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5,250 | 1 + 2^0 + 2^1\cdot ...\cdot 2^{P + (-1)} + 2^P = 2\cdot 2^P = 2^{P + 1} |
7,596 | \frac{1}{12} + \frac{1}{16} = \dfrac{4}{48} + \dfrac{3}{48} = 7/48 |
17,492 | \sin^2 x = 1/\csc^2 x |
-15,191 | \frac{1}{\frac{k}{a^2}\cdot \frac{1}{a^9\cdot k^{15}}} = \frac{a^9\cdot k^{15}}{\frac{1}{a^2}\cdot k}\cdot 1 |
-7,768 | \left(-20 + 4\times i + 20\times i + 4\right)/8 = \left(-16 + 24\times i\right)/8 = -2 + 3\times i |
-1,509 | \frac56*9/2 = \dfrac{9*1/2}{6*\frac{1}{5}} |
14,804 | 5/27 = 1/9 + \frac{4}{18}\cdot \frac13 |
-15,080 | \tfrac{p^5}{l^2\cdot p^4} = \dfrac{1}{(p^2\cdot l) \cdot (p^2\cdot l)\cdot \dfrac{1}{p^5}} |
-29,370 | \left(7 + y\right)\cdot \left(7 - y\right) = 7^2 - y^2 = 49 - y \cdot y |
46,413 | e^0 = 1 > 0 |
3,383 | -y^3 + z z z = (-y + z) (z^2 + z y + y^2) |
9,966 | \frac{1}{-q + 1}\cdot (-q^{x + 1} + 1) = \frac{-q^{x + 1} + 1}{-q + 1} |
-4,213 | \dfrac{1}{l^3} \cdot l^2 \cdot l \cdot 12 \cdot 12/(12) = 144/12 \cdot \tfrac{l \cdot l \cdot l}{l^2 \cdot l} |
42,103 | 3 \cdot 3^2 + 3^3 + 3^3 = 81 |
24,227 | (-1) + x^{10} = (x + (-1))\cdot (1 + x)\cdot (x^8 + x^6 + x^4 + x^2 + 1) |
5,925 | 3*6*4 = 72 = 6 * 6 + 6^2 |
36,859 | n^2 = 36 + (6 + n)\cdot \left(n + 6\cdot (-1)\right) |
-489 | e^{20 \cdot 3 \cdot \pi \cdot i/4} = (e^{\frac{1}{4} \cdot \pi \cdot 3 \cdot i})^{20} |
22,952 | \sin(\pi/3) = \frac{3^{1/2}}{2} |
-11,798 | \left(2/9\right)^2 = \frac{1}{81}\cdot 4 |
-20,041 | \dfrac{-9}{5} \times \dfrac{3t + 2}{3t + 2} = \dfrac{-27t - 18}{15t + 10} |
-502 | -24 \pi + \pi*49/2 = \dfrac12\pi |
19,722 | (k + 1)! \cdot k = (k + 1 + 1)! + 1 = \left(k + 2\right)! + (-1) |
24,116 | \dfrac{(1 - z) e^{z + \left(-1\right)}}{((-1) + z)*2} = -e^{(-1) + z}/2 |
-14,513 | \dfrac{1}{8 + 6\cdot (-1)}\cdot 6 = 6/2 = \dfrac{1}{2}\cdot 6 = 3 |
-10,559 | 8/(25*z)*3/3 = 24/(75*z) |
7,181 | \frac{1}{i + 2}\cdot (i + 1) = \frac{i + 1}{i + 2} |
6,538 | k\cdot 2 + (-1) = ((-1) + 2)\cdot \left(2\cdot k + (-1)\right) |
-2,660 | \sqrt{11} + 4\times \sqrt{11} = \sqrt{16}\times \sqrt{11} + \sqrt{11} |
-10,377 | -\frac{6 \cdot (-1) + y}{y + 3 \cdot (-1)} \cdot 2/2 = -\frac{1}{6 \cdot (-1) + y \cdot 2} \cdot \left(2 \cdot y + 12 \cdot (-1)\right) |
-3,184 | 5^{1 / 2} = (3 \cdot (-1) + 4) \cdot 5^{1 / 2} |
-18,335 | \frac{1}{l \cdot (l + 6)} \cdot \left(l + 6\right) \cdot (l + 10 \cdot (-1)) = \frac{1}{l \cdot l + 6 \cdot l} \cdot (l \cdot l - 4 \cdot l + 60 \cdot (-1)) |
-6,344 | \dfrac{4}{2(6 + x) \left(8 + x\right)} = \tfrac22*\frac{2}{(8 + x) \left(6 + x\right)} |
24,648 | \pi - \frac{\pi}{8} = \dfrac{7*\pi}{8} |
-5,616 | \frac{4}{2 \cdot (y + 6 \cdot (-1)) \cdot (y + 5)} = \tfrac{1}{2} \cdot 2 \cdot \frac{2}{(y + 5) \cdot (6 \cdot (-1) + y)} |
-15,121 | \tfrac{(\tfrac{1}{n^4})^3}{\left(\tfrac{1}{p^4}\cdot n\right)^5} = \frac{1}{\dfrac{n^5}{p^{20}}\cdot n^{12}} |
43,839 | \alpha \cdot \alpha = \alpha^2 |
-4,211 | \frac{144}{x * x^2*12}*x^3 = \frac{1}{x * x^2}*x^2 * x*\dfrac{144}{12} |
36,842 | \cos^2\left(x\right) = 1 - \sin^2\left(x\right) |
17,701 | 1^2 + 2 \times 2 + 3^2 + 4 \times 4 + 5^2 + 6 \times 6 = 91 |
-6,524 | \frac{4}{4(9(-1) + x) \left(5(-1) + x\right)} = \frac{4*\frac14}{(x + 9(-1)) (x + 5(-1))} |
42,226 | 3 * 3 * 3 + 4*3 * 3 + 14*3 + 9 = 8 + 17 + 4 + 9 = 0 |
-29,867 | x \cdot x \cdot x\cdot 8 + 3\cdot x \cdot x + 6\cdot x = d/dx (3\cdot x^2 + 2\cdot x^4 + x \cdot x^2) |
-1,634 | -7/4\cdot \pi + \pi = -\pi\cdot 3/4 |
-9,430 | x \cdot 2 \cdot 2 \cdot 2 \cdot x + 2 \cdot 2 \cdot 2 \cdot x = x^2 \cdot 8 + 8 \cdot x |
-6,640 | \tfrac{4}{(t + 10 \cdot \left(-1\right)) \cdot 2} = \frac{4}{20 \cdot (-1) + 2 \cdot t} |
3,297 | 2 \times x^2 - 2 \times x + 1 = x^2 + x^2 - 2 \times x + 1 = x \times x + (x + (-1))^2 |
31,827 | -9 = 4 (-1) + 35 + 60 (-1) + 20 |
10,756 | \frac{v}{d} - \dfrac{d}{g'} \frac{v}{d} = -v/g' + \frac{v}{d} |
5,823 | V^2\cdot V \cdot V\cdot V^2 = V^6 = V^3\cdot V^3 |
30,970 | m = 2\cdot 2\cdot m/4 |
3,904 | -2e + 4 = -e\cdot 2 + 5 + (-1) |
15,995 | -2\cdot \operatorname{atan}(R) = \operatorname{atan}(-R) - \operatorname{atan}(R) |
2,199 | 0 = 3 - z*2 - y \Rightarrow 3 - 2 z = y |
-25,875 | \frac{g^7}{g^6} = g^{7 + 6 \cdot (-1)} = g^1 |
-27,492 | 11*c*c*c = c^3*11 |
5,617 | d_{u + 2(-1)} d_{u + (-1)} = d_u^2 \Rightarrow d_{u + (-1)} d_{u + 2\left(-1\right)} d_u = d_u^3 |
8,797 | 2 \cdot \alpha + 1 + 2 \cdot \beta = (\alpha + \beta) \cdot 2 + 1 |
-11,639 | 7 + 9 \cdot i = 2 + 5 + i \cdot 9 |
-7,818 | \frac{-i*10 + 5}{-3*i + 4} = \frac{1}{4 - i*3}*(5 - 10*i)*\tfrac{4 + 3*i}{4 + 3*i} |
16,263 | 1 = \frac1a + \frac{1}{a + f} + \frac{1}{a + f + c} \geq \dfrac{1}{a + f + c}\cdot 3 |
12,835 | z^3 = z^2 + z + 2 \cdot \left(-1\right) + 2 \cdot \sqrt{1 + z^3 - z^2 - z} \implies (z^2 \cdot z - z^2 - z + 2)^2 = 4 \cdot (z \cdot z \cdot z - z^2 - z + 1) |
51,244 | \frac{(3 n + 4)!*7^{-(n + 1)}}{\frac{(3 n + 1)!}{n! \left(2 n + 1\right)!}*7^{-n}} \frac{1}{(n + 1)! \left(2 n + 1\right)!} = \frac{7^{-1 - n} n! (2 n + 1)! (3 n + 4)!}{(n + 1)! (2 n + 3)! (3 n + 1)!*7^{-n}} 1 = \dfrac{(3 n + 4)! (2 n + 1)!}{(n + 1)*7 (2 n + 3)! (3 n + 1)!} |
2,684 | \frac17*3/4 + 4/7*0 = 3/28 |
-6,697 | \frac{5}{100} + \frac{7}{10} = 70/100 + \frac{5}{100} |
-10,332 | -\tfrac{30}{r \times 50} = 10/10 \times \left(-\frac{3}{r \times 5}\right) |
32,600 | \frac{1}{M \cdot N} \cdot 2 = \dfrac{1}{N \cdot M} = N^T \cdot M^T = (M \cdot N)^T |
-28,795 | \frac{2\cdot \pi}{\frac13\cdot \pi\cdot 2} = 3 |
24,911 | 10 = 368 \cdot (-1) + 378 |
6,845 | (-1) \cdot (-2) \cdot 2 = (-2) \cdot \left(-2\right) |
37,986 | \sqrt{k!} \sqrt{k!} = k! |
23,178 | \frac{86}{100}*\dfrac{114}{100} = \frac{1}{10000}9804 \lt 1 |
34,521 | a^{W + m} = a^m a^W |
-11,535 | -2\cdot i + 23 = 15 + 8 - i\cdot 2 |
3,751 | x + 8 - 6\cdot \sqrt{x + (-1)} = x + (-1) - 6\cdot \sqrt{x + (-1)} + 9 = (\sqrt{x + (-1)} + 3\cdot (-1))^2 = \left(3 - \sqrt{x + (-1)}\right)^2 |
49,960 | x - y = x - y |
-8,901 | -1^5 = (-1) \cdot \left(-1\right) \cdot (-1) \cdot (-1) \cdot (-1) |
30,115 | 280/13 = \frac{1}{13}2 \cdot 7/3 \cdot 60 |
24,309 | (T_1 + T_2) \cdot (T_1 + T_2) - \left(T_1 - T_2\right)^2 = 4 \cdot T_1 \cdot T_2 |
27,431 | V_l/(C_l) = \frac{d_l \cdot V_l}{d_l \cdot C_l} = d_l/(C_l) \cdot V_l/(d_l) |
-16,607 | 6 \cdot \sqrt{16 \cdot 11} = \sqrt{176} \cdot 6 |
25,389 | 1 = \dfrac{1}{3} + \tfrac13 + \frac13 |
29,788 | c^2 \cdot a = |c \cdot c \cdot a| = 2/3 \cdot |c|^3 + |a|^3/3 |
27,261 | p^4 - 2p^2 + 1 = (p^2 + (-1))^2 |
-23,827 | 3 + \frac{1}{4}*4 = 3 + 1 = 4 |
36,349 | \frac{1}{1.5 + 2}\cdot 1.5 = \dfrac37 |
18,950 | Y\times \frac{e^x}{Y} = e^{Y\times \dfrac1Y\times x} |
13,726 | \frac{h_2}{b*1/(h_1)} = h_2*\frac{h_1}{b} |
13,301 | \binom{\nu + (-1)}{2} + 1 = \binom{\nu}{2} - \nu + 2(-1) |
-26,477 | 70 \times x = 2 \times 5 \times x \times 7 |
-11,968 | \dfrac{14}{45} = s/(6*\pi)*6*\pi = s |
1,794 | ((-1) + a)\cdot \left(a + 1\right) = \left(-1\right) + a \cdot a |
6,343 | BA + 0 = BA |
4,433 | \frac{\frac14}{-\frac{1}{4} + 1} = \dfrac13 |
-6,003 | \frac{3}{35 + x \cdot 5} = \frac{3}{\left(x + 7\right) \cdot 5} |
2,341 | r\cot(r) = 1 - r^2/3 - \frac{r^4}{45 ...} \approx exp(((-1) r^2)/3) (1 - \frac{1}{90 r^4}7 + ...) |
33,702 | c_2\cdot c_3 = c_3\cdot c_2 |
11,313 | -2^n\cdot (n + 2\cdot (-1)) - 2 = ((-1) + 2^n)\cdot 2 - n\cdot 2^n |
23,360 | 3{k + 1 \choose 4} = {{k \choose 2} \choose 2} |
2,365 | y_n y/y = y_n |
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