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24,820 | \dfrac{\sqrt{5}}{2} + \frac12 = \frac{1}{2}\cdot \left(\sqrt{5} + 1\right) |
41,308 | 0\cdot y = y\cdot 0 = y |
-5,270 | 10^4\times 0.89 = 10^{3\times \left(-1\right) + 7}\times 0.89 |
-4,588 | \frac{1}{9\cdot (-1) + y^2}\cdot (18 + y\cdot 4) = -\frac{1}{3 + y} + \frac{5}{y + 3\cdot (-1)} |
-27,339 | \cos{x} \sin{x}*2 = \sin{x*2} |
17,369 | \frac{1}{1/81} = \dfrac{1}{\frac{1}{3^4}} |
3,226 | \ln(f)/(\ln(b)) = \log_b(f) |
-11,563 | 4 i - 4 + 15 \left(-1\right) = 4 i - 19 |
15,085 | \|A - F\| \leq \|A - F\|^3 \implies A = F |
8,772 | \sqrt{x^2 c c} = \sqrt{x^2} \sqrt{c^2} = |x| |c| = -x c |
2,374 | (z + (-1))\cdot (z + 1) = z^2 + \left(-1\right) |
-3,932 | \dfrac{3}{r \cdot 11} = 1/11 \cdot 3/r |
17,941 | 5^\varepsilon = z \Rightarrow 5^{2\varepsilon} = (5^\varepsilon)^2 = z^2 |
12,053 | det\left(D\times E + 1\right) = det\left(D\times E + 1\right) |
10,715 | \frac{1}{1 - Z}\cdot \left(1 - Z^{n + 1}\right) = 1 + Z + Z^2 + ... + Z^n |
37,600 | 0.125 = \frac{1}{16}\times 2 |
-4,731 | \frac{1}{15\cdot (-1) + y^2 - y\cdot 2}\cdot (-y\cdot 2 + 26) = -\frac{1}{y + 3}\cdot 4 + \dfrac{2}{5\cdot (-1) + y} |
31,502 | 1 + z = \frac1z(z * z + z) |
8,461 | a \cdot (-A) = -a \cdot A = -a \cdot A |
15,311 | -\frac{8}{-216} = 1/27 |
-10,607 | -\frac{1}{j^2}*(2 + j*5)*\frac44 = -\frac{1}{j^2*4}*(j*20 + 8) |
51,708 | -x = (-x)^4 = x^4 = x |
23,349 | \binom{24}{8}*\binom{16}{8} = \tfrac{24!}{8!^3} = 9465511770 |
29,036 | 1/6 = 3/18 = 1/18 + 2/18 = \frac{1}{9} + 1/18 |
12,747 | 6 \lt Q + 3*(-1) \Rightarrow 9 \lt Q |
-3,651 | 8/9 \cdot q^2 = \dfrac{8}{9} \cdot q^2 |
-30,260 | (5 + y)\cdot \left(5 + y\right) = 25 + y \cdot y + y\cdot 10 |
49,189 | -80 - (-48) = -32 |
24,670 | \frac{1}{x^7 - x} = -\frac{7*x^6 + (-1)}{-x + x^7} + \dfrac{7*x^6}{-x + x^7} |
868 | (\frac1a)^n = a^{-n} = \tfrac{1}{a^n} |
18,974 | |x - (x + z)/2|^2 = |\frac{x}{2} - \frac{1}{2}\cdot z|^2 = |\frac{1}{2}\cdot \left(x + z\right) - z|^2 |
12,093 | y^2 - 3 \cdot y = y^2 - 3 \cdot y + \left(3/2\right) \cdot \left(3/2\right) - (3/2)^2 = \left(y - \frac32\right)^2 - \left(\frac{3}{2}\right)^2 |
2,074 | \sin\left(-s\cdot \pi + \pi\right) = \sin(\pi\cdot s) |
34,740 | \frac{4\times \binom{9}{5}}{\binom{52}{5}}\times 1 = 3/15470 |
-11,588 | -5 + 2 \cdot (-1) + i \cdot 3 = -7 + 3 \cdot i |
-20,538 | \dfrac{1}{15\cdot p + 10\cdot (-1)}\cdot \left(6\cdot (-1) + 9\cdot p\right) = 3/5\cdot \frac{1}{p\cdot 3 + 2\cdot (-1)}\cdot (p\cdot 3 + 2\cdot (-1)) |
-23,017 | \frac{1}{44}\cdot 77 = 7\cdot 11/(4\cdot 11) |
-3,651 | p^2\cdot 8/9 = 8p^2/9 |
21,638 | x x + (-1) = \left(x + 1\right) ((-1) + x) |
23,586 | (x + 3 \cdot x) \cdot 3 = x \cdot 12 |
18,535 | x^3 + 4*x^2 + 14*x + 9 = (x + 3*(-1))*(x^2 + 7*x + 16) = (x + 3*\left(-1\right))*(x + 5*(-1))*(x + 7*\left(-1\right)) |
-4,281 | \frac{r^5}{r} = r\times r\times r\times r\times r/r = r^4 |
7,465 | \sum_{r=0}^l {l \choose r}\times {l \choose l - r} = \sum_{r=0}^l {l \choose r}^2 |
29,258 | 2 \cdot 2\cdot 179 = 716 |
22,068 | 20 = (7 + 5 \cdot (-1))^2 + (8 + 4 \cdot \left(-1\right))^2 |
4,143 | \dfrac{1}{2^x \dfrac{1}{2}} = \frac{2}{2^x} |
16,184 | 2^{100} + 3^{100} \lt 4^{100} \Rightarrow 3^{100} < -2^{100} + 2^{200} |
23,047 | \frac{1}{221} + \dfrac{1}{221} \cdot 16 = \frac{1}{221} \cdot 17 = \frac{4}{52} |
-18,282 | \frac{-5 \cdot r + r^2}{r^2 - r \cdot 10 + 25} = \dfrac{(5 \cdot \left(-1\right) + r) \cdot r}{(r + 5 \cdot (-1)) \cdot (r + 5 \cdot (-1))} |
27,439 | k + 1 + (k + 2) \dotsm + 2k = k + k + \dotsm + k |
36,036 | 84 = \binom{7}{2} \cdot 4 |
14,625 | x*g*n = k*x * x/2 \Rightarrow x = \frac{2*n*g}{k} = 0.126*n |
30,271 | (y + (-1)) (1 + y y + y) = y^3 + (-1) |
28,965 | (-1) + \mu^2 = (\mu + (-1)) \cdot \left(\mu + 1\right) |
-25,791 | \frac{10}{7 \cdot 4} = \frac{10}{28} |
-9,378 | -11 \cdot 2 \cdot 5 - 2 \cdot 5 \cdot 7 \cdot r = -70 \cdot r + 110 \cdot (-1) |
3,572 | 0 = x,0 \neq y\Longrightarrow \frac{y}{x^4 + y^2} \cdot x^2 = 0 |
-20,968 | \frac{x + 3 \cdot (-1)}{3 \cdot x} \cdot \frac14 \cdot 4 = \frac{1}{12 \cdot x} \cdot \left(12 \cdot \left(-1\right) + 4 \cdot x\right) |
18,501 | x^2 - x \cdot \left(q + p\right) + q \cdot p = (x - q) \cdot (-p + x) |
12,371 | 2^{k + 1} + 2^{k + 1} + 2 \cdot \left(-1\right) = \left(2^{k + 1} + \left(-1\right)\right) \cdot 2 |
1,768 | [e, b] = \left[c,d\right]\Longrightarrow e = b,d = c |
15,352 | \overline{x + p} = \overline{x} + \overline{p} |
12,202 | 18 = \frac{1}{(-1) + 2} \cdot (2 \cdot (-1) + 20) |
27,146 | \operatorname{im}{(y)} = \sin{\pi \cdot \varepsilon/x} \Rightarrow e^{\dfrac{\varepsilon}{x} \cdot \pi \cdot i} = y |
23,532 | (\left(-1\right) + n)*2 + 2 = 2n |
32,336 | \frac{\mathrm{d}}{\mathrm{d}x} (-\cot\left(x\right) + 6) = -\csc^2(x) |
-19,505 | \frac56 \cdot \frac{1}{1} \cdot 2 = 1/6 \cdot 5/\left(\dfrac12\right) |
6,925 | (1 - m) (1 - c) (1 - z) = 1 - m - c - z + m c + m z + c z - m c z = m c + m z + c z - m c z |
-2,105 | -\pi \cdot 11/6 + \pi/6 = -\dfrac{1}{3} \cdot 5 \cdot \pi |
8,972 | \dfrac{p}{s} = \frac{p}{s} |
17,037 | D + D = 2\cdot D |
6,185 | z^2 + 2 \cdot z \cdot b + b^2 = (b + z) \cdot (b + z) |
18,558 | \sin{4\cdot z} = 2\cdot \sin{2\cdot z}\cdot \cos{2\cdot z} = 4\cdot \sin{z}\cdot \cos{z}\cdot (1 - 2\cdot \sin^2{z}) |
-29,570 | -x = -x^2/x |
25,537 | 4 = \frac{1}{1 - \frac{1}{2}} + 2 |
1,143 | y^{(-1) + c} c = 1 \implies 1/c = y^{c + (-1)} |
-21,657 | -\frac{1}{11}4 = -\frac{4}{11} |
6,001 | -37 37 + s s = (s + 37) (37 (-1) + s) |
31,847 | h^{k*2} + (-1) = (h^k + (-1))*(h^k + 1) |
26,029 | \cosh{q} + \sinh{q} = e^q |
38,027 | 32 = 16 \cdot 48/24 |
27,966 | \dfrac{1}{3 \cdot \sqrt{3}} \cdot 16 = \frac{16}{9} \cdot \sqrt{3} |
16,872 | m \geq w \Rightarrow w = m |
-7,107 | \frac{5}{66} = 5/11\cdot 2/12 |
-10,420 | 2/2 (-\frac{6}{10 a + 6(-1)}) = -\frac{1}{a\cdot 20 + 12 (-1)}12 |
20,637 | -2 \cdot y^2 + 16 \cdot y = -2 \cdot (y^2 + 8 \cdot (-1)) = -2 \cdot \left(y + 4 \cdot (-1)\right)^2 + 32 |
-499 | e^{17 i\pi/4} = (e^{\dfrac{\pi i}{4}})^{17} |
-23,227 | \frac{1/5}{5}\cdot 2 = 2/25 |
27,849 | 256 = \binom{4}{2} \cdot \binom{4}{1} \cdot \binom{10}{1} + 16 |
21,930 | 22 = 25 + 3 \times (-1) |
17,307 | \left(a \cdot 3 + 3 = 0 \implies a \cdot 3 = -3\right) \implies -1 = a |
45,378 | 20 = 6 + 5 + 3*3 |
1,983 | (g^4)^{\frac15}\cdot (g^6)^{\frac15} = g^{4/5}\cdot g^{6/5} = g^2 |
3,434 | \dfrac{158*\tfrac{1}{10}}{19*1/10} = 158/19 = 8.315 ... |
19,970 | \binom{n}{2*(-1) + n} = \binom{n}{2} |
30,645 | y^2 + (7\cdot y + 3\cdot (-1)) \cdot (7\cdot y + 3\cdot (-1)) = 50\cdot y^2 - 42\cdot y + 9 = 1 \Rightarrow 0 = 25\cdot y^2 - 21\cdot y + 4 |
34,697 | k \geq n/2 rightarrow n - k \leq \frac12 \cdot n |
21,563 | D \times G = D \times G |
24,179 | \dfrac{1/\left(-2\right)}{0} = \frac12*4/1 \dfrac{1^{-1}}{0}2 |
-14,526 | 9 + \tfrac{2}{2} = 9 + 1 = 9 + 1 = 10 |
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