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-20,787 | \frac{1}{3} \times 3 \times \frac{1}{(-1) \times 2 \times k} \times (3 \times (-1) - k \times 3) = \frac{1}{\left(-6\right) \times k} \times (-k \times 9 + 9 \times (-1)) |
20,795 | x = {k + x + 2 \cdot \left(-1\right) \choose k + \left(-1\right)} = {k + x + 3 \cdot \left(-1\right) \choose k + 2 \cdot (-1)} + {k + x + 3 \cdot (-1) \choose k + (-1)} |
-6,046 | \dfrac{2}{\left(a + 10\right)*2} = \frac{2}{20 + 2a} |
-20,525 | \frac{x + 8}{x + 8} \cdot 2/9 = \frac{16 + 2 \cdot x}{x \cdot 9 + 72} |
606 | \frac{1}{1 + 2*f * f*c} = 1 - \frac{2*f^2*c}{1 + 2*f^2*c} \geq 1 - \dfrac{f*c}{(2*c)^{1 / 2}} |
12,072 | -6u = e^{-u} \implies \frac{1}{e^u} = -u*6 |
20,680 | \frac{\mathrm{d}}{\mathrm{d}x} \operatorname{atan}\left(x\right) = \dfrac{1}{1 + x^2} |
-29,130 | 15 = 5\left(-2\right) + 5*5 + 0*5 |
-522 | -30*\pi + \pi*\frac{1}{12}*361 = \frac{\pi}{12} |
11,330 | \left(-u^2 + 1\right)^{1/2} \cdot 2 = \left(-u^2 \cdot 4 + 4\right)^{1/2} |
24,630 | G \cdot B = 0 \implies 0 = G\text{ or }B = 0 |
19,439 | 1 = n\times y + m\times z \implies -y\times n + 1 = m\times z |
7,151 | \left(1 + y + \cdots + y^5\right)^8 = (\frac{1 - y^6}{1 - y})^8 = \dfrac{\left(1 - y^6\right)^8}{(1 - y)^8} |
-25,843 | x^5 = \frac{x}{x} \cdot x \cdot x \cdot x \cdot x \cdot x |
-9,466 | -r \cdot 2 \cdot 2 \cdot 2 \cdot 3 - 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 = -24 \cdot r + 108 \cdot (-1) |
13,693 | r = \frac{\pi*r*2}{\pi*2} |
39,097 | -(-h + x)^2 = (f - g)^2 \implies (f - g)^2 + (x - h)^2 = 0 |
-7,528 | -g^2 + d^2 = (g + d)\cdot (d - g) |
-593 | π \cdot \frac{11}{6} = -π \cdot 4 + π \cdot \dfrac{35}{6} |
28,679 | 600 = 2*5*5!/2! |
10,389 | 0 = x \cdot x + x + 1 = (x + \frac12)^2 + 3/4 |
20,210 | 2^m/m! \cdot y^m = \frac{1}{m!} \cdot (2 \cdot y)^m |
15,417 | \left(\omega + 1\right)\cdot 0 = 0 = \omega\cdot 0 |
23,630 | x \times x + 10 \times x = 50 \implies 50 = 10 \times x + x^2 |
363 | \frac{1}{2!*2!*2!*3!}(9! + 107736 (-1)) = 5315.5 |
-10,435 | 5/5 (-\dfrac{1}{2(-1) + t \cdot 4}5) = -\frac{25}{20 t + 10 (-1)} |
-24,852 | u/3 - v/2 = -1/2*(u/3 + \frac{1}{2}*v) + 1 = (\left(-1\right)*u)/6 - \tfrac{v}{4} + 1 |
10,876 | \frac12*(\sin\left(a - b\right) + \sin(a + b)) = \cos(b)*\sin(a) |
-20,783 | -1/6 \cdot (-\dfrac{1}{-2} \cdot 2) = 2/(-12) |
16,617 | 2\cos^2{x} = 2 - \sin^2{x} \cdot 2 |
36,791 | \frac{W}{m \cdot m\cdot k} = \frac1m\cdot W\cdot \dfrac{1}{k\cdot m} |
13,737 | 9\cdot x^2 + 36\cdot (-1) = 3\cdot x^2 - 6 \cdot 6 = (3\cdot x + 6)\cdot (3\cdot x + 6\cdot (-1)) = 3\cdot (x + 2)\cdot (3\cdot x + 6\cdot (-1)) = 9\cdot (x + 2)\cdot (x + 2\cdot \left(-1\right)) |
14,197 | m \cdot y = -m \cdot (-y) |
-8,635 | 6/2 - 6/3 = 6\cdot 3/\left(2\cdot 3\right) - 6\cdot 2/(3\cdot 2) = 18/6 - \frac{1}{6} 12 = (18 + 12 (-1))/6 = 6/6 |
-19,042 | 29/30 = A_x/(25 \pi) \cdot 25 \pi = A_x |
7,684 | A^2 H^2 = (HA)^2 |
-3,792 | p^4/p\cdot 144/36 = 144 p^4/\left(p\cdot 36\right) |
-1,065 | -\frac{4}{5}*(-9/7) = \left((-4)*1/5\right)/(1/9*(-7)) |
5,465 | \frac{1}{(1 + (-1))! \cdot 1! \cdot 1!} \cdot \left(1 + (-1) + 1 + 1\right)! = \frac{2!}{0! \cdot 1! \cdot 1!} = 2! = 2 |
-9,097 | 101.3\% = \frac{1}{100}*101.3 |
-23,808 | \dfrac{45}{7 + 2} = 45/9 = \frac19*45 = 5 |
-4,368 | \frac{11}{t^3} \cdot \frac18 = \frac{1}{8 \cdot t^3} \cdot 11 |
-17,244 | -\dfrac{31}{3} = -\dfrac{31}{3} |
-27,505 | 4*a = 2*2*a |
10,972 | 4 = (g + h)^2 = g^2 + h^2 + 2 \cdot g \cdot h |
-2,792 | 6^{1/2} + 25^{1/2}\cdot 6^{1/2} - 6^{1/2}\cdot 9^{1/2} = 5\cdot 6^{1/2} - 3\cdot 6^{1/2} + 6^{1/2} |
3,050 | (-1)^{1/2} = \frac{2^{1/4} (-1)^{1/2}}{2^{\frac{1}{4}}} |
26,449 | \sqrt{(1/2)^2 + (1/2)^2 + 1^2} = \sqrt{\frac12 \cdot 3} |
23,959 | \tan{3\cdot x} = \tan(x + x\cdot 2) |
16,814 | \frac{r}{r} = \frac{r}{r} |
16,094 | -1/2*2*\pi*i = -\pi*i |
18,892 | 9 \left(-1\right) + z^2 = \left(3 + z\right) (z + 3 (-1)) |
-3,868 | \dfrac{b^4 \cdot 48}{b^2 \cdot 96} = \dfrac{b^4}{b^2} \cdot 48/96 |
-21,800 | 7/9 = \dfrac19\cdot 7 |
13,355 | 4/6 \cdot 1/5/4 = \frac{1}{6 \cdot 5} = 1/30 |
17,454 | \binom{m}{x} \times x/m = \binom{m + (-1)}{(-1) + x} |
12,856 | \alpha \cdot (x + \beta) = \beta \alpha + \alpha x |
14,586 | -\frac12\times (1 + \cos\left(x\times 2\right)) + 1 = \sin^2(x) |
37,155 | \left(k\cdot 2\right) \cdot \left(k\cdot 2\right) = (2\cdot l + 25)^2 + 549\cdot (-1) \implies \left(2\cdot l + 25\right) \cdot \left(2\cdot l + 25\right) - (2\cdot k)^2 = 549 = 3^3\cdot 61 |
44,999 | 69915 = \binom{65}{3} + \binom{55}{3} |
22,843 | 0.119 = 0.34\times 0.5\times 0.7 |
12,225 | 2\cdot z + (1 - 2\cdot z - \frac{1}{16}\cdot 15\cdot z - \frac{1}{16})/16 = 2\cdot z + \frac{1}{256}\cdot 15 - 47\cdot z/256 = 465\cdot z/256 + \dfrac{15}{256} |
19,187 | (\int_0^a c\,\mathrm{d}y)*2 = \int\limits_{-a}^a c\,\mathrm{d}y |
-3,899 | \frac{x^4 \cdot 14}{x^3 \cdot 6} = \frac{14}{6} \cdot \dfrac{1}{x \cdot x \cdot x} \cdot x^4 |
10,328 | -3*\cos{x}*\sin^2{x} + \cos^3{x} = \cos{x*3} |
28,693 | x\cdot 2\cdot x\cdot 3 = x x\cdot 6 |
-19,184 | 14/15 = A_p/(25*\pi)*25*\pi = A_p |
5,517 | c * c g = gc^2 |
28,805 | (x + (-1)) (1 + x x + x) = (-1) + x^3 |
6,375 | D = K\cdot A\cdot x_0/g\Longrightarrow x_0\cdot \dfrac{A}{g}\cdot K = D |
9,215 | (1 - \frac{1}{n})^2 = -\frac{1}{n} \cdot 2 + 1 + \frac{1}{n \cdot n} |
-4,301 | \frac{z^2}{z \cdot z^2} = \frac{z \cdot z}{z\cdot z\cdot z}\cdot 1 = \frac1z |
10,696 | 28 \cdot \frac{1}{100}/6 = \frac{7}{150} |
37,080 | 2.575 = \frac{1}{2} \cdot (2.58 + 2.57) |
7,004 | \pi*g + \xi^2 - \xi*\left(g + \pi\right) = (\xi - \pi)*(\xi - g) |
22,267 | \sin(\frac{4*\pi}{3}*1) = -\sin(\frac13*\pi) |
-27,401 | 148 = 2(-1) + 150 |
3,597 | \left(2 = w! \times 2 \implies 1 = w!\right) \implies w = \left\{1, 0\right\} |
27,439 | n + n + \cdots + n = n + 1 + (n + 2) \cdot \cdots + n \cdot 2 |
27,116 | \frac{1}{12}\cdot (b - a)^2 + ((b + a)/2)^2 = \frac13\cdot (a \cdot a + b^2 + b\cdot a) |
-27,637 | 3 + 1 + (-1) + 3\cdot (-1) = 4 + (-1) + 3\cdot \left(-1\right) = 3 + 3\cdot \left(-1\right) = 0 |
-23,064 | \frac72\cdot 1/2 = 7/4 |
22,650 | b^2 + f \cdot f + f \cdot b \cdot 2 = (f + b) \cdot (f + b) |
21,137 | (a + b + f + h)/4 = (\frac{1}{2} \times (a + b) + (f + h)/2) \times \frac{1}{2} |
-6,386 | \frac{i \cdot 9}{9(i + 6) (i + 9)} = \frac{i}{(i + 6) (i + 9)} \cdot 9/9 |
-21,431 | \frac{2}{10}\cdot \tfrac{10}{10} = \frac{20}{100} |
7,984 | 0 = 1/2 + \frac12*\left(-1\right) |
-26,004 | {\dfrac34} \div{\dfrac16}={\dfrac34}\times\dfrac61 =\dfrac{3\times6}{4\times1} =\dfrac{18}{4} =\dfrac92 |
31,795 | 8 - 4^3 - 4 4 - 10 (-4) = -32 |
13,059 | 1 + 5 + 5^2 + \dotsm + 5^{k + 1} = \left(5^{k + 1 + 1} + (-1)\right)/4 = \dfrac14(5^{k + 2} + (-1)) |
21,196 | BA = I \implies I = AB |
12,336 | e^{\dfrac{(-1) \cdot x^2}{2 \cdot a \cdot a}} \cdot e^{\frac{1}{a^2} \cdot \left((-2) \cdot x \cdot x\right)} = e^{\frac{1}{2 \cdot a \cdot a} \cdot \left((-1) \cdot x^2\right) - \dfrac{4}{a^2} \cdot x^2} = e^{\dfrac{1}{a^2} \cdot \left((-5) \cdot x^2\right)} |
-4,763 | 8 + y^2 + 6y = (y + 4) (2 + y) |
24,038 | \frac{1}{K \cdot b} = \dfrac{1}{b \cdot K} = b \cdot K |
28,841 | \left(1 + y^2\right) (1 + y) = y^3 + y + y^2 + 1 |
18,145 | \left(n^2 - 2 \cdot n + 3\right) \cdot 2^{1 + n} + 6 \cdot (-1) = 6 \cdot (-1) + 2^{n + 1} \cdot ((n + 2 \cdot (-1)) \cdot n + 3) |
1,428 | 12*\frac{1}{36}/24 + 3/32*\frac{24}{36} = 11/144 |
28,330 | 4m^2+37=(2m)^2+37 |
12,712 | (k + 1)\cdot k!\cdot (k + 2) + \left(-1\right) = (k + 1)\cdot (k + 2)\cdot k! + (-1) |
32,339 | 49 = 23 + 2\times (a\times b + b\times c + a\times c) \Rightarrow b\times a + b\times c + c\times a = 13 |
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