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19,778 | \frac{1}{\phi^2} = \frac{1}{\phi^2}\cdot (\phi^2 - \phi) = 1 - \tfrac{1}{\phi}\cdot \left(\phi \cdot \phi - \phi\right) = 2 - \phi |
-19,208 | \tfrac{1}{5} = \dfrac{X_q}{16\cdot \pi}\cdot 16\cdot \pi = X_q |
10,131 | 5^3 + 5 + 6^3 + 6 = 7^3 + 7 + 2 |
26,550 | \tfrac{(-1) + y^{\dfrac{1}{2}}}{\left(-1\right) + y} = \frac{1}{1 + y^{1 / 2}} |
37,253 | \frac27 = \tfrac{1}{7}\cdot 2 |
-10,269 | 3/3\cdot \frac{p\cdot 3 + 2\cdot (-1)}{p\cdot 8 + 4\cdot \left(-1\right)} = \tfrac{9\cdot p + 6\cdot (-1)}{24\cdot p + 12\cdot (-1)} |
8,430 | x \times 2 + 2 \times y = 5.9\Longrightarrow y = \frac{1}{2} \times (-x \times 2 + 5.9) |
25,959 | \frac{251^2*250^2}{4} = 984390625 |
4,664 | (c_2 - c_1)^2 = (c_2 + c_1)^2 - 4 \cdot c_2 \cdot c_1 |
307 | r_1 \cdot 2 \cdot m \cdot r_2 = r_1 \cdot r_2 \cdot m \cdot 2 |
-8,365 | -32 = 8 \cdot \left(-4\right) |
-20,818 | -\dfrac{2}{7} \cdot \frac55 = -\frac{1}{35} \cdot 10 |
-16,561 | \sqrt{48} \times 9 = \sqrt{16 \times 3} \times 9 |
15,301 | X = \operatorname{acos}(z) \Rightarrow \cos(X) = z |
31,674 | 10\cdot \left((-1) + 3\right) = 20 |
31,661 | 108^{\frac{1}{2}} + 10 = 10 + 6\cdot 3^{\frac{1}{2}} |
-2,824 | 10*6^{1/2} = 6^{1/2}*(5 + 1 + 4) |
31,661 | \sqrt{108} + 10 = \sqrt{3} \cdot 6 + 10 |
9,963 | 5^{n + 1}*(4 + 1) = 5^{1 + n} + 5^{n + 1}*4 |
-24,665 | \frac{6}{21} = \frac{2}{7 \cdot 3}3 |
10,193 | f^3 = f\times f^2 = f = f |
-3,419 | \sqrt{2}\cdot 6 = (2 + 1 + 3)\cdot \sqrt{2} |
23,381 | \frac{\mathrm{d}}{\mathrm{d}z} \operatorname{atan}(z) = \frac{1}{z^2 + 1} |
28,410 | (1 - i)^1 + (1 + i)^1 = 2 |
-9,500 | -r \times 10 = -r \times 2 \times 5 |
-2,447 | 45^{1 / 2} + 20^{\dfrac{1}{2}} = \left(9 \cdot 5\right)^{1 / 2} + \left(4 \cdot 5\right)^{\frac{1}{2}} |
24,430 | 2^m = 2^m \cdot k + 1 > 2^m \cdot k |
2,942 | x^4 - x^2*4 + 3 = \left((-1) + x^2\right)*(x^2 + 3*\left(-1\right)) |
8,923 | 0 = x^6 - 4x^3 + (-1) \Rightarrow x^3 = 2 ± \sqrt{5} |
10,150 | -\cos\left(\pi/2 + \theta\right) = \sin{\theta} |
7,386 | A*x^2 = A*x^2 |
-16,596 | 7 \cdot \sqrt{16 \cdot 5} = 7 \cdot \sqrt{80} |
3,145 | t - \frac{t}{1 + t^2} = \dfrac{t^3}{1 + t \cdot t} |
1,787 | -2\cdot z_1 \lt -2\cdot z_2 \Rightarrow z_2 < z_1 |
25,767 | -1/6 + 1/2 + 1 = \dfrac43 |
17,892 | B = \overline{x}\cdot B = B\cdot x |
-26,600 | 3y^2 + 147 (-1) = 3(y \cdot y + 49 (-1)) = 3\left(y + 7\right) (y + 7(-1)) |
-16,341 | 80^{\tfrac{1}{2}}*10 = 10*\left(16*5\right)^{\dfrac{1}{2}} |
15,646 | \tfrac{x + 2*(-1)}{4*(-1) + x * x} = \tfrac{1}{x + 2} |
7,403 | \mathbb{P}(x) = (x - d) \left(x - b\right) (x - c) = x^3 - (d + b + c) x \cdot x + (db + bc + cd) x - dbc |
23,667 | ((-1) + p)\cdot ((-1) + p)\cdot ((-1) + p) = (-1) + p \cdot p \cdot p - 3\cdot p^2 + p\cdot 3 |
-26,421 | \frac{x^F}{x^k} = x^{F - k} |
7,777 | -\frac{r}{3} + ((-1) \cdot r)/3 + r = r/3 |
31,494 | 2^2\cdot 3^3\cdot 5\cdot 7^2 = 26460 |
-2,288 | \frac{1}{20} = -\frac{1}{20}7 + \frac{8}{20} |
4,557 | k \geq w \implies -w \geq -k |
16,138 | \tfrac{1}{z^3}\cdot z^2 = \frac1z |
-22,937 | \frac{81}{9\cdot 5}\cdot 1 = \frac{1}{45}\cdot 81 |
8,455 | 1/3 = 0.33333 \cdot ... |
-2,659 | \sqrt{3} \sqrt{4} + \sqrt{3} \sqrt{25} = \sqrt{3}*2 + \sqrt{3}*5 |
8,924 | \dfrac{1}{(1 + n)^2} \cdot (n^2 + n \cdot 2 + 1 + (-1)) = \frac{1}{(n + 1)^2} \cdot ((-1) + (n + 1)^2) |
10,423 | 5 = 4\cdot k^2 + 4\cdot k + 1 = (2\cdot k + 1)^2 |
24,249 | r \times r = 2^2 + 5 = 9 \Rightarrow 3 = r |
20,508 | 503\cdot 497=(500+3)(500-3)=500^2-3^2=250000-9=249991 |
44,177 | 36047571 = 696\cdot 109376 - 40078125 |
-5,000 | 17.4*10^9 = 17.4*10^{3 + 6} |
-20,649 | -\tfrac{10}{-5\cdot n + 2\cdot (-1)}\cdot \frac{8}{8} = -\frac{80}{-n\cdot 40 + 16\cdot \left(-1\right)} |
1,639 | 3\cdot \lambda\cdot z_2^{\frac{1}{3}\cdot 4} = z_1^{1/3} \implies 9\cdot z_2^4\cdot \lambda^3 = z_1 |
-6,338 | \tfrac{3}{(n + 7)*5} = \frac{3}{35 + 5*n} |
18,836 | h - l = -(-h + l) |
9,678 | f \times a_2 = f \times a_2 |
12,846 | \frac12(1 + \sqrt{5}) = 1/2 + \frac{\sqrt{5}}{2} |
37,733 | \sin{y \cdot k} \cdot k/y = k^2 \cdot \frac{\sin{y \cdot k}}{k \cdot y} |
5,506 | 544320 = \binom{9}{2}*\binom{7}{2}*6! |
6,497 | x + 1 + (x + 2\cdot (-1))^n < 2\cdot x^2 - x = x + 2\Longrightarrow 1 \gt (x + 2\cdot (-1))^n |
3,692 | \vartheta \cdot z + r \cdot z = (\vartheta + r) \cdot z |
3,194 | exp(A)*exp(S) = exp(A + S) |
16,036 | \frac{2^7}{1000} = 2^7\cdot 1/8/125 = \tfrac{1}{125}\cdot 2^4 |
11,144 | \|z\|^2 = zz^T = zz^T |
-20,682 | \frac{4 - 2\cdot r}{-r\cdot 16 + 32} = \frac{1}{8}\cdot 1 |
24,894 | 0 = \dfrac{1}{120 \cdot \pi} \cdot (\sin{2 \cdot \pi} - \sin{0}) |
20,249 | 10 \cdot \frac{654321}{123456} = 6 \cdot 9 + (-1) + \frac{7}{123456} \cdot 6 \approx 53 |
16,943 | 2/10\cdot \frac{3}{10} = \frac{1}{100}\cdot 6 |
-15,167 | \frac{x^5}{t^{10} x^{10}} = \frac{1}{\frac{1}{\dfrac{1}{t^{10}} \frac{1}{x^{10}}}}x^5 |
7,366 | (\mathbb{E}[X'^2]\cdot \mathbb{E}[Y'^2])^{\frac{1}{2}} = \mathbb{E}[X'\cdot Y'] |
-30,858 | \frac{1}{x^3 - x^2}\cdot (-x \cdot x\cdot 3 + x^4 + 2\cdot x^3) = x + 3 |
34,623 | \frac{0.6}{0.4 \cdot 0.6} \cdot 0.4 \cdot 0.6 = 0.6 |
19,555 | \dfrac{2}{5} = (1 - \frac{1}{3}) \cdot (1 - 1/4) \cdot (1 - 1/5) |
8,677 | (\alpha + \beta)^2 - \beta \alpha*4 = (\alpha - \beta)^2 |
796 | h_1 + d + h_2 = d + h_2 + h_1 |
33,567 | 1 - \dfrac{n}{n \cdot 2 + 1} = \dfrac{1 + n}{n \cdot 2 + 1} |
-3,023 | (3 + 2)\cdot \sqrt{13} = 5\cdot \sqrt{13} |
-20,777 | \frac{p + 4}{4 + p}\cdot (-\frac{1}{7}\cdot 4) = \dfrac{1}{28 + 7\cdot p}\cdot \left(16\cdot \left(-1\right) - p\cdot 4\right) |
10,486 | 1 = 2\times Q^3 + Q = Q\times (2\times Q \times Q + 1) = \left(Q^3 + 1\right)\times (2\times Q^2 + 1) |
-28,892 | \left(100 + 200 + 150 + 150\right)/4 = \frac14*600 = 150 |
-1,585 | \dfrac{23}{12}\cdot \pi = -\pi/12 + \pi\cdot 2 |
-12,061 | 3/20 = \dfrac{s}{10 \cdot \pi} \cdot 10 \cdot \pi = s |
-2,702 | 10^{\frac{1}{2}} \cdot (5 + 2 + (-1)) = 6 \cdot 10^{1 / 2} |
4,587 | 5/18 = \frac{1}{216} \cdot 5/(1/12) |
-16,885 | -5 \cdot x = -5 \cdot x \cdot (-x) + -5 \cdot x \cdot 4 = 5 \cdot x^2 - 20 \cdot x = 5 \cdot x^2 - 20 \cdot x |
17,745 | \sin{x} = \sin\left(x + \pi \cdot 2\right) |
28,637 | \cos{\pi\cdot m\cdot 2} = \cos{6\cdot m\cdot \pi/3} |
22,325 | z*x*3/2 - \frac54 = -1/2 + 3/2*z*x - \frac14*3 |
3,985 | (-x^2 + 1)/2 = \frac{1}{2}\cdot (1 + x)\cdot (-x + 1) |
1,586 | g x H = H x g |
-1,593 | \frac{4}{3}*π = 4/3*π + 0 |
39,734 | 12/27 = \dfrac{96}{6^3}\times 1 |
-9,456 | t*2*2*2*3*5 + 2*2*3 = t*120 + 12 |
13,988 | (h + x)*(h - x) = h * h - x^2 |
-20,838 | -1/4 \frac{(-1) + q}{q + (-1)} = \frac{-q + 1}{4(-1) + 4q} |
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