id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-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
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-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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