |
25,613 | 1 + \frac{5^{1/2}}{2} = 1 + 5^{1/2}/2 |
7,555 | 10002 = \sqrt{(2 + 100*102)*(98*100 + 2) + (100*2)^2} |
606 | \frac{1}{1 + 2 \cdot b^2 \cdot d} = 1 - \tfrac{2 \cdot d \cdot b^2}{1 + 2 \cdot b \cdot b \cdot d} \cdot 1 \geq 1 - \frac{b \cdot d}{\sqrt{2 \cdot d}} |
13,764 | y^{2^k} = \left(y^4\right)^{2^{k + 2\left(-1\right)}} = (y + 1)^{2^{k + 2(-1)}} = y^{2^{k + 2(-1)}} + 1 |
17,817 | \left(5 \cdot (-1) + (-3) \cdot (-3)\right)/2 = 2 |
24,339 | (-1) + l^3 = (l + (-1))\cdot (l^2 + l + 1) |
7,160 | {l \choose k} = \frac{1}{(-k + l)! \cdot k!} \cdot l! |
-1,331 | \frac{\frac{1}{5}*7}{\frac13*7} = \frac{3}{7}*7/5 |
-10,518 | 3/3 \cdot (-\frac{1}{k \cdot 20} \cdot (5 \cdot k + 9 \cdot (-1))) = -\frac{1}{60 \cdot k} \cdot \left(27 \cdot (-1) + 15 \cdot k\right) |
10,847 | \frac{1}{16} + \dfrac{1}{9} = \tfrac{9}{144} + 16/144 = 25/144 |
24,035 | (x + z)^2 = x^2 + z \cdot x \cdot 2 + z \cdot z |
38,802 | \pi\cdot \mathrm{i} = \pi\cdot \mathrm{i} |
42,182 | \sin{30*5} = \sin{150} = \sin(60 + 90) |
9,994 | \frac{\partial}{\partial x} (z \cdot z + x) = \frac{\partial}{\partial x} (z + x^2) |
12,136 | \tfrac{1}{2} \cdot (\sqrt{21} + 3 \cdot (-1)) = -3/2 + \frac12 \cdot \sqrt{21} |
-8,046 | \dfrac{i + 4}{4*i - 1}*\frac{-1 - 4*i}{-1 - i*4} = \frac{4 + i}{-1 + 4*i} |
29,460 | i = \cos(\pi/2) + i\sin(\pi/2) = e^{i\pi/2} |
13,052 | \frac{5}{13} = \frac{2\cdot 10 + 10\cdot 9}{{13 \choose 3}} |
15,491 | |B\cdot Y| = |B\cdot Y| |
8,996 | x + (-1) > 0\Longrightarrow x \gt 1 |
19,170 | x\cdot 2/r = k \implies r = \frac{x}{k}\cdot 2 |
-5,469 | \dfrac{5}{s\cdot 3 + 6} = \dfrac{5}{\left(s + 2\right)\cdot 3} |
51,986 | s-\frac{5}{16}s-\frac{4}{16}s=\frac{16}{16}s-\frac{5}{16}s-\frac{4}{16}s=\frac{7}{16}s=\frac{70}{160}s |
-20,117 | \frac{1}{72 \times x + 18 \times (-1)} \times \left(-x \times 56 + 14\right) = -\frac79 \times \frac{2 \times (-1) + 8 \times x}{8 \times x + 2 \times (-1)} |
-13,313 | -\frac{36}{4 + 8\cdot (-1)} = -\frac{1}{-4}\cdot 36 = -36/(-4) = 9 |
-6,516 | \frac{1}{(h + 3*(-1))*3}*2 = \frac{1}{3*h + 9*\left(-1\right)}*2 |
1,624 | \left(z + 1\right)\cdot (1 + 4\cdot z)\cdot (1 + 2\cdot z)\cdot (1 + 2\cdot z) = 1 + 9\cdot z + 28\cdot z^2 + 36\cdot z^3 + 16\cdot z^4 |
10,236 | y\cdot b\cdot z = y\cdot z = y\cdot b\cdot z |
-1,487 | \frac{4 \cdot 1/3}{(-1) \cdot 1/7} = -7/1 \cdot 4/3 |
-11,483 | -5 + 25 + i*30 = 20 + i*30 |
-23,896 | \frac{1}{6 + 10}\cdot 64 = 64/16 = 64/16 = 4 |
-2,527 | \sqrt{2} + \sqrt{25} \cdot \sqrt{2} = 5 \cdot \sqrt{2} + \sqrt{2} |
14,223 | (-1) + r \cos{\theta}*2 = 0 \Rightarrow r \cos{\theta} = \frac{1}{2} |
29,338 | e^Y \cdot e^U = e^{U + Y} |
17,020 | \frac{e^x}{e^x + 1} = 1 - \frac{1}{1 + e^x} |
20,568 | 5/3 = \left(\dfrac{1}{2}*(1 + 1) + 2/1 + \frac21\right)/3 |
-4,411 | \frac{5 + 3 \cdot z}{12 \cdot (-1) + z^2 + z} = \frac{1}{3 \cdot (-1) + z} \cdot 2 + \frac{1}{z + 4} |
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