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23,572 | s \cdot (a + f) = s \cdot a + s \cdot f |
18,771 | \frac{1}{m}*\binom{\left(-1\right) + m + x}{x} = \binom{(-1) + m + x}{m}/x |
-9,082 | 38.1/100 = 38.1\% |
33,014 | x^{7 + l} = x^7 x^l = x^l |
30,275 | f + b + d = b + d + f |
14,262 | 23 \cdot \left(-1\right) + 2^6 = 41 |
-3,965 | \frac{n\cdot 35}{14 n^4} = \dfrac{35}{14} \frac{1}{n^4}n |
35,584 | 24 = 0 + \left\lfloor{\frac15\cdot 100}\right\rfloor + \left\lfloor{\frac{100}{25}}\right\rfloor |
26,899 | \cos(2x) = 1 - \sin^2(x)\cdot 2 \implies \sqrt{(-\cos(2x) + 1)/2} = \sin(x) |
36,012 | 2 = -(-2) - 0 |
19,835 | 3^{2 + n} = 9\cdot 3^n |
26,972 | (x + z)^2 = z^2 + x * x + 2*z*x |
4,390 | (l + (-1))!\cdot \left((-1) + l\right) = l! - ((-1) + l)! |
45,554 | \xi^{m + 1} = \xi^{m_j} - d*w*(\xi^{m_j} - \xi^{m_{j + (-1)}})/x = (1 - \frac{1}{x}*d*w)*\xi^{m_j} + d*w/x*\xi^{m_{j + \left(-1\right)}} |
-1,409 | 7/2\cdot \dfrac72 = 7\cdot 1/2/(2\cdot 1/7) |
5,612 | 0 \lt 3/4\cdot (2 - \dfrac34) = 0.9375 \lt 1 |
13,895 | \left(C_2 + C_1\right)^2 = C_1 \cdot C_1 + 2\cdot C_1\cdot C_2 + C_2^2 |
-2,040 | -\frac{19}{12} \cdot \pi = \frac{\pi}{3} - \pi \cdot 23/12 |
26,426 | -1/2 = \dfrac12 + (-1) |
-18,147 | 17 = 2 \cdot (-1) + 19 |
-2,707 | \sqrt{5} + \sqrt{16\cdot 5} + \sqrt{9\cdot 5} = \sqrt{5} + \sqrt{80} + \sqrt{45} |
23,788 | \left(\frac{1}{40} \cdot 9 + \frac{3}{40}\right) \cdot 100 = 30 |
-186 | \tfrac{8!}{5! \cdot (5 \cdot (-1) + 8)!} = \binom{8}{5} |
-473 | π*7/4 = 63/4*π - 14*π |
11,792 | -5^{1 / 2} + 7^{\frac{1}{2}} - 6^{1 / 2} - 6^{\frac{1}{2}} = 5^{\frac{1}{2}} + 7^{1 / 2} - 6^{\dfrac{1}{2}}\cdot 2 |
32,114 | -b + b\cdot a - a = (b + (-1))\cdot a - b |
1,515 | 0z + xz = zx |
-7,793 | (-20 + 20 i)/(-4) = -\frac{20}{-4} + i \cdot 20/(-4) |
7,896 | 61 = 7 * 7 + 3 * 3 + 1^2 + 1^2 + 1^2 = 5^2 + 5^2 + 3^2 + 1 * 1 + 1 * 1 |
15,346 | y + c + h = h + y + c |
39,502 | \cos(\pi - x) = -\cos(x) |
5,798 | x*F * F = X_D*x * x - X_D*F^2 = X_B*x^2 - X_B*F^2 = X_B*x^2 - (X_D*X_B - X_D*F)^2 |
-26,506 | (9\cdot (-1) + x\cdot 8)^2 = x \cdot x\cdot 64 - x\cdot 144 + 81 |
-2,885 | 3^{\frac{1}{2}}*2 = (5 + 1 + 4*\left(-1\right))*3^{\frac{1}{2}} |
-7,740 | -8 \cdot i/\left(-4\right) + \dfrac{1}{-4} \cdot 12 = \dfrac{1}{-4} \cdot (12 - i \cdot 8) |
39,883 | -\sin{a} = \sin{-a} |
21,861 | 4 \cdot x + \left(-1\right) = (\sqrt{x + 2} + 3 \cdot (-1))^2 = x + 2 - 6 \cdot \sqrt{x + 2} + 9 = x + 11 - 6 \cdot \sqrt{x + 2} |
36,414 | x^4+1=0 \implies x^4=-1 \implies x^8=1 |
-9,500 | -10 s = -s \cdot 2 \cdot 5 |
4,558 | 1 = \frac{1}{100} + \frac{1}{25} + 1/5 + \dfrac14 + \dfrac{1}{2} |
-27,273 | \sum_{m=1}^\infty \tfrac{1}{m*7^m}*(-11 + 4)^m*(m + 6) = \sum_{m=1}^\infty \tfrac{(-7)^m}{m*7^m}*(m + 6) = \sum_{m=1}^\infty \frac{7^m}{m*7^m}*(-1)^m*\left(m + 6\right) = \sum_{m=1}^\infty \left(-1\right)^m*(m + 6)/m |
6,432 | (x/N \cdot N)^m = x^m/N \cdot N |
-2,516 | 6 \cdot 5^{1 / 2} = (4 + 5 + 3 \cdot (-1)) \cdot 5^{1 / 2} |
9,829 | \cos(y) = \sin(y) \Rightarrow \tan(y) = 1 |
11,724 | (a + x \cdot i)^{-1} = \frac{1}{a^2 + x^2} \cdot (a - x \cdot i) = a - x \cdot i |
-15,998 | 5/10 - \frac{1}{10}*9*10 = -\frac{85}{10} |
-5,781 | \frac{2}{(8(-1) + z)*5} = \frac{2}{5z + 40 (-1)} |
19,672 | ((-1) + 2*n)*\left(2*n + 1\right) = (-1) + 4*n^2 |
-23,266 | \frac25 = 3/5 \cdot 2/3 |
-1,197 | -8/7 \cdot (-8/5) = \frac{1}{\dfrac{1}{8} \cdot (-7)} \cdot ((-1) \cdot 8 \cdot \dfrac15) |
21,582 | C_2^3 + C_1^3 = (C_1 + C_2) \cdot (C_1^2 + C_2 \cdot C_2 - C_2 \cdot C_1) |
12,349 | (1 - t)^3 = -t^3 + 1 - 3 t + t^2 \cdot 3 |
2,977 | (X - \frac{1}{2}n)/\left(\sqrt{n/4}\right) = -\sqrt{n} + X*2/(\sqrt{n}) |
-5,163 | \frac{0.48}{100} = \dfrac{1}{100} \cdot 0.48 |
17,056 | \mathbb{E}(B_n\cdot X_n) = \mathbb{E}(X_n)\cdot \mathbb{E}(B_n) |
28,418 | N/g = \dfrac{N}{g} |
34,629 | (\dfrac12)^5\cdot \left(1/2\right)^5\cdot {10 \choose 5} = \dfrac{63}{256} |
24,959 | 3^{1/2}/2 \times 3^{1/2}/2 = 3/4 |
11,210 | X + I = -X + I + 2\cdot X |
11,534 | (-z + r) \times (r^{b + (-1)} + r^{2 \times (-1) + b} \times z + \dotsm + r \times z^{b + 2 \times (-1)} + z^{(-1) + b}) = r^b - z^b |
34,621 | \frac{{71 \choose 11}}{{80 \choose 20}} = \dfrac{17}{23471690} |
-19,458 | \frac{2}{7\cdot 1/3}1/3 = \frac23\cdot \dfrac37 |
-26,000 | -72/\left(-8\right) = 9 |
16,875 | 34 = 21 \cdot 2 + 8 \cdot (-1) |
4,416 | \frac{2\cdot (q + 263)}{2\cdot q + \left(-1\right)} = \frac{2\cdot q + 526}{2\cdot q + (-1)} = 1 + \frac{527}{2\cdot q + (-1)} |
16,195 | (-c + d) (c + d) = d * d - c^2 |
20,575 | \mathbb{E}\left[\sin(Z)\right] = \sin(\mathbb{E}\left[Z\right]) |
-12,383 | 5 \cdot 5 \cdot 6 = 150 |
6,315 | 2^{N + 1} = (1 + 1)^{N + 1} = {N + 1 \choose 0} + {N + 1 \choose 1} + ... + {N + 1 \choose N + 1} |
7,914 | 1 + 2 + \dots + n + \left(-1\right) + n - n = 1 + 2 + \dots + n + (-1) |
14,575 | e + 4 + 36 + 4 \cdot b + 12 \cdot h = 0 \Rightarrow 4 \cdot b + 12 \cdot h + e = -40 \cdot ... \cdot 3 |
38,382 | B_0*x_0 = B_0*x_0 |
33,217 | c = c \cdot 2 - c |
-409 | \frac{7!}{3!*4!} = 35 |
8,635 | 3/5 = \frac1r*((-1) + p) \Rightarrow 3/5*r + 1 = p |
-4,484 | (2\cdot (-1) + z)\cdot (z + 3\cdot \left(-1\right)) = 6 + z^2 - z\cdot 5 |
25,360 | \tfrac{p \cdot 1/q}{\frac{1}{q} \cdot p + 1} = \frac{1}{1 + y} \cdot y \Rightarrow \dfrac{p}{q} = y |
20,909 | \left(i*\sin\left(-\pi\right) + \cos\left(-\pi\right)\right)*8 = -8 |
-2,279 | 2/13 = -\frac{6}{13} + 8/13 |
31,354 | |x| = \|\dfrac12\cdot (x + y) + (x - y)/2\| \leq \frac{1}{2}\cdot (|x + y| + |x - y|) |
39,218 | -bd = -b d |
3,597 | \left(w!*2 = 2 \Rightarrow w! = 1\right) \Rightarrow w = \left\{0, 1\right\} |
35,529 | \frac{y^f}{y^b} = y^{f - b} = \frac{1}{y^{b - f}} |
-1,933 | -\dfrac{1}{4}*\pi = \pi/3 - 7/12*\pi |
31,722 | \sin(x) + \sin(B) + \sin(z) = 0 = \cos(x) + \cos(B) + \cos\left(z\right) |
6,448 | 2*3^k + 3^{k + 1} c_{k+1} = 3*3^k c_{k+1} + 3^k*2 |
53,969 | (4/9 - \dfrac59)\cdot 2\cdot \pi\cdot i\cdot (-\frac{1}{i}) = \dfrac{\pi\cdot 2}{9} |
35,307 | d \cdot 3 + 3f = 3\left(d + f\right) |
-22,375 | n^2 + n\cdot 7 + 12 = (n + 3)\cdot (4 + n) |
29,907 | x^4 - 5x^3 + 5x^2 + 5x + 6(-1) = (x^2 - 2x + 3(-1)) (x^2 - 3x + 2) = (x + 1) (x + 3\left(-1\right)) (x + \left(-1\right)) (x + 2(-1)) |
-8,095 | \dfrac{-2 + i*16}{-1 - i*5} = \tfrac{1}{-5i - 1}(-2 + 16 i) \frac{-1 + i*5}{i*5 - 1} |
7,075 | \frac{17}{4 \cdot 17} \cdot 3 = \frac{51}{68} |
36,995 | -2 \cdot x = \frac{\mathrm{d}}{\mathrm{d}x} (-x^2) |
18,664 | (R^4 + R^3 + R^2 + R + 1)\cdot (\left(-1\right) + R) = \left(-1\right) + R^5 |
7,332 | 197431271037 = (3 \cdot 7 \cdot 11 \cdot 13) \cdot (3 \cdot 7 \cdot 11 \cdot 13) \cdot 21893 |
-15,423 | \dfrac{1/y}{y^6\cdot x^2}\cdot x^2 = \frac{x^2\cdot \frac{1}{y}}{(y^3\cdot x)^2} |
283 | \dfrac{k}{1 + k} + \frac{1}{\left(k + 1\right)\cdot \left(k + 2\right)} = \frac{k + 1}{k + 2} |
6,179 | \frac{1}{S_2} \cdot (S_2 - C_2) = 1/4 \Rightarrow S_2 = C_2 \cdot 4/3 |
19,645 | 18a+6b=6\cdot(3a+b) |
21,607 | 123*345*x = 123*x*345 |
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