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-18,272 | \dfrac{x}{(x + 7\cdot \left(-1\right))\cdot (x + 6)}\cdot (6 + x) = \frac{x^2 + x\cdot 6}{x^2 - x + 42\cdot (-1)} |
-21,683 | -\frac153 = -\frac{1}{5}3 |
-28,759 | x^2 \cdot 2 - 2 \cdot x + 6 - \dfrac{23}{x + 3} = \frac{1}{3 + x} \cdot \left(2 \cdot x^3 + 4 \cdot x^2 + 5 \cdot (-1)\right) |
32,611 | t^{-l} = \frac{1}{t^l} |
31,877 | 212/39 = \frac{17}{39} + 5 |
-20,201 | \frac17 \cdot 5 \cdot \tfrac{(-1) + a}{(-1) + a} = \frac{1}{7 \cdot (-1) + 7 \cdot a} \cdot (5 \cdot (-1) + 5 \cdot a) |
-4,024 | \tfrac{10}{3}\cdot t = t\cdot 10/3 |
-20,823 | (80 (-1) - 60 p)/(30 p) = (8(-1) - p*6)/(3p) \frac{1}{10}10 |
-25,584 | \frac{d}{dt} (-\frac3t) = \frac{3}{t^2} |
15,233 | \tfrac{1}{350} \cdot 1807 = 57/350 + 5 |
-27,710 | \frac{d}{dz} (-\cos{z}\cdot 12) = \sin{z}\cdot 12 |
17,306 | 6\cdot (-1) + 2\cdot x^2 - 4\cdot x = -(9\cdot x - x^3\cdot 3 + 6\cdot x^2) - x^3\cdot 3 + x^2\cdot 8 + 5\cdot x + 6\cdot \left(-1\right) |
-19,682 | \frac45\cdot 10 = 40/5 |
54,286 | \frac{1}{1 + 4 + 1}\cdot \left(1\cdot 2 + \frac{1}{2}\cdot 4 + 0\right) = \left(2 + 2\right)/6 = 4/6 = 2/3 |
-22,338 | (y + 9\times (-1))\times (1 + y) = y^2 - 8\times y + 9\times (-1) |
32,778 | (n-2i)+(i) = (n-i) |
18,055 | \tfrac{1}{25}*25 = 1 |
31,082 | 1+\frac1{1+\frac1{\frac53}}=1+\frac1{1+\frac1{1+\frac23}} |
21,880 | 1 - n + n\cdot 2 - 2\cdot n + (-1) = -n |
4,778 | 4 + l^2 + l\cdot 4 = (l + 2) \cdot (l + 2) |
-24,216 | 8 \times (10 + 5) = 8 \times 15 = 120 |
-5,970 | \frac{4}{5 \cdot y + 40} = \frac{1}{(y + 8) \cdot 5} \cdot 4 |
-11,136 | \left(x + 9\cdot (-1)\right)^2 + b = (x + 9\cdot (-1))\cdot (x + 9\cdot (-1)) + b = x^2 - 18\cdot x + 81 + b |
7,349 | det\left(k\cdot C\right) = k^{29}\cdot det\left(C\right) = k\cdot det\left(C\right) |
5,146 | \tfrac{1}{t + 1} = 1 - t + t^2 - \frac{1}{1 + t} t^3 |
5,663 | \frac{1}{b\cdot R} = 1/(R\cdot b) \implies R\cdot b = R\cdot b |
-3,070 | 3^{1 / 2} \cdot 8 = (1 + 5 + 2) \cdot 3^{\tfrac{1}{2}} |
5,808 | \binom{n}{2} \binom{n + 2 \left(-1\right)}{l}/(\binom{n}{l}) = \binom{-l + n}{2} |
23,420 | q = \frac{1}{3} + \frac{2}{3} (\dfrac{1}{3} + \dfrac{q}{3}) = 5/9 + \frac{2}{9} q |
-1,600 | 2 \cdot \pi - 5/12 \cdot \pi = \pi \cdot 19/12 |
253 | \sin(\frac{1}{12}) = \sin(-\frac{1}{4} + \frac{1}{3}) |
15,017 | \frac{1}{1 + e^{-z}} = \dfrac{e^z}{e^z + 1} |
13,258 | 17 = 563 + 546 \cdot (-1) = g - 4 \cdot a - 5 \cdot a - g = 2 \cdot g - 9 \cdot a |
21,132 | x\cdot y^2 + t\cdot y + s = (1 + 4\cdot k)\cdot \pi \Rightarrow -\pi\cdot (1 + k\cdot 4) + y \cdot y\cdot x + t\cdot y + s = 0 |
24,512 | ( z_k^1, z_k^2, z_k^3 \dotsm) = z_k |
8,459 | d/dx \sqrt{x} = 1/\left(\sqrt{x}*2\right) |
7,805 | \dfrac14*3*\int A^{-1/3}\,\text{d}A = (\int \tfrac{1}{A^{1/3}}\,\text{d}A)*\tfrac34 |
-5,456 | \frac{2}{10 + 2 \cdot m} = \frac{2}{2 \cdot (5 + m)} |
-1,650 | \pi \dfrac{1}{12}11 + \pi \cdot 4/3 = 9/4 \pi |
27,331 | \left(a + d\right)^3 = a^3 + 3\cdot a^2\cdot d + a\cdot d \cdot d\cdot 3 + d \cdot d \cdot d |
8,832 | |\bar{y}^2/y| = |\bar{y}|^2/|y| = \frac{|y|^2}{|y|} = |y| |
12,353 | -3 \times y \times z + \left(-z + x\right)^2 + (x - 3 \times y)^2 + 2 \times x^2 = x^2 \times 4 + 9 \times y^2 + z^2 - 6 \times x \times y - 3 \times y \times z - 2 \times x \times z |
35,442 | \sum_{n=2}^\infty \frac{14^n}{3^{3n+4}(3n+7)}\leq\sum_{n=2}^\infty \frac{14^n}{7\cdot 3^{3n+4}}=\frac{1}{7}\sum_{n=2}^\infty \frac{14^n}{3^4\cdot 27^n}=\frac{1}{7\cdot 81}\sum_{n=2}^\infty \left(\frac{14}{27}\right)^n |
-26,148 | -4\cdot 25^{\frac12\cdot 3} - -4\cdot 0^{\frac32} = -500 + 0 = -500 |
32,420 | 2 \cdot (5 \cdot n + 11) + n + 2 = 24 + 11 \cdot n |
-18,332 | \frac{1}{(10 + y)\cdot (3 + y)}\cdot (y + 10)\cdot y = \frac{10\cdot y + y^2}{30 + y \cdot y + 13\cdot y} |
28,659 | 2*\cos^2(Z) + (-1) = \cos\left(Z*2\right) |
1,912 | \binom{m}{r} = \dfrac{1}{r!*(m - r)!}*m! |
-12,557 | 172 + 123 (-1) = 49 |
29,236 | h^k \cdot h^x = h^{x + k} |
-20,580 | \frac{1}{10 \cdot n + 10 \cdot \left(-1\right)} \cdot (n \cdot 5 + 15 \cdot (-1)) = 5/5 \cdot \frac{3 \cdot (-1) + n}{2 \cdot \left(-1\right) + n \cdot 2} |
9,494 | z \cdot 3 + z + (-1) = z \cdot 4 + (-1) |
28,779 | 1 + i_1 = 21 \implies 20 = i_1 |
2,301 | j^2\cdot 32 = \dfrac{1}{2}\cdot \left(j\cdot 8\right)^2 |
28,535 | d^{m + 1} = d^m\cdot d^1 |
11,426 | \|X\| = \|X + F - F\| \leq \|X + F\| + \|F\| |
27,878 | g^{k_1}*g^{k_2} = g^{k_1 + k_2} |
21,479 | \frac12 \lt \dfrac{1}{y^2 + 1}y\Longrightarrow 0 \gt (y + (-1))^2 |
7,694 | 200 = (300 \cdot (-1) + 500 - 200 + 0)/2 + 200 |
-20,400 | -\frac{1}{n*9 + 90*\left(-1\right)}*63 = -\frac{1}{10*\left(-1\right) + n}*7*9/9 |
32,787 | R_b \cdot R_a = R_b \cdot R_a |
-7,562 | \frac{1}{41}(60 - 130 i + 48 i + 104) = \frac{1}{41}(164 - 82 i) = 4 - 2i |
-4,026 | x^2/3 = \frac13 \cdot x \cdot x |
27,716 | 7^B = (1 + 6)^B |
-12,686 | 40 = 112 \cdot (-1) + 152 |
4,684 | \dfrac{1}{4} = (-1/2)^2 |
12,948 | \left(\sqrt{T} \cdot 2 = T \implies T^2 = T \cdot 4\right) \implies -T \cdot 4 + T^2 = 0 |
10,433 | -\dfrac12 = \cos(2\pi/5) + \cos(\pi\cdot 4/5) |
-13,757 | 2 + \frac{1}{6} 24 = 2 + 4 = 2 + 4 = 6 |
32,371 | bg + bh + gh = ((g + h + b)^2 - h \cdot h + b^2 + g^2)/2 |
6,375 | \frac{1}{d}\cdot K\cdot A\cdot \epsilon_0 = C \Rightarrow \epsilon_0\cdot \frac{K}{d}\cdot A = C |
-1,987 | \pi = \pi*\frac{7}{12} + \pi*5/12 |
7,046 | \frac{3^2\cdot 7\cdot 11\cdot 19}{13\cdot 17\cdot 50\cdot 49} = \tfrac{13167}{541450} |
52,616 | \sqrt{y^2-2y}-y=\left(\sqrt{y^2-2y}-y\right)\cdot\frac{\sqrt{y^2-2y}+y}{\sqrt{y^2-2y}+y} |
-24,170 | \tfrac{66}{7 + 4} = \frac{1}{11} \cdot 66 = 66/11 = 6 |
15,711 | \sin(x+\pi)=-\sin x |
-2,174 | 2/14 = -\frac{3}{14} + 5/14 |
39,604 | 65536 = 4096\times 2^4 |
-474 | \pi\cdot 95/3 - 30\cdot \pi = \pi\cdot 5/3 |
20,693 | g \cdot b = t \cdot f \Rightarrow t = g \cdot b/f |
-5,462 | \frac{2}{3\cdot r + 30} = \frac{1}{(10 + r)\cdot 3}\cdot 2 |
27,833 | 1/17 + \dfrac{1}{16} \cdot 2 = 1/16 + \frac{1}{16} + 1/17 |
3,223 | \sum_{r=0}^n a^r \cdot b^{n - r} = \sum_{r=0}^n (\frac{a}{b})^r \cdot b^n = b^n \cdot \sum_{r=0}^n (a/b)^r |
13,385 | 2\cdot \pi = 6\cdot \pi/3 |
-25,581 | \frac{d}{dt} (2t^3 + 6) = 3 \cdot 2t^2 = 6t^2 |
-2,117 | -\pi/3 = 19/12\cdot \pi - 23/12\cdot \pi |
16,038 | 13*(3 * 3^2*5)^2 = 236925 |
29,211 | y^d \cdot y^c = y^{c + d} |
-22,277 | x^2 - 13\cdot x + 30 = (x + 10\cdot (-1))\cdot (x + 3\cdot (-1)) |
4,138 | y^2 + 2\cdot y + 3 = \frac{1}{(-1) + y}\cdot \left(3\cdot (-1) + y^3 + y \cdot y + y\right) |
37,348 | 1 + \dfrac{17}{24} = 41/24 |
-503 | -\pi\cdot 6 + \frac{1}{12}\cdot 77\cdot \pi = 5/12\cdot \pi |
3,893 | 3\cdot c_1 + x\cdot 6 = 0 \implies -x\cdot 2 = c_1 |
24,921 | \frac{1}{2 + 3 + (-1)}*(3 + \left(-1\right)) = 2/4 = 1/2 |
19,674 | a^2 - 2xa + x \cdot x = (-x + a) \cdot (-x + a) |
-11,500 | 12 + 8 - i \cdot 10 = -10 \cdot i + 20 |
19,240 | (-1/3 + \frac{1}{2})\cdot 5 = \tfrac{1}{2}\cdot 3 - 2/3 |
31,451 | x + |1|*c_2 = 0 \Rightarrow x = -c_2 |
4,458 | \sigma\times g_2/\sigma\times g_1 = \dfrac{g_1}{\sigma}\times \sigma\times \sigma\times g_2/\sigma |
21,152 | 62/132 = \tfrac{31}{66} |
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