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14,009 | s*x + x*s*2 + s*3*x + \cdots + x*s*36 = 1 - x*s*0 |
13,600 | \frac13 + \dfrac{2}{9} = \tfrac39 + 2/9 = \dfrac59 |
41,602 | X^4 + 1 = X^4 - a * a = (X^2 + a) (X * X - a) |
17,802 | \left(1 + x\right)^2 = x \cdot x + 2\cdot x + 1 |
36,855 | 114 = 166 - 4\cdot (-1) + 33 + 23 |
11,190 | \tfrac{1}{15}\cdot \left(2 + 3\right) = \frac{1}{15}\cdot 5 |
14,290 | 2\cdot \sin{r}\cdot \cos{r} = \sin{r\cdot 2} |
14,540 | \dfrac{b}{h} = \frac{1}{\frac{1}{b} \cdot h} |
-11,531 | i - 13 = i - 3 + 10*\left(-1\right) |
16,552 | (\cos(y) + i\sin\left(y\right))^n = e^{iny} = \cos\left(ny\right) + i\sin(ny) |
4,442 | 12*y^3 + 8*y^2 - y + \left(-1\right) = (y + 1/2)*(12*y^2 + 2*y + 2*(-1)) = 2*(y - \frac{1}{2})*\left(6*y^2 + y + (-1)\right) |
19,710 | 65 = 1 * 1 + 8 * 8 |
7,678 | \frac{1}{\frac{1}{\frac{1}{1/2 + 42} + 5} + 1} + 0 = \frac{427}{512} |
-25,802 | 5*\dfrac13/7 = 5/21 |
-24,656 | 5/30 = \frac{5}{6*5}1 |
-20,847 | \frac{x \cdot (-48)}{18 \cdot x} = -8/3 \cdot \frac{6}{x \cdot 6} \cdot x |
1,821 | -\frac13 + \frac12 = \tfrac16 |
14,588 | (1 + k) \left(2 + k\right) ... \cdot 2 = (k + 2)! |
15,151 | (3 - \sqrt{2})^4 = \left(\left(3 - \sqrt{2}\right)^2\right)^2 = (11 - 6\cdot \sqrt{2}) \cdot (11 - 6\cdot \sqrt{2}) = 193 - 132\cdot \sqrt{2} |
4,055 | y_2 \cdot y_2 = y_1 \cdot y_1 \implies y_2 = y_1 |
5,811 | \frac12\cdot (x \cdot x + x) = x + \dfrac12\cdot (x^2 - x) |
-11,136 | (y + 9(-1)) * (y + 9(-1)) + b = (y + 9\left(-1\right)) (y + 9(-1)) + b = y^2 - 18 y + 81 + b |
14,451 | 1 + y - 2\cdot y \cdot y = (1 + 2\cdot y)\cdot (-y + 1) |
13,679 | v = (x^2\cdot 4 + 4)^{\frac{1}{2}} \Rightarrow x^2\cdot 4 + 4 = v \cdot v,(v^2 + 4\cdot (-1))/4 = x \cdot x |
37,808 | 4! = (12 + 8(-1))! |
38,390 | (e^0)^{1 / 2} = e^0 |
5,015 | 84\times 9 = 84\times 10 + 84\times (-1) = 840 + 84\times (-1) = 800 + 44\times (-1) = 756 |
6,726 | \left(2 \cdot k\right)^2 = 0 + 2 \cdot k \cdot k \cdot 2 |
21,594 | x R y rightarrow y R x |
-11,084 | (z + 7\cdot (-1)) \cdot (z + 7\cdot (-1)) + f = (z + 7\cdot (-1))\cdot (z + 7\cdot (-1)) + f = z^2 - 14\cdot z + 49 + f |
4,477 | (g h/h)^2 = g h g h/h/h = g^2 h/h |
-1,579 | \pi*3/2 = \pi/6 + \pi \frac{1}{3} 4 |
18,040 | \int_1^\infty \cos{t}/t\,\mathrm{d}t = \sum_{m=0}^\infty \int_{1 + m \cdot \pi}^{1 + (m + 1) \cdot \pi} \cos{t}/t\,\mathrm{d}t = \int_1^{\pi + 1} \cos{t} \cdot \sum_{m=0}^\infty \frac{(-1)^m}{t + m \cdot \pi}\,\mathrm{d}t |
12,403 | \frac{1}{10 \times 10} = 1/100 |
-20,153 | -\dfrac{7}{2} \cdot \frac{t \cdot (-3)}{(-3) \cdot t} = \frac{21 \cdot t}{t \cdot (-6)} |
39,303 | 260 = 4^4+4^1 |
27,276 | 6\cdot l + 9\cdot x = 2\cdot 3\cdot l + 3\cdot 3\cdot x = 3\cdot \left(2\cdot l + 3\cdot x\right) |
25,701 | r^2 + r\cdot 6 + 9 = \left(r + 3\right)^2 |
23,098 | h\frac{d}{d + h} = \frac{1}{1/d + \frac{1}{h}} |
18,412 | \dfrac{1}{2}\cdot (1 - \sqrt{5}) = \frac12 - \sqrt{5}/2 |
29,110 | \|x\| = 0 \Rightarrow 0 = x |
-5,970 | \frac{4}{y\cdot 5 + 40} = \frac{4}{5 (y + 8)} |
34,591 | E_x = E_x |
3,571 | 1 + x^4 = 1 + 2\times x^2 + x^4 - 2\times x^2 = \left(1 + x^2\right)^2 - \left(\sqrt{2}\times x\right)^2 |
-30,831 | \frac134 \pi \cdot 9 \cdot 9 \cdot 9 = 972 \pi |
11,007 | \left(|d| = 1 \Rightarrow d \in A\right) \Rightarrow |A\cdot d| = 1! |
33,120 | 2x+5x = (2+5)x = 7x |
29,966 | 20!/\left(3!\cdot 17!\right) = 1140 |
33,735 | 0 = q^2 + (-1) = (q + (-1))*\left(q + 1\right) |
22,641 | (h_2 + h_1 + b) \cdot (h_1^2 + b^2 + h_2^2 - h_1 \cdot b - h_1 \cdot h_2 - b \cdot h_2) = h_1 \cdot h_1 \cdot h_1 + b^3 + h_2^3 - h_2 \cdot b \cdot h_1 \cdot 3 |
-4,761 | \frac{-z + 17 (-1)}{3 \left(-1\right) + z z - z\cdot 2} = \frac{4}{1 + z} - \tfrac{5}{3 (-1) + z} |
14,971 | 2\cdot 2\cdot y + 4\cdot y = 8\cdot y |
18,759 | \frac{1}{2}20! = 18! \frac{19}{2}20 |
28,708 | \frac{1}{n! + (1 + n)! + (n + 2)!} = \frac{1}{(n + 2)^2\cdot n!} |
19,997 | 7 = 3^2 - 3 + 1 \cdot 1 |
-13,927 | \frac{36}{2 + 7} = \frac1936 = \tfrac{36}{9} = 4 |
24,730 | \sum_{k=1}^{1 + m} k^3 = \left(m + 1\right)^3 + \sum_{k=1}^m k^3 |
-10,509 | -\frac{y \cdot 4}{12 \cdot \left(-1\right) + 12 \cdot y} \cdot 1 = 4/4 \cdot (-\frac{y}{3 \cdot y + 3 \cdot (-1)}) |
9,776 | (x + y) \cdot (x + l \cdot y) = x^2 + l \cdot x \cdot y + x \cdot y + l \cdot y^2 \geq x^2 + (l + 1) \cdot x \cdot y |
14,249 | 13\cdot \left(-1\right) + 7\cdot a = 71 \Rightarrow a = 12 |
-2,253 | 2/16 = 7/16 - \frac{1}{16}*5 |
31,169 | -\sin{G} = \sin{-G} |
-7,821 | \frac{-3 + i*15}{-i*2 + 3}*\frac{1}{3 + 2*i}*(3 + 2*i) = \frac{1}{-2*i + 3}*(-3 + i*15) |
-29,559 | y^5 \cdot 6/y = 6 \cdot y^4 |
-3,321 | 208^{1/2} - 117^{1/2} = (16*13)^{1/2} - (9*13)^{1/2} |
26,013 | 5 * 5 = \frac{1}{2}(7^2 + 1^2) |
22,944 | \left(-1\right) + x^l = ((-1) + x)\cdot (-e^{\frac{2}{l}\cdot \pi} + x)\cdot \cdots\cdot e^{\dfrac{2}{l}\cdot \pi\cdot \left(l + (-1)\right)} |
-10,440 | 3/3 \cdot (-\dfrac{t}{t^3}) = -\frac{t \cdot 3}{3 \cdot t^3} |
6,640 | \tanh{x} = \sinh{x}/\cosh{x} = \frac{1}{e^x + e^{-x}} \cdot \left(e^x - e^{-x}\right) |
10,383 | \int_d^c j\,\mathrm{d}y = \int_d^c j\,\mathrm{d}y |
17,191 | \cos(x + z) = -\sin(x)*\sin(z) + \cos(z)*\cos(x) |
19,144 | \pi/3 = \frac{\pi}{\sin(\pi/6) \cdot 6} |
15,841 | \left|{X\cdot x\cdot x^T}\right| = \left|{X}\right|\cdot \left|{x\cdot x^T}\right| = \left|{X}\right|\cdot x\cdot x^T |
33,921 | 6 * 6 * 6 + \left(y*5\right)^3 = 216 + 125 y^2 * y |
-22,221 | ((-1) + t) (t + 6) = t^2 + t\cdot 5 + 6\left(-1\right) |
21,737 | x^3 - x^2\cdot 12 + x\cdot 36 + 32 (-1) = (x + 2(-1))^2 (8(-1) + x) |
16,167 | {n \choose k} = \frac{n!}{k! \cdot (n - k)!} = {n \choose n - k} |
11,377 | 1/2 + \frac14*4 + 9/8 = 21/8 |
26,625 | \sin{\theta \cdot 2}/2 = \cos{\theta} \cdot \sin{\theta} |
22,706 | 1^2 \times \tfrac{1}{2^{\frac{1}{2}}} \times 2 = 2^{1 / 2} |
16,331 | (x + 4\cdot (-1))\cdot (x + 1) = 4\cdot (-1) + x^2 - 3\cdot x |
-1,741 | \pi*\frac{13}{6} = 19/12*\pi + 7/12*\pi |
14,188 | \frac{1}{3}(16 + 4\left(-1\right)) = 6 \lt 7 |
-9,318 | -30t - 50 = - (2\cdot3\cdot5 \cdot t) - (2\cdot5\cdot5) |
-9,429 | -10 t^3 = -2*5 t t t |
-3,060 | \sqrt{11} + \sqrt{11}\cdot 2 = \sqrt{11}\cdot \sqrt{4} + \sqrt{11} |
-26,706 | \sum_{k=1}^\infty \dfrac{5^k}{k \cdot 5^k} = \sum_{k=1}^\infty 1/k |
-5,969 | \tfrac{3}{(s + 1) \cdot \left(6 + s\right)} = \frac{1}{6 + s \cdot s + s \cdot 7} \cdot 3 |
5,920 | \cos\left(x + s\right) = \cos(s)*\cos\left(x\right) - \sin(x)*\sin\left(s\right) |
11,795 | z\cdot 3 = \frac{\mathrm{d}}{\mathrm{d}z} (z^2\cdot 3/2 + 1/2) |
13,323 | -\frac{D_{15}}{15!^2} \cdot 15! + 1 = -D_{15}/15! + 1 |
51,658 | 100040004 = 10002^2 |
-10,494 | -\frac{3}{60\cdot q^2} = 3/3\cdot (-\frac{1}{20\cdot q^2}) |
14,474 | r = \cos(\arccos{r}) |
-10,807 | \dfrac19*189 = 21 |
10,281 | a/g \cdot g = \frac{g}{g^2} \cdot g \cdot a |
-23,014 | \frac{1}{56}63 = \frac{7\cdot 9}{7\cdot 8} |
16,241 | {(-1) + n \choose k + \left(-1\right)} n/k = {n \choose k} |
18,956 | a \cdot a \cdot a - b^3 = \left(a \cdot a + b \cdot a + b^2\right) \cdot \left(a - b\right) |
18,948 | 1 = (z_1 + z_2)^2 \leq 2(z_1 \cdot z_1 + z_2^2) |
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