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ddrg
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math_formulas

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1,921
n^{-\frac{1}{3}} = \frac{1}{n^{\dfrac{1}{3}}}
21,788
(a + b)*(a^2 - b*a + b^2) = a * a^2 + b^3
14,774
19 = (\dfrac{3}{2}) \cdot (\dfrac{3}{2}) \cdot (\dfrac{3}{2}) + (5/2)^3
159
\cos{A}*\cos{R} - \sin{R}*\sin{A} = \cos(A + R)
22,648
\frac{\partial}{\partial x} x^n = n \cdot x^{n + \left(-1\right)}
9,362
\tfrac{\pi}{2}Z^2 + \pi Z^2/2 = \frac{4Z^2 \pi}{4}
52,786
189 = 27\times 7
316
0 = 2\cdot s^2\cdot a - s\cdot a^2\cdot 3\Longrightarrow \tfrac{s\cdot 2}{3} = a
25,572
x^6 = x^3\cdot x \cdot x^2 = x^2\cdot x^2\cdot x^2
7,505
G \cdot G + x \cdot G + G \cdot C + C \cdot x = (G + C) \cdot (G + x)
-5,441
2.36 \cdot 10 = \dfrac{23.6}{1000} \cdot 1 = 2.36/100
17,109
\sin\left(2 \cdot G\right) = 2 \cdot \sin(G) \cdot \cos(G)
3,636
\frac{1}{(2\cdot \left(-1\right) + m)!\cdot 2} + \frac{1}{\left((-1) + m\right)!} = \frac{m + 1}{(m + (-1))!\cdot 2}
13,849
(-1)^k*(-1) = (-1)^{1 + k}
31,451
o + |1| \times x = 0\Longrightarrow -x = o
32,405
-(2 - \sqrt{7}) (2 + \sqrt{7}) = 3
2,885
3630 = 6!\cdot 121/24
27,143
(5^{1 + x} + (-1))/4 + 5^{x + 1} = 1 + 5 + \dots + 5^x + 5^{x + 1}
17,953
\left(-205\times s + 120\times x = s\Longrightarrow x\times 120 = 206\times s\right)\Longrightarrow x = s\times 103/60
-6,628
\tfrac{1}{5 \cdot x + 20} \cdot 3 = \dfrac{1}{(x + 4) \cdot 5} \cdot 3
8,288
B^6 = B^3 * B^3
-2,175
-\pi/6 = \pi\cdot \frac{7}{4} - \pi\cdot 23/12
-25,584
\frac{d}{dq} (-3/q) = \frac{3}{q^2}
16,334
(j\cdot 2)^2 = j^2\cdot 4
-12,364
50 = 5 * 5*2
-28,786
\int x^5\,\mathrm{d}x = \frac{x^{5 + 1}}{5 + 1} + F = x^6/6 + F
24,522
0 = \left(\sqrt{l}\right)^2 - n\Longrightarrow n = l
22,215
\frac{1}{6^3} \cdot 3^3 = 1/8
20,141
\sqrt{A}^2=A
25,488
(a_m + (-1))\times (a_m + 1) = a_m^2 + \left(-1\right)
27,281
\sin{q} = \cos(q - \dfrac{\pi}{2})
3,507
z^2 + 2vz + 2v^2 = z \cdot z + 2vz + v \cdot v + v^2 = (z + v) \cdot (z + v) + v^2
13,981
-2 \cdot (x_1 \cdot x_2 + x_3 \cdot x_1 + x_3 \cdot x_2) + (x_3 + x_1 + x_2) \cdot (x_3 + x_1 + x_2) = x_1 \cdot x_1 + x_2^2 + x_3 \cdot x_3
37,925
\frac{6!}{3! \times 4!} = 5
2,653
\left(2 + (-1)\right) \cdot (k + 2 + (-1)) = k + 1
13,890
1 + x \cdot x + x = 1 + (x + 1)^2 - 1 + x
8,299
97^2 = (100 + 3\times (-1))^2 = 10000 + 600\times (-1) + 9
9,449
g + a - b = a - -g + b
18,757
( (2 \pi)^2, \sin(\pi \cdot 2)) = ( (-2 \pi)^2, \sin(-2 \pi))
3,292
(-(af \cdot 2)^{1/2} + a + f) (a + f + (fa \cdot 2)^{1/2}) = a^2 + f \cdot f
-23,349
1/28 = \frac{1}{4 \cdot 7}
-20,839
-\dfrac76 \cdot \dfrac{2 + 3 \cdot p}{3 \cdot p + 2} = \frac{1}{12 + 18 \cdot p} \cdot \left(14 \cdot (-1) - 21 \cdot p\right)
16,943
\tfrac{1}{10}3\cdot 2/10 = 6/100
-7,933
(36 - 8 \times i - 9 \times i + 2 \times (-1))/17 = (34 - 17 \times i)/17 = 2 - i
31,017
2/7 + \dfrac{1}{7}*2 = \frac47
25,524
1/(a*\frac1c) = c/a
13,958
(1 + X + X^2)^s = (\frac{1 - X^3}{1 - X})^s = (1 - X^3)^s*\left(1 - X\right)^{-s}
5,099
d*E*z = d*z*E
3,624
v*G_0*v = v*G_0^{\frac{1}{2}}*G_0^{1/2}*v = G_0^{\frac{1}{2}}*v
15,956
\frac{2 \times \tan{z}}{\tan^2{z} + 1} = \sin{2 \times z}
41,640
(-1)^{1/2} \cdot (-1)^{1/2} \cdot (-1)^{1/2} = -(-1)^{1/2}
-9,259
d^2\cdot 26 = d\cdot 2\cdot 13\cdot d
25,385
x^a x^h = x^{h + a}
14,279
\cos^{-1}(\cos{2\cdot \pi}) = \cos^{-1}(\cos{0})
9,963
\left(4 + 1\right)\cdot 5^{l + 1} = 5^{1 + l} + 4\cdot 5^{l + 1}
26,898
y^2 \cdot 25 + 13 = \left(y^2 + \frac{13}{25}\right) \cdot 25
849
\dfrac{2890}{6^5}*0 + 1*\frac{2611}{6^5} + 2*\frac{1}{6^5}*2275 = \frac{7161}{6^5}
-9,370
n*4 + 20 = 2*2*n + 2*2*5
15,105
-c^2 + h^2 = (c + h)\cdot (h - c)
-4,338
110*n/\left(n*99\right) = 110/99*\dfrac1n*n
-2,687
\left(3 + 4 + 5 \cdot \left(-1\right)\right) \cdot \sqrt{6} = 2 \cdot \sqrt{6}
9,439
(l_2 + l_1)\cdot 2 = l_2 + l_1 + l_2 + l_1
21,767
\left(1 + z\right)^2 = z^2 + 2\cdot z + 1
21,300
(-1) + a^2 = (1 + a) \times \left(a + \left(-1\right)\right)
9,755
4181 = 3100 + 930 + 155 + 4\cdot (-1)
-20,541
6/6 \cdot \frac{1}{-8} \cdot (-10 \cdot t + 4) = \left(24 - t \cdot 60\right)/(-48)
52,136
3^{\frac{1}{2}} + 7^{1 / 2} = 3^{1 / 2} + 7^{\frac{1}{2}}
15,926
-\left(z + \left(-1\right)\right)\cdot (3 + z) = 3 - z^2 - z\cdot 2
8,588
1 + n = 1 + 3 + n + 3\cdot (-1) = 3 + n + 2\cdot (-1) = 3 + n + 1 + 3\cdot (-1)
-8,775
42 \pi + \pi \cdot 9 + \pi \cdot 9 = \pi \cdot 60
-553
(e^{\dfrac{17*\pi*i}{12}})^{17} = e^{17*17*\pi*i/12}
-20,441
-\tfrac{2}{-2} (-5/4) = 10/(-8)
28,808
x*6 - 3*y = 3*(2*x - y)
1,874
((-1) + 2^{33}) \cdot (2^{33} + 1) = 2^{66} + \left(-1\right)
-6,725
\frac{8}{10} + 9/100 = 80/100 + \frac{9}{100}
-28,413
x^2 + 10 \cdot x + 41 = x \cdot x + 10 \cdot x + 25 + 16 = (x + 5)^2 + 16 = (x + 5)^2 + 4 \cdot 4
10,050
Y*x*Y^Y = x*Y*Y = Y*Y*x
21,101
5\cdot (g_1^2 + g_2^2) = (2\cdot g_1 - g_2)^2 + (g_2\cdot 2 + g_1)^2
6,209
\frac{1}{2} = \ln(2)/(\ln(4))
9,230
t^m\cdot b_m = t^m\cdot b_{m + 1}\cdot t \implies b_m = b_{1 + m}\cdot t
23,477
\sin(z)\cdot \cos\left(a\right) + \sin(a)\cdot \cos(z) = \sin(a + z)
5,116
1/2 - \cos{x \cdot 2}/2 = \sin^2{x}
10,748
5 + 2 + 4 = 5 + 2 + 4
-7,731
\frac{-32 + 8\cdot i}{3\cdot i + 5}\cdot \frac{-i\cdot 3 + 5}{-3\cdot i + 5} = \frac{1}{i\cdot 3 + 5}\cdot (i\cdot 8 - 32)
21,173
\lim_{h \to 0} (-x \times x + (h + x)^2)/h = \lim_{h \to 0}(2 \times x + h)
-4,397
\frac{q^5}{q^2} \cdot \frac{36}{9} \cdot 1 = 36/9 \cdot \frac{1}{q^2} \cdot q^5
34,755
3*(-1) + n^2 = \left(n + 2\right)*(n + 2*(-1)) + 1
9,782
\frac{(x\cdot 2 + (-1))!}{(-1) + 2\cdot x} = (2\cdot (-1) + x\cdot 2)!
39,529
(SF)^T Y = F^T S^T Y = F^T SY
29,443
\dfrac28/7 \times 2 = 1/14
20,445
\frac{x^3 + \left(-1\right)}{\left(-1\right) + x} = x^2 + x + 1
-20,889
\frac{2 - 5*k}{10 - k}*\dfrac{2}{2} = \frac{-10*k + 4}{-2*k + 20}
32,390
\left(1 + n\right)! = n! + n! n
34,360
(-1) + x x + x^2 - x + x^2 - x + x^2 - 2 x + 1 + x^3 - x^2\cdot 3 + 3 x = -x + x^3 + x^2
25,590
( a, f) + \varphi\cdot b' = \left( \varphi + a, b' + f\right)
4,538
(k_1 + s k_2)/(k_2) = s + k_1/(k_2)
19,461
2 \cdot \sqrt{21} + 10 = (\sqrt{7} + \sqrt{3}) \cdot (\sqrt{7} + \sqrt{3})
25,378
-\sin(x) \cdot \sin\left(\beta\right) + \cos(\beta) \cdot \cos(x) = \cos\left(x + \beta\right)
-5,487
\frac{4}{x \cdot 5 + 10 \cdot (-1)} = \dfrac{4}{(x + 2 \cdot (-1)) \cdot 5}
-22,346
y^2 - y \cdot 13 + 36 = \left(4 \cdot (-1) + y\right) \cdot (y + 9 \cdot (-1))