id int64 -30,985 55.9k | text stringlengths 5 437k |
|---|---|
-3,048 | 6\times \sqrt{11} = \left(1 + 5\right)\times \sqrt{11} |
-16,427 | 2\cdot 176^{1/2} = 2\cdot (16\cdot 11)^{1/2} |
19,174 | 2 \cdot (1 + \sqrt{10}) = 2 + \sqrt{10} \cdot 2 |
19,044 | 3 \cdot \tfrac{\pi \cdot 4}{9^{1 / 2}} \cdot 1 = 4 \cdot \pi |
18,794 | 4 \cdot 4 + 7^2 = 1 \cdot 1 + 8^2 |
-6,129 | \frac{1}{5\cdot \left(y + 4\right)}\cdot 2 = \frac{2}{20 + 5\cdot y} |
15,864 | 1^3 = 10 \cdot C + 1 \Rightarrow 0 = C |
-11,956 | \dfrac{7}{10} = \frac{p}{8\pi}*8\pi = p |
33,155 | x^2 + 2\cdot x = \left(-1\right) + (\left(-1\right) + x) \cdot (\left(-1\right) + x) + x\cdot 4 |
13,220 | \sqrt{17}>4\implies-1-\sqrt{17}<-5\implies\dfrac{-1-\sqrt{17}}4<-1 |
24,306 | \left(1 = -1 \Rightarrow (-1)^2 = 1^2\right) \Rightarrow 1 = 1 |
13,152 | \frac{1}{3} \cdot 2 = \sqrt{\frac{1}{9} \cdot 4} |
34,621 | \frac{1}{{80 \choose 20}} \cdot {71 \choose 11} = 17/23471690 |
-10,632 | \frac{\dfrac{1}{3} \cdot 3}{x \cdot 5 + 20 \cdot (-1)} = \frac{3}{x \cdot 15 + 60 \cdot \left(-1\right)} |
18,199 | a - f = a - f = -f + a = -f + a |
-579 | (e^{\tfrac{5}{3} \cdot \pi \cdot i})^{16} = e^{\pi \cdot i \cdot 5/3 \cdot 16} |
19,419 | (-1) + \cos^2(A)\cdot 2 = \cos(2A) |
11,874 | 1997 + 1997^l\cdot (1997 + (-1)) = 1996\cdot 1997^l + 1997 |
39,404 | 5(-1) + y^4 = (-\sqrt{5} + y \cdot y) \left(\sqrt{5} + y \cdot y\right) |
53,866 | 2\pi\int_0^4(x)(x)^{3/2} dx = 2\pi\int_0^4x^{5/2} dx = 2\pi\left[\frac{2}{7}x^{7/2}\right]_0^4 = \frac{512\pi}{7} |
9,886 | 10 \cdot x - x = 9 \cdot x = 9 \Rightarrow x = 1 |
-28,797 | \dfrac{\pi*2}{\pi*2*\frac{1}{24}}1 = 24 |
21,809 | \frac{1}{1 + \sin^2{x}}\times \sin^2{x} = 1 - \dfrac{1}{1 + \sin^2{x}} = 1 - \frac{\sec^2{x}}{2\times \tan^2{x} + 1} |
-12,164 | \frac19 = \dfrac{x}{18 \cdot \pi} \cdot 18 \cdot \pi = x |
15,568 | -i*N*M + i*M*N = -i*N*M + i*N*M |
4,242 | \left(x - b\right) (x + b) = -b^2 + x^2 |
22,302 | 105 = \frac{15}{2} \cdot 14 |
-20,596 | 8/8 \frac{5r}{-r + 5(-1)} = \frac{40 r}{-8r + 40 (-1)} |
32,700 | p = -(\dfrac12\cdot (p + (-1)))^2 + ((1 + p)/2)^2 |
14,480 | A = X\cdot Y\Longrightarrow Y\cdot X = A |
1,688 | (z + 3 \cdot (-1)) \cdot (2 \cdot (-1) + z) \cdot (z + (-1)) = 6 \cdot (-1) + z^3 - 6 \cdot z^2 + z \cdot 11 |
30,219 | \cos{z_1}\cdot \cos{z_2} - \sin{z_2}\cdot \sin{z_1} = \cos(z_1 + z_2) |
8,054 | \frac{29\cdot 28\cdot 27}{3}=7308 |
-18,966 | \frac{7}{18} = A_p/(100 \pi)*100 \pi = A_p |
-15,375 | \frac{x^5 \cdot q^4}{x^{10} \cdot q^{25}} = \frac{x^5}{x^{10}} \cdot \frac{q^4}{q^{25}} = \frac{1}{x^5 \cdot q^{21}} = \dfrac{1}{x^5 \cdot q^{21}} |
33,824 | 2 = -11 \cdot 2 + 3 \cdot 8 |
-27,699 | -10*\sin(x) = \frac{d}{dx} (10*\cos(x)) |
-10,484 | 3/3 \cdot (h \cdot 5 + (-1))/h = \tfrac{1}{h \cdot 3} \cdot (3 \cdot \left(-1\right) + h \cdot 15) |
-3,364 | -\sqrt{4\cdot 11} + \sqrt{25\cdot 11} + \sqrt{16\cdot 11} = \sqrt{275} + \sqrt{176} - \sqrt{44} |
1,153 | \frac12 + \dfrac14\cdot 5 = \frac14\cdot 7 |
-1,760 | 4/3 \pi + \dfrac16\pi = \pi*3/2 |
6,089 | x + 3 \geq 2\cdot (\left(-1\right) + x) \Rightarrow x \leq 5 |
21,729 | \left(1 + n\right) \cdot \left(n + 1\right) \cdot (1 + n) = \left(1 + n\right)^3 |
30,998 | 216 = 2^2 \times 2\times 3^3 = 6^3 |
6,844 | -t + t^2 = 1 + t \cdot (1 + t) - t - t + 1 |
-10,649 | -15 = -x + 3 + 20\cdot (-1) = -x + 17\cdot (-1) |
18,022 | \left(F*x = g \Rightarrow F*x/F = g/F\right) \Rightarrow \frac{g}{F} = x |
-9,662 | (\left(-23\right) \times \frac{1}{25})/1 \times (-\frac{1}{4}) = \dfrac{1}{25 \times 4} \times 23 = 23/100 |
28,095 | -x^4 + x^2\cdot 34 + 225\cdot (-1) = -(x^2 + 9\cdot \left(-1\right))\cdot (x \cdot x + 25\cdot (-1)) |
10,107 | A_x\times A_j = A_x\times A_j |
3,499 | \frac{109^2 + 11^2 - 100^2}{11 \cdot 109 \cdot 2} = \frac{1}{2 \cdot 109 \cdot 136} \cdot (-75^2 + 109 \cdot 109 + 136 \cdot 136) |
30,769 | \frac{49^3}{50^6}15\cdot 50 = \frac{1}{62500000}352947 = 0.005647152 |
-4,480 | 8 + x^2 + 6\cdot x = (4 + x)\cdot (2 + x) |
23,527 | n^2 = 9*k^2 + 6*k + 1 = 3*(3*k^2 + 2*k) + 1 \implies 3*(3*k^2 + k*2) = (-1) + n^2 |
5,709 | 1 - \frac{1}{100}*95 = 5/100 |
-30,912 | \frac{1}{150} \cdot h \cdot 3 = h/50 |
14,278 | \binom{m}{k} + \binom{m}{k + (-1)} = \binom{1 + m}{k} |
15,830 | x*a_2*a_1 = a_2*a_1*x |
20,874 | x A_2^2 + K^2 B' + C' A_1^2 = C'^2 K + x^2 A_1 + A_2 B' B' |
47,007 | \left(-38\right) \cdot 34 + 3 \cdot 431 = 1 |
35,924 | y^2 \cdot x^2 \cdot 4 = y^2 \cdot x \cdot 2 \cdot x \cdot 2 |
22,520 | 7^{1 / 2} \cdot 2 \cdot 4 = 2 \cdot 4 \cdot 7^{1 / 2} |
-2,947 | 8\cdot 2^{1/2} = 2^{1/2}\cdot (1 + 2 + 5) |
-23,221 | 5/8\cdot \frac59 = \frac{25}{72} |
7,201 | \frac38 - \dfrac78 = -\dfrac{4}{8} = -\dfrac12 |
-3,537 | 2\cdot 7/(2\cdot 50) = \dfrac{1}{100}14 |
-10,700 | \frac{1}{z*10 + 6}*9*3/3 = \dfrac{27}{z*30 + 18} |
-22,217 | z^2 + z*12 + 35 = (7 + z) (z + 5) |
-1,215 | -1/2 \cdot (-\frac12 \cdot 3) = \dfrac{(-1) \cdot (-3)}{2 \cdot 2} = \frac14 \cdot 3 |
-28,792 | \int x^9\,\mathrm{d}x = \frac{x^{9 + 1}}{9 + 1} + G = x^{10}/10 + G |
35,248 | {2 + 2 \choose 2} + \left(-1\right) = 5 |
-4,773 | \dfrac{1}{1 + y} 5 - \dfrac{1}{2 (-1) + y} 3 = \frac{1}{2 \left(-1\right) + y^2 - y} (13 (-1) + y \cdot 2) |
-30,239 | (2\cdot (-1) + y)\cdot (y + 10\cdot \left(-1\right)) = y^2 - 12\cdot y + 20 |
9,456 | 6*\tan^2\left(y\right) + \tan\left(y\right) + \left(-1\right) = \tfrac{1}{\cos^2(y)}*5 = 5*(1 + \tan^2\left(y\right)) |
29,756 | y^{1/X} = y^{\dfrac{1}{X}} |
28,313 | 28/p = \tfrac{7}{p}*4/p = \frac{7}{p} |
13,167 | x = \dfrac12\cdot (x + y - \varphi + x + \varphi - y) \geq \sqrt{(x + y - \varphi)\cdot (\varphi + x - y)} |
2,686 | m - j \cdot 2 + 1 = m - j - (-1) + j |
39,170 | 0.05*0.5*(3000 + 2\psi) = 0.025*\left(3000 + 2\psi\right) = 75 + 0.05 \psi |
9,231 | 1 + (1 - \sqrt{5})/2 = \left((-\sqrt{5} + 1)/2\right)^2 |
30,604 | \cos(-D) = \cos(D) |
-10,594 | -\frac{1}{s*60}*(s*100 + 80) = -(s*5 + 4)/(3*s)*20/20 |
9,758 | -i = (Z + i \cdot B) \cdot (Z + i \cdot B) = Z^2 - B^2 + 2 \cdot Z \cdot B \cdot i |
28,490 | \sin\left(90 - x\right) = -\sin(x + 90 (-1)) = \sin\left(x + 90 (-1) + 180\right) = \sin(90 + x) |
-20,592 | \dfrac{8 \times \left(-1\right) + k}{-k \times 6 + 10} \times \frac77 = \frac{56 \times (-1) + 7 \times k}{70 - k \times 42} |
19,585 | r^{\frac{n}{2}}*f = f*r^{((-1)*n)/2} = f*r^{\frac{n}{2}} |
3,135 | (1 + x)^{k + n} = (1 + x)^k \cdot (1 + x)^n |
31,820 | \left(5^{\frac{1}{2}} + 1\right)\cdot (1 - 5^{\tfrac{1}{2}}) = -4 |
26,846 | {n \choose \phi} = {n \choose -\phi + n} |
-1,158 | -\frac{45}{72} = \frac{(-45)\cdot 1/9}{72\cdot 1/9} = -\frac{5}{8} |
21,459 | \frac{4^x + 3^x}{2^x + 5^x} = \frac{1}{1 + (\frac{2}{5})^x}*(\left(4/5\right)^x + (\frac{3}{5})^x) |
30,236 | 30 = 1890/63 |
5,481 | x^2 - 3 \cdot x + 4 \cdot (-1) = (1 + x) \cdot (4 \cdot (-1) + x) |
45,313 | \frac{1}{-1}\cdot 0 = 0 |
25,767 | \dfrac{1}{3} \cdot 4 = \frac12 + 1 - \dfrac16 |
24,128 | 23 = 3 + 5\times 4 |
5,297 | (a_2 + a_1)*\frac1t = \tfrac1t*a_2 + \frac{a_1}{t} |
7,204 | (\left(-1\right) + A) (A + 1) = (-1) + A^2 |
-24,693 | \sqrt{150*z^6} = \sqrt{5^2*2*3*z^3 * z^3} = \sqrt{5 * 5}*\sqrt{6}*\sqrt{(z^3)^2} = 5*\sqrt{6}*z^3 = 5*z^3*\sqrt{6} |
14,370 | x \cdot 2 + 4 \cdot j = x^2 \cdot 2 \Rightarrow x^2 \cdot 2 = 2 \cdot (x + j \cdot 2) |
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