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-5,498 | \frac{5}{q^2 - 8q + 9\left(-1\right)}q = \frac{5}{(q + 9(-1)) \left(1 + q\right)}q |
-1,770 | -\frac{1}{3}\pi + \pi \tfrac{11}{6} = \pi \dfrac{3}{2} |
-7,013 | 2 \times 10^{-1}/9 = \frac{1}{45} |
33,160 | A = (Y \cap A) \cup (Y' \cap A) = (Y \cup Y') \cap A |
-24,449 | 4 + \tfrac{60}{10} = 4 + 6 = 10 |
299 | \dfrac{1}{n}\cdot (n + 1) = 1/n + 1 |
-17,787 | 80 + 13 \cdot (-1) = 67 |
9,621 | (x + 1) \cdot \left(x + \left(-1\right)\right) = \left(-1\right) + x \cdot x |
-2,677 | 6^{1/2} = 6^{1/2}*(2 + 4*(-1) + 3) |
3,952 | 99 = 11*9 = (3 * 3 + 2*1^2)*3 * 3 = (3^2 + 2*1^2) (1 * 1 + 2*2^2) |
-12,018 | \frac{19}{24} = \frac{1}{12 \cdot \pi} \cdot s \cdot 12 \cdot \pi = s |
21,994 | \dfrac{\sin\left(x\right)}{1 + \sin(x)} = \dfrac{1}{\sin(x) + 1}(1 + \sin(x) + (-1)) = 1 - \dfrac{1}{1 + \sin\left(x\right)} |
-1,294 | 6/12 = \frac{6*\frac16}{12*\frac16} = 1/2 |
35,053 | 1328 = 3^6 \cdot 2 + 2 \cdot (-1) - 2^7 |
10,635 | (\sin(\frac12 \cdot x) + \cos\left(x/2\right))^2 = 1 + 2 \cdot \sin\left(x/2\right) \cdot \cos(\frac12 \cdot x) = 1 + \sin(x) |
-19,253 | \tfrac{8}{15} = A_s/(100\cdot \pi)\cdot 100\cdot \pi = A_s |
7,884 | v_1 \cdot x_2 \cdot x_1 = v_1 \cdot x_1 \cdot x_2 |
-29,432 | \frac{39}{44} = 3*13/(11*4) |
31,607 | 60 = 3\cdot 17 + 9\Longrightarrow 60 - 3\cdot 17 = 9 |
-30,620 | (3 + x^2) \cdot 4 = 12 + x^2 \cdot 4 |
37,932 | 58261 = 7 * 7*29*41 |
32,505 | -\sqrt{3} + 2 = (\left(\sqrt{3} - 1\right)/\left(\sqrt{2}\right))^2 |
24,364 | \left(1 + x\right)^{m_1}*(1 + x)^{m_2} = (x + 1)^{m_1 + m_2} |
28,714 | \frac{1}{f_2\cdot f_1} = 1/\left(f_1\cdot f_2\right) |
4,192 | \sin{\vartheta} = 1/\csc{\vartheta} |
13,299 | \left(-f + h\right) (h \cdot h + fh + f^2) = -f^3 + h^3 |
20,099 | \left(x_1 + x_2\right)^2 - 2*x_1*x_2 = x_2^2 + x_1^2 |
-19,015 | \frac{1}{20} \cdot 3 = \frac{A_s}{16 \cdot \pi} \cdot 16 \cdot \pi = A_s |
-27,506 | 21*x^2 = 3*x*x*7 |
20,984 | \frac{a x}{a + x} 1 = a - \frac{a^2}{a + x} = x - \tfrac{1}{a + x} x^2 |
-25,816 | \frac{5}{6*3}*1 = \frac{5}{18} |
9,083 | e^{-i\cdot x} = (e^{i\cdot x})^{-1} |
30,087 | p \cdot x^W = p \cdot x^W |
17,357 | f*\tau = f*\tau |
-598 | e^{\frac{i}{12} \cdot \pi \cdot 15} = (e^{i \cdot \pi/12})^{15} |
2,545 | v - \dfrac{1}{2}*(v + 1) = ((-1) + v)/2 |
15,251 | {20 \choose 2}^{10} = {20 \choose 2} {20 \choose 2} \ldots {20 \choose 2} |
27,277 | 3^{4 n + 3} = 3^3 (10 + (-1))^{2 n} = 3^3 \left(1 + 10 \left(-1\right)\right)^{2 n} |
-1,634 | -\frac{3}{4} \cdot \pi = -\pi \cdot 7/4 + \pi |
51,561 | 9825757^4 - 2104527924 \times 2104527924 \times 2104527924 = -137318688623 |
-1,500 | -\dfrac{1}{9}4 \left(-\frac{1}{8}9\right) = \frac{(-9)\cdot 1/8}{\frac{1}{4} (-9)} |
-11,602 | 22*i - 7 = 8 + 15*(-1) + 22*i |
14,618 | \frac{1^k + 1^k}{1 + 1} = 1^{k + (-1)} |
24,492 | \mathbb{E}(T Y) = \mathbb{E}(T) \mathbb{E}(Y) |
18,662 | a^{x + f} = a^f\times a^x |
6,402 | 1 \leq 4\cdot x \lt 2\Longrightarrow 1 + x\cdot 4 = x\cdot 4 |
-9,360 | 60\cdot o = 2\cdot 2\cdot 3\cdot 5\cdot o |
23,125 | y/y = 1 = \frac{y}{y} |
17,633 | p^n = p^{(-1) + n} \times p |
26,595 | (-2 + (4 + 30)^{\dfrac{1}{2}})/2 = -1 + \dfrac{34^{\frac{1}{2}}}{2} |
-25,049 | \frac{5}{13}*4/12 = 20/156 = \tfrac{5}{39} |
11,239 | (b^{j_1})^{j_2} = b^{j_1 j_2} = b^{j_2 j_1} |
31,435 | \sin(z + \dfrac{1}{2}*\pi) = \cos(z) |
-10,646 | 3/3*\frac{6}{5*\rho + 15} = \dfrac{18}{\rho*15 + 45} |
1,914 | fz^{-x + i} = z^{i - x} f |
5,804 | (y^2 + y*5 + 6)^{\frac{1}{2}} = (\left(y + 3\right)*(2 + y))^{\dfrac{1}{2}} |
-2,607 | -7^{1 / 2} \cdot 3 + 5 \cdot 7^{\frac{1}{2}} + 7^{1 / 2} \cdot 4 = 25^{\frac{1}{2}} \cdot 7^{\frac{1}{2}} + 16^{\frac{1}{2}} \cdot 7^{\frac{1}{2}} - 9^{\frac{1}{2}} \cdot 7^{\tfrac{1}{2}} |
22,068 | (4\cdot (-1) + 8)^2 + (5\cdot (-1) + 7) \cdot (5\cdot (-1) + 7) = 20 |
20,316 | 0 = (-1 - -1) + \left(0 - -1\right)*0 |
6,892 | -3\cdot a\cdot h\cdot f + a^3 + f^3 + h^3 = \left(a \cdot a + f^2 + h \cdot h - a\cdot f - f\cdot h - h\cdot a\right)\cdot (h + a + f) |
15,929 | {6 \choose 2}*4! = \frac{6!}{2!*4!}*4! = \frac{6!}{2!} = 360 |
32,115 | 3 (-1) + 45 + 6 (-1) + 3 \left(-1\right) = 33 |
42,958 | 1 + 2 + 3 + \cdots + 6 = 21 |
33,196 | i\times (i + (-1))! = i! |
21,199 | c^{t + s} = c^s c^t |
7,745 | \int \frac{1}{y}\,dy = \int 1/y\,dy |
-3,269 | 3\cdot \sqrt{6} + 4\cdot \sqrt{6} = \sqrt{6}\cdot \sqrt{9} + \sqrt{6}\cdot \sqrt{16} |
19,526 | 23 + c^2 = (c + 1) (c + (-1)) + 24 |
-5,539 | \frac{1}{2 (k + 9)} = \frac{1}{2 k + 18} |
41,840 | 3^{560}=81^{140}=(140*80*1+1) |
11,242 | 9/48 + \frac{3}{54} = 3/16 + 1/18 = \dotsm |
31,107 | \tfrac13 + 1*\frac13*2/2 = \frac23 |
7,532 | (-1) + 2^{2 \cdot m} = \left(1 + 2^m\right) \cdot (2^m + (-1)) |
3,666 | p = y + 2 \Rightarrow y = p + 2\cdot (-1) |
8,204 | -3 \cdot r^2 + r \cdot 12 + 40 = (6 \cdot \left(-1\right) + r)^2 - ((-1) + r^2 - 6 \cdot r) \cdot 4 |
20,697 | \arccos(\cos(\pi - \arccos{t})) = \arccos{-t} \Rightarrow \arccos{-t} = \pi - \arccos{t} |
36,669 | 2^{1/2} = \dfrac{7 \cdot 1/5}{\left(-1/50 + 1\right)^{1/2}} |
-5,490 | \frac{6}{(q + 2) \cdot (7 + q) \cdot 2} = \tfrac12 \cdot 2 \cdot \dfrac{3}{\left(7 + q\right) \cdot (2 + q)} |
11,020 | z^2 + y^2 - z*2 - 2by + 8(-1) = 0 \Rightarrow \sqrt{b^2 + 9} * \sqrt{b^2 + 9} = (z + (-1))^2 + (-b + y)^2 |
-444 | (e^{\pi\cdot i\cdot 7/12})^{15} = e^{15\cdot \frac{7}{12}\cdot \pi\cdot i} |
14,505 | 216 = 6^3 = 2^3 \cdot 3 \cdot 3^2 |
10,305 | \left(b\cdot a = b + a \implies 0 = -b + a\cdot b - a\right) \implies (a + (-1))\cdot (b + (-1)) = 1 |
19,927 | (r + h)^2 = r^2 + 2 \cdot h \cdot r + h^2 |
931 | y*e^y = x \Rightarrow e^{-y}*x = y |
-1,820 | \pi \cdot \dfrac{13}{6} = \pi/4 + \pi \cdot 23/12 |
30,271 | (z + (-1)) (1 + z^2 + z) = z^3 + (-1) |
34,793 | 20 = \frac{5!}{3!\cdot 1!\cdot 1!} |
34,697 | l/2 \leq k \Rightarrow \frac{l}{2} \geq l - k |
-21,126 | \frac{2*\frac12}{2} = 2/4 |
17,497 | \dfrac12 = 99/100 \cdot \frac{1}{99} \cdot 49 + 1/100 |
-20,802 | \frac{k \cdot 10 + 9}{k \cdot 10 + 9} \cdot 4/1 = \frac{40 \cdot k + 36}{10 \cdot k + 9} |
-11,986 | \dfrac{29}{30} = \dfrac{s}{10 \cdot \pi} \cdot 10 \cdot \pi = s |
34 | \lambda^{32} = \lambda^{16}\cdot \lambda^{16} |
8,449 | \int (-y^{\frac{3}{2}} + y^{1/2})\,\mathrm{d}y = \int \sqrt{y}\cdot (1 - y)\,\mathrm{d}y |
12,864 | \dfrac{1}{\dfrac{1}{\alpha}} = \alpha |
24,242 | 1007 = \frac12 \cdot (2013 + 1) |
-3,884 | \dfrac{1}{y^5}*y^2*\frac39 = \dfrac{3}{9*y^5}*y^2 |
-20,001 | \frac99*\frac{1}{6(-1) + x*10}9 = \frac{81}{x*90 + 54 (-1)} |
-13,629 | \frac{20}{2 + 8} = 20/10 = 20/10 = 2 |
8,479 | -39 = 14 \cdot (-1) + (-25) |
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