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19,320 | \frac{1}{\tan(2\cdot y)} = 0 \Rightarrow 1 = \tan(2\cdot y)\cdot 0 |
7,491 | x^0 = \tfrac{1}{x^4}\cdot x^4 |
29,355 | f_1^2 + 2\cdot f_1\cdot f_2 + f_2^2 = (f_2 + f_1)^2 |
38,796 | (-1) + 3^8 - 4\times 3^7 + 3^6\times 2 + 3^4 + 3^4 = -568 |
-1,290 | -\frac{28}{42} = \frac{1}{42\cdot 1/14}((-28)\cdot 1/14) = -2/3 |
15,950 | z^4 + x^4 - x^2\cdot z^2\cdot 11 = x^4 - 9\cdot x^2\cdot z \cdot z - x^2\cdot z^2\cdot 2 + z^4 |
20,533 | 3\cdot 2\cdot 16 x = 96 x |
-19,514 | 1/(2*\frac18) = 1^{-1}*8/2 |
15,950 | x^4 - x^2 \cdot y^2 \cdot 11 + y^4 = y^4 + x^4 - 9 \cdot y^2 \cdot x^2 - 2 \cdot y^2 \cdot x^2 |
3,226 | \dfrac{\ln\left(c_1\right)}{\ln(c_2)} = \log_c_2(c_1) |
8,474 | 3y^2 - 12 y = (y + 2(-1)) \cdot (y + 2(-1))\cdot 3 + 12 (-1) |
14,325 | \int\limits_0^{z + 8} z\,\mathrm{d}t = \int_{8 + z}^0 (-z)\,\mathrm{d}t |
5,561 | \frac{1}{x \cdot 2}(x \cdot 2 + (-1)) = d_x \Rightarrow d_x = 1 - 1/\left(2x\right) |
-20,937 | \left(9*(-1) + 9*c\right)/(\left(-63\right)*c) = \left((-1) + c\right)/((-1)*7*c)*\frac{9}{9} |
13,876 | \cos(Z) + \cos(2 \cdot Z) + \cos\left(3 \cdot Z\right) = 0 = \cos(2 \cdot Z) \cdot (1 + 2 \cdot \cos\left(Z\right)) |
-26,392 | \frac{1}{5^{12}} 5^{10} = 5^{10 + 12 (-1)} = 1/25 |
2,998 | 4j^4 = j^4 + j^4 + j^4 + j^4 |
-27,216 | \sum_{k=1}^\infty \dfrac{(-5)^k}{k\cdot 5^k} = \sum_{k=1}^\infty \dfrac{\left(-1\right)^k\cdot 5^k}{k\cdot 5^k} = \sum_{k=1}^\infty (-1)^k/k |
23,441 | \frac{1}{1 - y}*(1 - y^{k + 1}) = 1 + y + y^2 + \ldots + y^k |
10,847 | 1/16 + \frac19 = \frac{9}{144} + 16/144 = 25/144 |
20,883 | X = \frac{1}{F - x}*F = (X - x)*F |
39,440 | \binom{3n-1}{r-1}=\frac{(3n-1)!}{(3n-1-(r-1))!(r-1)!} = \frac{(3n-1)!}{(3n-r)!(r-1)!} |
12,129 | 5^{1/2} = 3 + (3*(-1) + 5^{1/2})/2*2 |
8,863 | \frac{5}{4} + \frac{5}{2} = 15/4 |
26,026 | I\cdot e\cdot A = A\cdot I\cdot e |
-9,406 | 48 + 36\cdot x = x\cdot 2\cdot 2\cdot 3\cdot 3 + 2\cdot 2\cdot 2\cdot 2\cdot 3 |
364 | 3 \cdot r = \cot(\frac{\pi}{4}) \cdot (r + r \cdot 2) |
22,038 | \frac{1}{z^{\tfrac{1}{2}}} = z^{-1/2} |
23,335 | z^2\cdot D^2 - 6\cdot z\cdot D + 9 = (z\cdot D) \cdot (z\cdot D) - 7\cdot z\cdot D + 9 = \left(z\cdot D - 3.5\right)^2 - 3.25 |
33,915 | \sqrt{l + 1} = \dfrac{l + 1}{\sqrt{l + 1}} |
-22,760 | 28\cdot 3/(2\cdot 28) = 84/56 |
40,932 | 2^{17} > 17^4\Longrightarrow 83521 < 131072 |
39,470 | a^2 = c^2 = 1\Longrightarrow 0 = -c^2 + a^2 |
18,170 | \dfrac{3}{7} = \dfrac{1}{70} \cdot 30 |
13,825 | 2^l + 2^{(-1) + l} \cdot l/s = \tfrac1s \cdot (2 \cdot s + l) \cdot 2^{l + (-1)} |
19,845 | \left\{1, 2, ..., 3\right\} = \mathbb{N} |
-15,782 | \frac{10}{10} - \tfrac{1}{10} \cdot 9 \cdot 7 = -53/10 |
-18,521 | 4k + 3 = 3(k + 4\left(-1\right)) = 3k + 12 (-1) |
17,487 | 8 = 3\cdot (2^{\beta + \left(-1\right)} + 3\left(-1\right)) - 2^{\beta + (-1)} + (-1) = 2^{\beta} + 8(-1) |
-2,878 | \sqrt{275} - \sqrt{44} = -\sqrt{4*11} + \sqrt{25*11} |
-19,304 | \tfrac{1/4 \cdot 3}{\dfrac{1}{3} \cdot 7} = \frac34 \cdot 3/7 |
-28,129 | \frac{\mathrm{d}}{\mathrm{d}x} \left(-2*\cot(x)\right) = -2*\frac{\mathrm{d}}{\mathrm{d}x} \cot(x) = 2*\csc^2(x) |
-24,985 | 4\cdot \pi = 2\cdot \pi\cdot 2 |
365 | (2\cdot 5)^{1/4} = 10^{\tfrac14} |
20,311 | ba = b\cdot a |
-20,241 | -\frac{1}{6}\cdot \frac{1}{5\cdot (-1) - z\cdot 5}\cdot (-5\cdot z + 5\cdot (-1)) = \frac{1}{30\cdot (-1) - z\cdot 30}\cdot (5 + z\cdot 5) |
31,552 | z^3 + 1 = z^3 + (-1) = (z + (-1))\cdot (z^2 + z + 1) = (z + 1)\cdot (z \cdot z + z + 1) |
12,565 | p^{5/2} = \frac{p^3}{p^{\frac{1}{2}}} |
-11,798 | 4/81 = (2/9)^2 |
9,188 | 648 = 900 + 81 \times (-1) + 81 \times (-1) + 81 \times (-1) + 9 \times (-1) |
14,736 | \frac{1}{1 + m} + \dfrac{...}{(m + 1)^2} = 1/m |
19,316 | 2*n*\left(2*n + 1 - 2*n\right) = 2*n |
10,515 | (-1) + A^3 = (A + (-1)) \left(A^2 + A + 1\right) |
15,077 | \frac{1}{x \cdot 365} = \dfrac{1}{x \cdot 365} |
17,694 | \frac12 = 2*3/6*\frac{2}{6} + \frac{1}{6}2*\frac36 |
-19,300 | \frac{7 \cdot \dfrac19}{4 \cdot \frac{1}{7}} = \dfrac{7}{4} \cdot 7/9 |
15,429 | (-v + u*3)^2 + (v - u)*(3*u - v) - (v - u)^2 = -v^2 + u^2*5 |
6,870 | \dfrac{1}{(M + (-1))!}\cdot ((-1) + V - M + M)! = \dfrac{1}{(\left(-1\right) + M)!}\cdot (V + (-1))! |
21,739 | h_1\cdot h_2\cdot k_2\cdot k_1 = h_1\cdot k_1\cdot k_2\cdot h_2 |
2,746 | -1 \geq 2/x + \left(-1\right) \Rightarrow \frac{2}{x} \leq 0 |
-9,191 | -7*2*3 - 2*2*2*2*3 n = 42 (-1) - n*48 |
-17,567 | 1 = 22 + 21 (-1) |
-12,239 | \frac{1}{45} \cdot 41 = \frac{t}{10 \cdot \pi} \cdot 10 \cdot \pi = t |
10,356 | \left(1/A = A*3 \Rightarrow 3*A^2 = x\right) \Rightarrow A^2 = x/3 |
-26,718 | \sum_{n=1}^\infty \dfrac{\left(-1\right)^n}{n^2} = \sum_{n=1}^\infty \dfrac{1}{n^2} \left(2 + 3 (-1)\right)^n |
40,799 | \binom{9}{6} + 7 \cdot \left(-1\right) = 77 |
-3,963 | \frac{5}{n^3\times 2} = \tfrac{1}{n^3}\times 5 / 2 |
10,976 | \frac{1}{\frac{1}{h}\cdot x} = \frac1x\cdot h |
15,371 | \left( d_1 d_1, d_2 d_2\right) = ( d_1, d_2) ( d_1, d_2) |
-15,700 | \dfrac{1/f\cdot \frac{1}{x^4}}{x^3\cdot f^3} = \frac{\dfrac{1}{x^4}\cdot \frac1f}{x^3\cdot f^3} |
-3,278 | 2*11^{1 / 2} = (3 + 1 + 2\left(-1\right))*11^{\frac{1}{2}} |
1,844 | (1 + \sqrt{7}) \cdot \left(\sqrt{7} + (-1)\right) = 6 |
-2,323 | \frac{1}{17}*5 - \frac{1}{17}*2 = 3/17 |
28,817 | \frac14 \cdot 3 = \frac14 \cdot 3 |
-20,028 | \frac{q \cdot 6 + 36 \cdot (-1)}{48 \cdot q + 48 \cdot \left(-1\right)} = \frac{1}{q \cdot 8 + 8 \cdot (-1)} \cdot (6 \cdot (-1) + q) \cdot \frac{1}{6} \cdot 6 |
-20,219 | \dfrac{t + 7}{56 + 8 \cdot t} = \frac18 \cdot 1 |
-20,443 | \frac{1}{4 \cdot r + 5} \cdot (15 \cdot (-1) - 12 \cdot r) = \frac{1}{4 \cdot r + 5} \cdot (5 + r \cdot 4) \cdot \left(-\dfrac31\right) |
16,362 | 8 = |4 + 3| + |3 \cdot (-1) + 4| |
37,365 | \alpha = \arctan{-4} \implies -4 = \tan{\alpha} |
-8,057 | a * a - h^2 = (a - h)*(h + a) |
-18,493 | 4\cdot n + 2 = 10\cdot (3\cdot n + 9\cdot (-1)) = 30\cdot n + 90\cdot (-1) |
44,020 | h \cdot h\cdot f^2 + f \cdot f\cdot c^2 + c \cdot c + x \cdot x\cdot h \cdot h = (h \cdot h + c^2)\cdot (f^2 + x^2) \leq (h \cdot h + f^2 + c^2 + x^2)^2/4 |
-9,588 | 0.01 (-87) = -87.5/100 = -\dfrac{1}{8}7 |
-19,382 | \frac{1}{7}\cdot 4\cdot 9/4 = \dfrac{\frac{1}{4}\cdot 9}{\frac{1}{4}\cdot 7} |
20,498 | (x - f)*(x + f) = -f^2 + x^2 |
14,666 | \lim_{x \to 0} \frac1xx = \lim_{x \to 0} 1 |
43,265 | (\dfrac{n}{n + 1})^n = (\tfrac{1}{n + 1}(n + 1 + (-1)))^n = (\frac{n + 1}{n + 1} - \frac{1}{n + 1})^n = \left(1 - \frac{1}{n + 1}\right)^n = \frac{1}{n}(n + 1) (1 - \frac{1}{n + 1})^{n + 1} |
-21,004 | \frac{27 \cdot U}{U \cdot 90} = \tfrac{U \cdot 9}{9 \cdot U} \cdot \frac{1}{10} \cdot 3 |
9,484 | 5 + (k + 1)^2 = k^2 + 2 \cdot k + 6 |
34,603 | \tan(\theta)=1 \implies \theta=\frac{\pi}{4} |
13,470 | (-1) + \tan(\pi/2) = 1 + \tan(\pi/2) |
-10,419 | \frac{20}{20}\cdot \tfrac{n + 10\cdot (-1)}{n + 1} = \dfrac{20\cdot n + 200\cdot (-1)}{20 + n\cdot 20} |
48,732 | \frac{1}{2}(3\frac{d}{dx}x^2 + \frac{d}{dx}1) = \frac{1}{2}(3(2x) + 0) = \frac{1}{2}6x = 3x |
-19,010 | \tfrac{1}{8}7 = \frac{1}{9\pi}G_s\cdot 9\pi = G_s |
13,174 | f^5 \cdot d^5 = \left(f \cdot d\right)^5 |
54,656 | \binom{N}{\frac12*(N + s)} = \dfrac{1}{2^N}*\frac{1}{\left(\frac{1}{2}*(N + s)\right)!*(N - \dfrac12*(N + s))!}*N! = \dfrac{N!}{2^N}*\dfrac{1}{((N + s)/2)!*((N - s)/2)!} |
6,835 | -5\cdot (9 + 16\cdot y^2 + y\cdot 24) + 1 = 1 - 80\cdot y^2 - 120\cdot y + 45\cdot (-1) |
-12,052 | \frac79 = \tfrac{t}{4*\pi}*4*\pi = t |
15,985 | 2^x \cdot \left(2^{\eta - x} + (-1)\right) = -2^x + 2^\eta |
-20,171 | \frac{1}{-r*6 + 2}*(r + 3)*\frac{1}{4}*4 = \frac{4*r + 12}{-r*24 + 8} |
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