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15,598 | 2*\sin(\frac12*x)*\cos(\dfrac{1}{2}*x) = \sin(x) |
24,826 | \frac{1}{1+\frac{a}{x}} = \frac{x}{a+x}=\frac{-a + a +x}{a+x} = 1 - \frac{a}{a+x} |
26,072 | x\cdot x! = \left(x + 1 + (-1)\right)\cdot x! = (x + 1)! - x! |
12,267 | 1 \geq \frac1l \Rightarrow 2 \geq 1 + 1/l |
26,820 | \left((-6) + 9 \cdot B = 3 \implies 9 \cdot B = 3 + 6\right) \implies B = 1 |
24,547 | n \cdot 5 + 1 + n \cdot 7 + 1 = 2 + n \cdot 12 |
-22,291 | \left(x + 2\times \left(-1\right)\right)\times \left(x + 9\times (-1)\right) = x^2 - x\times 11 + 18 |
8,215 | -2\cdot x \cdot x + 8\cdot z = 0 rightarrow z\cdot 4 = x^2 |
22,013 | 2 = 1\cdot 2 = \left(4 + 2\right)\cdot (4 + 2\cdot (-1)) = 4^2 - 2^2 |
-16,381 | (25\times 13)^{1 / 2}\times 2 = 2\times 325^{1 / 2} |
13,600 | \frac{1}{3} + \frac{2}{9} = 3/9 + \dfrac{2}{9} = 5/9 |
368 | \tfrac{1}{2 \cdot 2} + \frac{1}{3 \cdot 2} = 5/12 |
6,579 | 100*17 * 17 + 17*20 = 73*100*2^2 + 2*20 |
21,466 | 1/(bg) = \dfrac{1}{bg} |
5,812 | 1^i = e^{2x\pi i i} = e^{-2x\pi} |
-4,458 | \frac{1}{z^2 + 3 \cdot z + 10 \cdot (-1)} \cdot (z \cdot 3 + 20 \cdot (-1)) = -\frac{1}{z + 2 \cdot (-1)} \cdot 2 + \dfrac{5}{z + 5} |
36,931 | \frac{\partial}{\partial x} (c_2 \cdot c \cdot c_1) = c \cdot c_2 \cdot \frac{\partial}{\partial x} c_1 + c \cdot c_1 \cdot \frac{\partial}{\partial x} c_2 + c_2 \cdot c_1 \cdot \frac{\text{d}c}{\text{d}x} |
4,275 | x^4 + \left(-1\right) = \left(x^2 + \left(-1\right)\right) \cdot (x^2 + 1) = \left(x + (-1)\right) \cdot \left(x + 1\right) \cdot (x^2 + 1) |
17,919 | -1/8 + 1/2 = \dfrac18\cdot 3 |
-4,765 | -\frac{1}{4 + y} \cdot 5 - \dfrac{1}{y + 2} \cdot 3 = \frac{-8 \cdot y + 22 \cdot (-1)}{y \cdot y + y \cdot 6 + 8} |
5,260 | \binom{5}{4}\cdot 1^5 + 5^5 - 4^5\cdot \binom{5}{1} + 3^5\cdot \binom{5}{2} - \binom{5}{3}\cdot 2^5 = 5! |
23,004 | eae = aee |
-10,607 | -\frac{k\cdot 20 + 8}{k^2\cdot 4} = \frac44\cdot (-\dfrac{1}{k^2}\cdot (2 + k\cdot 5)) |
-11,763 | (\frac17*10)^2 = \frac{100}{49} |
27,980 | 2^{m + 1} + 2^{m + 1} = 2 \cdot 2^{m + 1} |
25,832 | \frac{1}{6}\cdot 5/7 = \frac{5}{42} |
27,822 | x \cdot D = x \cdot D |
3,150 | \frac{1}{11 + y} \cdot (y \cdot y + y \cdot 9 + a) = y + 2 \cdot \left(-1\right) + \frac{22 + a}{11 + y} |
21,094 | \frac{a*1/b}{c} = a*1/b/c = \frac{a}{b*c} |
5,060 | -1 = \frac{1}{-1} \cdot \left(2 \cdot |-1| - (-1)^2\right)^{1/2} |
-20,575 | \frac{18 + 9*g}{16*(-1) - g*8} = \frac{-g + 2*(-1)}{-g + 2*(-1)}*(-9/8) |
14,065 | z^3 + 3\cdot z^2 + 6 = (z + 1)^3 - 3\cdot z + (-1) + 6 = (z + 1) \cdot \left(z + 1\right)^2 - 3\cdot (z + 1) + 8 |
5,626 | 67 = 1 + 11 \times 2 \times 3 |
1,041 | (x^k)^{12} = 1 \Rightarrow x^k |
8,404 | ((-1) + n) \cdot n = n^2 - n |
14,207 | \frac1I = 1/(\dfrac{1}{\dfrac1I}) |
38,630 | P*((-1) + 3) + a = 2*P + a |
5,421 | \operatorname{E}[R_D]*\operatorname{E}[R_H] = \operatorname{E}[R_D*R_H] |
-25,818 | 5/40 = \dfrac{5}{4 \cdot 10} |
26,587 | x! \dfrac{x}{((-1) + x)!} = x^2 |
-30,319 | 6*(-1) + 8 = 2 |
1,052 | \left(a + b\right)*(a^2 - a*b + b^2) = a^3 - a^2*b + a*b * b + a * a*b - a*b^2 + b^3 = a^3 + b^3 |
35,406 | \sqrt{(-5) \cdot (-5)} = \sqrt{25} = 5 |
31,007 | f + w + f + w = 2*(f + w) = 2*f + 2*w = f + f + w + w = f + f + w + w |
-11,557 | -5 + 8\times (-1) + 18\times i = -13 + i\times 18 |
27,874 | \frac1x \times \left(\sqrt{1 + x + x^2} + \left(-1\right)\right) = -\frac1x + \sqrt{1 + x + x \times x}/x |
17,092 | m^2 + m + 1 = 1 + (1 + m) \cdot (1 + m) - 1 + m |
-1,387 | ((-1)*1/9)/(\frac{1}{7}*9) = -1/9*\frac79 |
14,073 | \frac{\sinh(y)}{\cosh(y)} = \tanh\left(y\right) |
-20,815 | \frac{c + 5 \cdot (-1)}{5 \cdot (-1) + c} \cdot (-\frac17) = \frac{5 - c}{7 \cdot c + 35 \cdot (-1)} |
-22,384 | 11*\left(-1\right) + 6 = -5 |
1,662 | -2 \cdot \frac{f'}{a^3} = \frac{f'}{a} \cdot \frac{f'}{a} \cdot 2 |
15,739 | (3^{19} - 2^{20} + 1) \cdot 3 = 3^{20} - ((-1) + 2^{20}) \cdot 3 |
4,629 | 1 = \frac{1}{2^{\frac{1}{2}}}\cdot 2^{1 / 2} |
-15,617 | \frac{k^{15}}{k\cdot \frac{1}{a^2}} = \dfrac{1}{\frac{1}{a^2}\cdot k\cdot \frac{1}{k^{15}}} |
14,599 | \left(n^4*2 - 2n * n + 1\right)^2 + (n*2 + n^5 - 2n^3) * (n*2 + n^5 - 2n^3) = 1 + n^{10} |
10,097 | \tan{2 \times x} + \tan{x} = 0\Longrightarrow \tan{x} = 0 |
2,967 | (1 - d) \cdot (1 - e) = 1 - d - e + d \cdot e \geq 1 - d - e |
-7,712 | \frac{1}{25}\cdot (104 - 28\cdot i + 78\cdot i + 21) = \frac{1}{25}\cdot (125 + 50\cdot i) = 5 + 2\cdot i |
-2,732 | 5*\sqrt{7} + 2*\sqrt{7} = \sqrt{4}*\sqrt{7} + \sqrt{25}*\sqrt{7} |
-20,015 | \frac{r + 9*(-1)}{-r*2 + 3}*\frac{6}{6} = \frac{54*\left(-1\right) + r*6}{18 - r*12} |
12,349 | 1 - 3 \cdot s + 3 \cdot s^2 - s^3 = (1 - s)^2 \cdot \left(1 - s\right) |
33,058 | \frac13\cdot 6\cdot 2 = 6/3\cdot 2 |
38,291 | 303 = 30\cdot 10 + 3 |
27,167 | 1.0 = 1.0 = ... = 1 \cdot ... |
6,467 | \left((-1) + k\right)\cdot 2 + 1 = (-1) + 2\cdot k |
-30,542 | \frac{dy}{dx} = \dfrac{1}{y \cdot x^3} = \frac{1}{x^3 \cdot y} |
5,927 | y^6 + \left(-1\right) = (1 + y^4 + y^2) \cdot (y^2 + (-1)) |
-2,847 | \sqrt{4} \cdot \sqrt{3} + \sqrt{3} = \sqrt{3} + \sqrt{3} \cdot 2 |
28,432 | I + x \cdot E = \left(x + 1\right) \cdot (-\frac{x}{1 + x} \cdot (-E + I) + I) |
21,666 | \left(x = (d + x)^{\dfrac{1}{2}} \Rightarrow x * x - x - d = 0\right) \Rightarrow \frac{1}{2}*\left((1 + 4*d)^{\frac{1}{2}} + 1\right) = x |
6,844 | q^2 - q = q*(1 + q) - q - q + 1 + 1 |
-20,926 | \frac{-k\cdot 2 + 9\cdot (-1)}{-2\cdot k + 9\cdot (-1)}\cdot \dfrac{1}{10}\cdot 3 = \tfrac{-6\cdot k + 27\cdot \left(-1\right)}{90\cdot (-1) - 20\cdot k} |
23,143 | (x^2 + 6\cdot x + 6) \cdot (x^2 + 6\cdot x + 6) - x^2 = (1 + x)\cdot (x + 6)\cdot (x + 3)\cdot (x + 2) |
4,172 | \frac{10\cdot \pi^3}{81\cdot \sqrt{3}} = 10\cdot \pi \cdot \pi^2\cdot \sqrt{3}/243 |
16,115 | 5 \cdot a + \sqrt{5} \cdot b = \sqrt{5} \cdot (b + a \cdot \sqrt{5}) |
-9,267 | -27\cdot a + a^2\cdot 30 = a\cdot 2\cdot 3\cdot 5\cdot a - 3\cdot 3\cdot 3\cdot a |
23,256 | 10 + 10^3\cdot 3 - 3\cdot 10^2 = 2710 |
-22,204 | 2 + k^2 - k\cdot 3 = \left(k + (-1)\right)\cdot (k + 2\cdot (-1)) |
1,845 | 1 = -B \cdot 4\Longrightarrow -1/4 = B |
-22,055 | \frac{1}{12} \times 28 = \frac13 \times 7 |
26,898 | (x^2 + 13/25)\cdot 25 = 13 + 25\cdot x^2 |
20,995 | -\sin{-\psi}\cdot (-1) = \sin{-\psi} = -\sin{\psi} |
31,915 | \left((-1) + x\right)^2 = x^2 - 2*x + 1 \Rightarrow (-1) + (x + (-1))^2 = -x*2 + x^2 |
13,257 | (-1)*4 + 9 = \frac{(-1)*8}{2} + 9 |
-29,348 | x\cdot \left(-4\right) (x + 6(-1)) = x^2 - 6x - 4x + 24 = x \cdot x - 10 x + 24 |
5,146 | -\dfrac{t^3}{1 + t} + 1 - t + t^2 = \frac{1}{1 + t} |
17,665 | i + k < l \Rightarrow i < l - k |
9,802 | \frac{-q^{2k} + 1}{1 - q^k} = q^k + 1 |
6,300 | \sqrt{g_2} \cdot \sqrt{g_2} \cdot \sqrt{g_1} \cdot \sqrt{g_1} = g_2 \cdot g_1 |
31,982 | 1010 \cdot x - x \cdot 404 = x \cdot 606 |
18,556 | 1 - \mathbb{P}\left(A\right) - \mathbb{P}\left(H\right) + \mathbb{P}(A) \cdot \mathbb{P}(H) = \left(1 - \mathbb{P}(A)\right) \cdot \left(-\mathbb{P}\left(H\right) + 1\right) |
-6,465 | \frac{1}{4 (q + 8)} = \frac{1}{32 + 4 q} |
-20,023 | (7 - a*56)/14 = (1 - 8a)/2*\frac{7}{7} |
11,101 | \sec{x}*p = r*\csc{x} \implies \frac{r}{p} = \tan{x} |
33,825 | e^{\dfrac12 \cdot ((-1) \cdot \theta)} = (e^{\frac{1}{4} \cdot ((-1) \cdot \theta)})^2 |
14,979 | 6 + 2*((-5)^{1 / 2} + 1) = 8 + 2*\left(-5\right)^{\frac{1}{2}} |
9,091 | \frac{g^l}{z}*z = (z*\tfrac{1}{z}*g)^l |
39,123 | (a + b)^2 = a \cdot a + 2ab + b^2 \geq a^2 + b^2 |
12,054 | 2 \sin{i} \sin{D} = -\cos(D + i) + \cos(-D + i) |
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