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27,522 | \tan(\phi) = \frac{1}{\cos(\phi)}\cdot \sin(\phi) |
-7,656 | \frac{1}{1 + i}\cdot (1 + i)\cdot \frac{1}{-i + 1}\cdot \left(-4 - i\cdot 2\right) = \frac{1}{1 - i}\cdot (-2\cdot i - 4) |
10,522 | 20 = 4\times (-1) + 24 |
185 | (w + x) c = xc + cw |
-22,338 | x^2 - x \cdot 8 + 9 \cdot (-1) = (x + 9 \cdot (-1)) \cdot (x + 1) |
-1,249 | -5/7 (-\frac65) = \frac{(-5) \frac17}{1/6 (-5)} |
24,843 | f^2 - f\cdot 3 + 19\cdot (-1) = -\left(4 + f\right)\cdot 17 + \left(f + 7\right) \cdot \left(f + 7\right) |
-1,767 | 19/12 \cdot \pi - \pi \cdot \frac{1}{4} \cdot 3 = 5/6 \cdot \pi |
-6,598 | \frac{4}{z \cdot 4 + 40 \cdot (-1)} = \frac{1}{4 \cdot (z + 10 \cdot \left(-1\right))} \cdot 4 |
-20,821 | \dfrac{1}{21\cdot p + 70\cdot (-1)}\cdot (35 + p\cdot 7) = \frac{p + 5}{p\cdot 3 + 10\cdot (-1)}\cdot 7/7 |
-19,187 | 9/10 = \frac{1}{4 \pi} G_q\cdot 4 \pi = G_q |
-21,051 | 4/6 = 2/2*\frac{1}{3}2 |
11,005 | (1 + l \cdot 2) \cdot (\left(-1\right) + 2 \cdot l) + m \cdot 4 + 1 = 4 \cdot (l^2 + m) |
-9,951 | 0.01\times (-78) = -78/100 = -\frac{1}{50}\times 39 |
5,588 | \left(f - 5 \cdot a\right) \cdot (-2 \cdot a + f) = 10 \cdot a^2 - 7 \cdot f \cdot a + f^2 |
11,619 | 3^{k\cdot 4} = 9^{2\cdot k} |
29,700 | -z^2 + \rho \cdot \rho = (\rho - z)\cdot \left(\rho + z\right) |
8,627 | y^3 + 3\cdot y + 4\cdot (-1) = (y^2 + y + 4)\cdot ((-1) + y) |
29,611 | 0 = 3\cdot (3 + 2\cdot (-1)) - 1\cdot (2\cdot (-1) + 1) + (2 - 3\cdot 2) |
15,537 | 20000 = \tfrac{1}{(1/100)^2} 2 |
3,343 | -(-m + m^2) + m \cdot m = m |
5,373 | \sqrt{\frac{w}{v}} = \sqrt{\dfrac{w^2}{w\cdot v}} = \frac{w}{\sqrt{w\cdot v}} |
-6,220 | \frac{1}{y \cdot y + 3 \cdot y + 4 \cdot (-1)} \cdot y \cdot 3 = \frac{3 \cdot y}{(y + (-1)) \cdot (4 + y)} |
-25,015 | 1 - x^2 + x^4 - x^6 - \dotsm = \frac{1}{1 + x^2} |
1,693 | 2*(\frac12*147*2 + 1/2*74*3 + 1/2*146*2) = 808 |
-2,618 | 7^{1 / 2}\cdot (2 + 4) = 6\cdot 7^{1 / 2} |
23,335 | x^2*D^2 - 6*x*D + 9 = (x*D)^2 - 7*x*D + 9 = (x*D - 3.5) * (x*D - 3.5) - 3.25 |
29,596 | 3*\theta^3 + \theta*6 = (\theta + (-1))^3 + \theta^3 + (1 + \theta)^3 |
29,204 | \left(\left(-1\right) + a\right)\cdot ((-1) + b) + 1 = a\cdot b - a + b + 2 |
-5,102 | 10^2 \cdot 10\cdot 40.0 = 40\cdot 10^{4 - 1} |
4,357 | 1 + s * s^2 = (s + 1)*(s * s - s + 1) |
18,596 | (-1) + T^9 = (1 + T^6 + T^3)\cdot (T \cdot T \cdot T + (-1)) |
24,077 | \frac{1}{4} = \frac{1}{9} + 1/9 + \dfrac{1}{36} |
36,629 | \overline{u} + \overline{y} = \overline{u + y} |
39,393 | -89\cdot 2^2\cdot 5\cdot 11\cdot 13 + 3\cdot 7\cdot 17\cdot 23\cdot 31 = 1 |
-26,655 | \left(2\cdot (-1) + 7\cdot q^2\right)\cdot (7\cdot q \cdot q + 2) = -2^2 + (7\cdot q^2) \cdot (7\cdot q^2) |
-16,003 | 0 = 4/10*9 - \dfrac{6}{10}*6 |
5,118 | (1 + x)! \coloneqq \left(x + 1\right)*x! |
-24,692 | 7 + i \cdot 27 = 18 + 4 \cdot i - 11 + 23 \cdot i |
-3,071 | 2^{1 / 2}*25^{1 / 2} + 2^{\frac{1}{2}}*4^{\dfrac{1}{2}} = 5*2^{\tfrac{1}{2}} + 2*2^{1 / 2} |
3,195 | \dfrac{1}{3} = \dfrac{30}{10 + 20 + 30}*\frac{1}{10 + 20}20 |
27,617 | -\binom{9}{3} + \binom{15}{3} = -\binom{5 + 4}{3} + \binom{6 + 5 + 4}{3} |
-10,772 | \frac{1}{4 \cdot x + 3 \cdot (-1)} \cdot (6 + x) \cdot 5/5 = \tfrac{1}{x \cdot 20 + 15 \cdot (-1)} \cdot (x \cdot 5 + 30) |
-20,094 | \frac55\cdot (3\cdot s + 2\cdot (-1))/\left(3\cdot s\right) = \frac{1}{s\cdot 15}\cdot (15\cdot s + 10\cdot (-1)) |
3,492 | x \cdot x\cdot z^2\cdot y + x^5 = (x\cdot y\cdot z - y \cdot y^2)\cdot \left(x\cdot z + y^2\right) + x^5 + y^5 |
-19,048 | 4/15 = \frac{B_p}{9 \cdot \pi} \cdot 9 \cdot \pi = B_p |
13,910 | \frac{1}{3}\cdot 16 = 16/12 + 16/4 |
-20,866 | \frac{9}{9}\cdot \dfrac{8 + r}{10 + r} = \frac{1}{90 + r\cdot 9}\cdot (r\cdot 9 + 72) |
26,454 | \dfrac{60*20}{60 + 20 (-1)} = 30 |
929 | x^2 + a \cdot x \Rightarrow (\dfrac{1}{2} \cdot a + x)^2 - (a/2)^2 |
-15,797 | 15/10 = -5/10*6 + 9*\frac{5}{10} |
5,832 | 2\cdot (1 + 2 + 3 + \cdots + \dfrac{1}{2}\cdot (\left(-1\right) + m)) = 2 + 4 + \cdots + m + (-1) |
33,239 | 0 = -\frac{1}{x^2}*(V - x) + \frac{1}{x}\Longrightarrow x*2 = V |
23,266 | 4^{a + 1} + 15\cdot (a + 1) + \left(-1\right) = 4\cdot 4^a + 15\cdot a + 15 + (-1) = 4^a + 15\cdot a + (-1) + 3\cdot (4^a + 5) |
19,350 | x*x + i*x*3 - i*x - 3*i^2 = (x - i)*\left(x + 3*i\right) |
15,927 | y^2 = 2\cdot \dfrac{1}{2}\cdot y \cdot y |
5,670 | (-1) + b^2\times 2 - b\times 2 = 0\Longrightarrow b = \dfrac12\times \left(1 \pm 3^{1 / 2}\right) |
4,150 | \dfrac{1}{1 - y} = 1 + y + y^2 + y^3 \cdot \dots |
12,662 | 4^{l + 1} + (-1) = 4 \cdot 4^l + (-1) = 4 \cdot (4^l + \left(-1\right) + 1) + (-1) = 4 \cdot (4^l + (-1)) + 4 \cdot 4 + \left(-1\right) = 4 \cdot (4^l + (-1)) + 15 |
5,998 | |x^2 + 25 \cdot (-1)| = |(5 \cdot (-1) + x) \cdot (x + 5)| |
19,236 | \frac{1}{1 + y^2}\cdot (1 - y^2) = \frac{2 - 1 + y^2}{1 + y \cdot y} = \tfrac{1}{1 + y \cdot y}\cdot 2 + (-1) |
-27,460 | 135 = 45\cdot 3 |
-15,771 | -\frac{1}{10} 8*8 + \dfrac{2}{10}*10 = -44/10 |
-5,780 | \dfrac{1}{5(k + 3)} = \tfrac{1}{15 + k*5} |
11,168 | 333338 = 10\cdot \dfrac{1}{3}\cdot (10^5 + \left(-1\right)) + 8 = (10^6 + 10\cdot (-1) + 24)/3 = (10^6 + 14)/3 |
-7,088 | 5/12 \cdot \frac{1}{11} 4 = 5/33 |
-16,798 | -4 = -4 \cdot 3 \cdot q - 4 = -12 \cdot q - 4 = -12 \cdot q + 4 \cdot \left(-1\right) |
-4,292 | 10\cdot \frac{1}{9}/n = 10/(9\cdot n) |
12,940 | (a + i)^3 - a^3 = \left(a + 1 - a\right) \times \left((a + 1)^2 + (a + 1) \times a + a^2\right) = 3 \times a^2 + 3 \times a + 1 |
18,828 | p^{r - s} = \frac{1}{p^s} \times p^r |
42,273 | \frac{1}{15} \cdot 10 = 2/3 |
7,811 | \left(x + y\right)\cdot (x - y)\cdot (x^4 + x^2\cdot y \cdot y + y^4) = (x^2 + y \cdot y)\cdot \left(x^4 + x \cdot x\cdot y^2 + y^4\right) = x^6 - y^6 |
-23,413 | 0.24 ^ 8 = (1 - 0.76)^8 |
2,623 | E\left(Z\cdot A\right) = E\left(Z\right)\cdot E\left(A\right) |
27,026 | 9^3 = (1 + 2^3)*4 * 4 * 4 + 1^3 + 3^3 + 5^3 |
19,592 | \left(a_1,a_2\right) = \frac{a_1}{a_1} \cdot 1 = a_1^{a_2}/(a_1) |
28,399 | \|a \cdot x\|_1 = \sum_{j=1}^m |a \cdot x_j| = |a| \cdot \sum_{j=1}^m |x_j| |
26,410 | \frac{180 + 64 (-1)}{2} = 58 |
42,651 | e^2/25 - 1 = -1 + e \cdot e/25 |
37,876 | 32\cdot 2 + 72 + 58 = 194 |
32,393 | 47 \cdot (-1) + 24 \cdot 2 = -(47 + 24 \cdot (-1)) + 24 |
8,786 | \frac{x}{z} = \frac1z\cdot x |
-19,622 | 8*\dfrac13/(1/3*5) = \frac83*\frac{3}{5} |
50,652 | 2\Rightarrow1 |
11,005 | (n^2 + i) \cdot 4 = (2 \cdot n + (-1)) \cdot (1 + n \cdot 2) + 4 \cdot i + 1 |
42,849 | \cos(22\cdot s) + \cos(10\cdot s) = \frac12\cdot 4\cdot \cos\left(6\cdot s\right)\cdot \cos(16\cdot s) = 2\cdot \cos(16\cdot s)\cdot \cos\left(6\cdot s\right) |
1,512 | 1/2\cdot 8\cdot 4 - \dfrac{1}{2}\cdot 2 = 15 |
-12,565 | 35 = 188 + 153 (-1) |
36,843 | \mathbb{E}(Q)\cdot \mathbb{E}(X) = \mathbb{E}(X\cdot Q) |
14,340 | \tan(z + y) = \frac{\tan(z) + \tan(y)}{1 - \tan(z) \cdot \tan(y)} \geq \tan(z) + \tan(y) |
24,115 | 2 \cdot 2 + 13 \cdot 3^2 = 4 + 117 = 121 = 11^2 |
-10,433 | 20/20 \cdot \left(-\frac{4 \cdot r + (-1)}{4 \cdot r}\right) = -\frac{1}{80 \cdot r} \cdot (20 \cdot \left(-1\right) + 80 \cdot r) |
7,174 | \frac{1}{2}\cdot (10 + 2\cdot (-1)) + (-1) = 3 |
19,917 | x \cdot x + x + 1 = (x + \frac{1}{2})^2 + 3/4 |
3,734 | i=sba=sab |
25,729 | \frac{e^z}{(1 + z)^2}\cdot z = \frac{\mathrm{d}}{\mathrm{d}z} (\frac{e^z}{1 + z}) |
16,266 | 0 = 5 \cdot \tan^2{\tfrac{1}{10} \cdot \pi} + 10 \cdot (-1) + \cot^2{\frac{\pi}{10}} |
-11,919 | \frac{1}{100}8.046 = 8.046*0.01 |
8,792 | 1.0000006^2 = (1 + \dfrac{6}{10^7})^2 = (1 + \tfrac{1}{5*10^6}*3)^2 |
-18,581 | -\frac{1}{12} \cdot 17 = -17/12 |
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