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-20,346 | \frac{1}{x \cdot 12 + 30 \cdot \left(-1\right)} \cdot (-20 \cdot x + 50) = \dfrac{10 \cdot (-1) + 4 \cdot x}{4 \cdot x + 10 \cdot (-1)} \cdot (-\dfrac{1}{3} \cdot 5) |
-468 | \left(e^{\frac12 \cdot \pi \cdot i}\right)^7 = e^{7 \cdot \frac{\pi}{2} \cdot i} |
2,753 | (1 + x)^n*(x + 1) = \left(x + 1\right)^{n + 1} |
20,281 | w H_1/\sin(H_2) = w H_2/\sin\left(H_1\right) = H_1 H_2/\sin(w) |
30,293 | 1365 = 19^0*16 + 14*19^1 + 3*19 * 19 |
22,550 | \left(-1\right) + y^3 = (y + (-1))*\left(y^2 + y + 1\right) |
729 | |Z\cdot F| + 27 = 27 + |F\cdot Z| |
13,355 | \frac{\dfrac{2}{15}}{4}\cdot 1 = 1/\left(6\cdot 5\right) = \frac{1}{30} |
27,613 | \left(1 + k\right)*2 = 2*k + 2 |
-4,417 | (4 + y) \left(y + 4(-1)\right) = y^2 + 16 (-1) |
8,353 | 1/\lambda = 700 \Rightarrow 1/700 = \lambda |
-16,369 | 9 \cdot 4^{1/2} \cdot 13^{1/2} = 9 \cdot 2 \cdot 13^{1/2} = 18 \cdot 13^{1/2} |
31,783 | 5\cdot m + 3 = 4\cdot \left(2\cdot m + 1\right) - 3\cdot m + (-1) |
-6,335 | \frac{p \cdot 3}{p p + p + 6 (-1)} = \dfrac{p \cdot 3}{\left(p + 3\right) (p + 2 (-1))} 1 |
23,216 | |h|*|e| = |e*h| |
10,530 | \dfrac{1}{2^m}*m!*\frac{1}{2}*(m + 1) = \dfrac{\left(m + 1\right)!}{2^{m + 1}} |
28,500 | S = Y \cap \left(C \cup S\right) = \left(C \cap Y\right) \cup (S \cap Y) = S \cup (C \cap Y) |
15,774 | \sin(\tan^{-1}{x}) = \tfrac{x}{\sqrt{1 + x^2}} |
25,341 | \sin(\theta + \frac{1}{2}*\pi) = \cos{\theta} |
18,663 | \binom{n}{2} + \binom{n}{0} + \binom{n}{1} = (n^2 + n + 2)/2 |
39,267 | 1/36 = \frac{1}{6^2} = \left(\dfrac16\right)^2 |
35,619 | 1/2 = 1/12321 + 12319/24642 |
29,835 | \|z\|^4 = (\left(z_1 \cdot z_1 + z_2^2\right)^{1/2})^4 = (z_1^2 + z_2^2)^2 |
36,427 | (1 - q)^4 \cdot q + \left(1 - q\right)^5 = \left(1 - q\right)^4 \cdot (q + 1 - q) = (1 - q)^4 |
-20,026 | \frac{1}{48 \cdot (-1) + t \cdot 48} \cdot (56 \cdot \left(-1\right) + 56 \cdot t) = \frac{t \cdot 8 + 8 \cdot (-1)}{t \cdot 8 + 8 \cdot \left(-1\right)} \cdot \frac{1}{6} \cdot 7 |
21,970 | \frac{1}{(1 - z)^2}\cdot z = z + z^2\cdot 2 + 3\cdot z^3 + \ldots |
33,263 | \cos(x + d) = -\sin(x)\cdot \sin(d) + \cos(x)\cdot \cos(d) |
6,998 | 15 \leq k \implies k \geq k\cdot 14/15 + 1 |
-27,774 | \frac{\mathrm{d}}{\mathrm{d}y} (-\csc{y}) = -\frac{\mathrm{d}}{\mathrm{d}y} \csc{y} = \csc{y}*\cot{y} |
21,470 | \frac{2}{100 + 2 (-1)} = \tfrac{1}{49} |
-23,381 | 1/7\cdot 3/5 = \frac{1}{35}\cdot 3 |
6,848 | -t + t^2 = (t + 2 \cdot (-1)) \cdot (t + 1) + 2 |
17,999 | x \times \theta = x \times \theta |
26,956 | \left(2 + 2\right)\cdot 2 = 8 |
-20,923 | \frac{1}{-18} \cdot (16 - i \cdot 4) = 2/2 \cdot (8 - 2 \cdot i)/\left(-9\right) |
20,390 | \sin{2} = \cos{\frac12 \cdot (\pi + 4 \cdot (-1))} |
5,606 | (x + 1)^{2 \cdot n} = \left(1 + x\right)^n \cdot (1 + x)^n |
5,026 | 0 = 1 + \tan^4{\pi/10} \cdot 5 - \tan^2{\pi/10} \cdot 10 |
10,474 | x \cdot y + y' \cdot z = x \cdot y + z \cdot y' + z \cdot x |
9,682 | 2 x = \lambda \cdot 3 x^2 \implies \dfrac{1}{x \cdot 3} 2 = \lambda |
41,138 | t = \frac{1}{\sqrt{1 + 1}} \cdot |t + t - b| = |2 \cdot t - b|/(\sqrt{2}) = \sqrt{2} \cdot t - b/(\sqrt{2}) |
7,513 | \frac11\cdot y = (1 - z)/3 = t \Rightarrow y = t,-3\cdot t + 1 = z |
-1,899 | 5/6\cdot \pi = \pi\cdot 4/3 - \frac{\pi}{2} |
9,718 | v\cdot (-I \lambda + A B) = 0 \Rightarrow 0 = (-\lambda I + A B) v B |
8,915 | u_1^X*x_1 = x_1*u_1^X |
-19,180 | 25/36 = A_r/\left(81\cdot \pi\right)\cdot 81\cdot \pi = A_r |
12,818 | 30 \times 31/2 \times 3 = 1395 |
-4,125 | \frac{1}{3 \cdot y^3} \cdot 2 = \frac{2}{y^3} \cdot \frac13 |
2,296 | x + 1/g = E\Longrightarrow \frac{1}{E - x} = g |
-524 | (e^{\pi i \cdot 19/12})^{19} = e^{19 i\pi \cdot 19/12} |
6,876 | (-a + y)^2 + d \cdot d = d^2 + y^2 - 2 \cdot y \cdot a + a^2 |
-5,222 | \dfrac{1}{100}4 = \dfrac{1}{100}4.0 |
41,441 | \frac{3}{2} = \tfrac12*3 |
15,891 | \frac{(-1) + z^6}{1 + z + z^2 + z^3 + z^4 + z^5} = z + (-1) |
-16,727 | {-1} = 4q^{2} - 28q + ({-1} \times{-q}) + ({-1} \times{7}) = 4q^{2} - 28q + q - 7 |
26,404 | \left(x + y\right)^2 - xy \cdot 2 = x^2 + y^2 |
33,176 | -\frac{1}{2 + \lambda_k + z}\cdot (-z + \lambda_k) + 1 = \frac{2\cdot z + 2}{2 + \lambda_k + z} |
23,792 | 2 \times 3 \times \dotsm \times k = k! |
7,308 | 4 + m \cdot 3 + 2 = 3 \cdot (2 + m) |
6,698 | 61 = \left\lceil{\frac{1}{\pi + 3\left(-1\right) - 1/8}}\right\rceil |
-22,368 | y^2 - y \cdot 7 + 10 = (y + 2 \cdot (-1)) \cdot (y + 5 \cdot (-1)) |
-6,295 | \frac{1}{(n + 2\cdot (-1))\cdot 4} = \frac{1}{8\cdot (-1) + 4\cdot n} |
3,867 | 1/2 = 2 - \tfrac{1}{2^1} (1 + 2) |
-22,912 | 112/140 = \dfrac{28\cdot 4}{28\cdot 5} |
-4,893 | 2.72 \cdot 10 = \frac{10}{100} \cdot 2.72 = \frac{2.72}{10} |
-4,368 | \frac{1}{t^3\cdot 8}\cdot 11 = \frac{11\cdot \frac{1}{8}}{t^3} |
3,667 | \left(\frac{1 - y^{11}}{1 - y}\right)^4 = \left(1 + y + y \cdot y + y^3 + \dots + y^{10}\right)^4 |
24,453 | (v + w) k = kv + wk |
21,205 | \sqrt{n + 1} - \sqrt{n} = \dfrac{1}{\sqrt{n} + \sqrt{1 + n}} |
11,335 | \cos^2(\alpha) - \sin^2(\alpha) = \cos\left(2\cdot \alpha\right) |
47 | (\frac14)^{3/2} = (\sqrt{1/4})^3 = \sqrt{\frac{1}{64}} |
47,719 | 7 7^2 = 343 |
-3,564 | 3 \cdot r^2/4 = r^2 \cdot 3/4 |
13,158 | p = \frac{m^2}{n^2} \Rightarrow m^2 = pn * n |
21,633 | \frac{2*1/5}{4} = \frac{1}{10} |
20,354 | e^{\tfrac{\ln\left(e^{i*r}\right)}{4}} = (e^{r*i})^{1/4} |
35,731 | 18 = 4\cdot 5 + 2\cdot (-1) |
-10,295 | \frac15 \cdot 5 \cdot \frac{i + 1}{i \cdot 4 + 8 \cdot (-1)} = \frac{1}{40 \cdot (-1) + i \cdot 20} \cdot \left(5 + 5 \cdot i\right) |
-23,158 | \frac{16}{27} = -2/3\cdot (-\tfrac{8}{9}) |
-29,896 | \frac{\mathrm{d}}{\mathrm{d}z} (2\cdot z^4) = 2\cdot \frac{\mathrm{d}}{\mathrm{d}z} z^4 = 2\cdot 4\cdot z^3 = 8\cdot z^2 \cdot z |
25,966 | \frac1x = \frac{1}{x^2} \cdot x |
8,942 | (3^{1/2} \cdot i - 1)/2 + \left(-1 - 3^{1/2} \cdot i\right)/2 = -1 |
7,557 | X + V + Z = X + V + Z |
40,192 | |Z_2 Z_1 - Ix| = |-Ix + Z_2 Z_1| |
-6,133 | \frac{3}{\left(9\cdot (-1) + x\right)\cdot (x + 5\cdot (-1))}\cdot \frac{4}{4} = \tfrac{12}{\left(x + 5\cdot \left(-1\right)\right)\cdot (9\cdot (-1) + x)\cdot 4} |
-17,823 | 83 = (-1) + 84 |
3,658 | 1 = 1 - r^n = \left(1 - r\right)*\left(1 + r + \dotsm + r^{n + (-1)}\right) |
6,395 | r*c*a = c*a*r |
29,046 | \frac{0.6*0.3}{0.6*0.3}*0.3 = 0.3 |
12,829 | (y + z * z) (y - z^2) = -z^4 + y * y |
2,107 | U\cdot N = U\cdot N |
-18,933 | 1/8 = \frac{1}{16\cdot \pi}\cdot A_r\cdot 16\cdot \pi = A_r |
-10,784 | \frac{40}{80*z^3} = 5/5*\tfrac{8}{16*z^3} |
13,343 | S/3 = (S \cdot 3 - 2 \cdot S)/3 |
2,638 | \sqrt{l \cdot 16 + 99^2} = \sqrt{9801 + 16 \cdot l} |
10,162 | -\frac{2}{(s + 2)^2 + 1} + \dfrac{s + 2}{(2 + s)^2 + 1} = \frac{1}{1 + (s + 2)^2}\cdot s |
4,238 | z = 4 - x^2 - y * y \Rightarrow x^2 + y^2 + z + 4*(-1) = 0 |
19,388 | (-x \times h + g \times w)^2 + (w \times h + x \times g)^2 = (g^2 + h \times h) \times (w^2 + x^2) |
-26,592 | 25 x \cdot x + 16 (-1) = (x\cdot 5 + 4(-1)) \left(5x + 4\right) |
6,105 | 1/4\cdot \frac{1}{2} = \frac18 |
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