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ddrg
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math_formulas

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-20,357
\frac{z\cdot \left(-14\right)}{28\cdot z + 63\cdot (-1)} = \frac{z\cdot (-2)}{z\cdot 4 + 9\cdot (-1)}\cdot 7/7
35,198
1 \cdot 1^2 = 1^2 = (-1)
2,092
2^{k + (-1)} (2 k + 2 \left(-1\right)) = 2 \cdot k \cdot 2^{k + (-1)} - (2^{12})^{k + (-1)} (k + (-1)) = 2^k \cdot (k + (-1))
33,485
-1 = \sin(\dfrac{3}{2}\cdot π)
10,229
\sin(3 \cdot π/2) = -1
23,401
(5 + 3*(-1))*\left(5 + 2*(-1)\right)*5*(5 + \left(-1\right)) = 5*4*3*2
12,556
2^{x + 1} = 2*2^x \geq 2*(x^2 + (-1))
-19,351
\frac{5 \cdot \frac{1}{8}}{4 \cdot 1/9} = \tfrac{5}{8} \cdot 9/4
14,360
|d - b| + |b - h| = -(d - b) + b - h = -d + 2b - h
-19,339
\tfrac{1/9*7}{3*1/5} = \frac{5}{3}*7/9
-4,388
\frac{y^2}{y \cdot y^2} = \tfrac{y \cdot y}{y \cdot y \cdot y} = 1/y
3,145
r - \frac{r}{1 + r^2} = \frac{r^3}{r^2 + 1}
11,464
f^{k_2}\cdot f^{k_1} = f^{k_1 + k_2}
13,231
d\cdot x + b\cdot x = (b + d)\cdot x
11,885
\cos \frac{\pi}{8} = \frac{\sqrt{2 + \sqrt{2}}}{2}
12,248
1 + \frac{2 - r}{(-1) + r} = \frac{1}{r + (-1)}
11,474
u = \alpha x x \Rightarrow \sqrt{\frac{u}{\alpha}} = x
9,682
x^2 \cdot 3 \cdot \lambda = 2 \cdot x \Rightarrow \frac{2}{x \cdot 3} = \lambda
42,130
-\frac{1}{3^{1/2}} = -3^{1/2}/3
3,308
k^2\cdot \dfrac{1}{1 - \frac{1}{k^3}}\cdot (1 - \frac{1}{k^5}) = \frac{\left(-1\right) + k^5}{k^3 + (-1)}
42,672
( 1, 0)*( 0, 1) = ( 2, 0)*\left( 0, 1\right) = 0
6,880
\frac{1}{2}(a + (2(-1) + \tau) d + a + d\tau) = d*(\tau + (-1)) + a
-4,510
\frac{2}{1 + x} - \frac{1}{x + 5} = \frac{x + 9}{x^2 + 6\cdot x + 5}
-7,036
2/3\cdot 0 = 0
-6,992
2/13 = \frac{1}{12}*6*\dfrac{4}{13}
8,086
\frac{1}{2}*((2*m + \left(-1\right)) * (2*m + \left(-1\right)) + 1) = 2*m^2 - 2*m + 1 = m^2 + (m + \left(-1\right))^2
11,487
\left(\sqrt{3} + \sqrt{2}\right)^3 = 11\cdot \sqrt{2} + \sqrt{3}\cdot 9
-15,832
\frac{1}{10} 30 = \frac{8}{10}*6 - \frac{2}{10}*9
272
3 \cdot 7! \cdot 2! + 9! - 3 \cdot 2! \cdot 8! = 151200
8,994
m_1\cdot 5 = m_2 \implies m_2\cdot 3 = 15\cdot m_1
30,804
1 = a\cdot 5 \Rightarrow a = \tfrac15
-13,297
10 + \frac1545 = 10 + 9 = 10 + 9 = 19
-29,111
2.0\cdot 10^6\cdot 9.0\cdot 10^{-5} = 2\cdot 10^6\cdot \frac{9}{10^5}
27,840
156 = 12 \cdot 13 \cdot 2/2
-15,743
\frac{q}{q^{25} \cdot \tfrac{1}{m^{15}}} = \dfrac{q}{\tfrac{1}{m^{15}}} \cdot \dfrac{1}{q^{25}} = \frac{m^{15}}{q^{24}} = \frac{m^{15}}{q^{24}}
24,752
8/h - \frac{3}{g} = 1\Longrightarrow 8 \cdot g - 3 \cdot h = h \cdot g
51,780
0.3375 = \frac{27}{80}
17,484
n^3 = ((-1) + n) * ((-1) + n)^2 + 3((-1) + n)^2 + ((-1) + n)*3 + 1
11,805
\sin(y) = \dfrac{\tan(y/2)\cdot 2}{1 + \tan^2(y/2)}
17,949
\tfrac{\sin{q}}{\cos{q}} = \tan{q}
5,878
|ZB| = |B| |Z|
15,571
b^p = b^p*p!/(0!*p!)
4,098
(-1)^p = (-1)^{-p} = (-1)^{2 \cdot (x - k)} \cdot (-1)^{-p} = (-1)^{x - k} \cdot \left(-1\right)^{x - k - p}
2,460
\frac{1}{1 + \cos^2{z}} \cdot (\left(-2\right) \cdot \sin{z}) = \frac{\mathrm{d}}{\mathrm{d}z} \tan^{-1}(\cos{z})
39,554
z \cdot x = z \cdot x + 0 \cdot x
515
z^2 + z\cdot y + y \cdot y = \frac{z^3 - y^3}{z - y}
-22,234
18 + z^2 - 9\cdot z = (z + 3\cdot (-1))\cdot \left(6\cdot (-1) + z\right)
30,911
hh = h^2
21,575
1 + (3000*\left(-1\right) + 3333)/3 = 112
-18,070
84 + 18\times \left(-1\right) = 66
224
7 = |A \cap x| \implies A = x
-18,999
\dfrac19 = \frac{A_s}{81 \pi}*81 \pi = A_s
25,761
9/8 = \dfrac{1/4 \cdot 3}{\dfrac{1}{3} \cdot 2}
14,542
\left(d + g\right) \cdot \left(d + g\right) - d \cdot g \cdot 2 = d^2 + g^2
-5,411
10^{0 + 1}\cdot 31.2 = 31.2\cdot 10^1
779
4 = \frac{10}{1 - t} \Rightarrow t = -\dfrac{3}{2}
1,412
x x x^6 = x^8
-20,242
\tfrac{7 + l}{-l\times 2 + 10}\times 8/8 = \frac{1}{-16\times l + 80}\times (56 + 8\times l)
13,429
0 = p \times 2^{\frac{1}{2}} + q \times 5^{1 / 2} + \beta \times 10^{1 / 2} + t = t + p \times 2^{\frac{1}{2}} + (q + \beta \times 2^{\frac{1}{2}}) \times 5^{1 / 2}
-21,142
\dfrac{1}{3}2 = \dfrac{1}{6}4
-20,729
\dfrac{-50*y + 45*(-1)}{63 + 70*y} = -5/7*\frac{9 + y*10}{y*10 + 9}
3,525
a^2 + (23*(-1) + a)^2 = 289\Longrightarrow 240 + a * a*2 - 46*a = 0
3,966
0 = (c - x)\cdot (c^2 + c\cdot x + x^2) = c^3 - x^3
35,449
(-1) + l^2 = (l + 1) \times ((-1) + l)
-5,306
24\cdot 10^1 = 24.0\cdot 10^{-1 + 2}
21,770
1/\left(a\cdot f\right) = 1/(a\cdot f) = 1/(f\cdot a)
20,095
\frac{\dfrac{9!}{3! \cdot 2!} \cdot 5 \cdot 4}{\frac{1}{3! \cdot 2!} \cdot 11!} = \frac{1}{11} \cdot 2
-10,584
\frac155\cdot 4/(q\cdot 12) = 20/(60 q)
4,275
x^4 + (-1) = (x^2 + \left(-1\right))\cdot (x^2 + 1) = \left(x + (-1)\right)\cdot \left(x + 1\right)\cdot (x^2 + 1)
14,120
2*(37 + 2 c^2 + c*2) = (2 c + 1)^2 + 73
25,848
\mathbb{E}\left(\mathbb{E}\left(U_1\right)*U_2\right) = \mathbb{E}\left(U_2\right)*\mathbb{E}\left(U_1\right)
18,173
\left(-1\right) + (x + (-1))^2 + 2\cdot x = x^2
14,289
\sin{\dfrac{8*\pi}{32}} = \dfrac{1}{2^{1/2}}
23,639
x = \frac{1}{2}(x + Tx) = x/2 + T\frac{x}{2}
33,567
1 - \frac{m}{2\cdot m + 1} = \tfrac{m + 1}{2\cdot m + 1}
26,091
i * i = ii
2,455
B \cdot I = B \cdot I
-9,701
0.01\cdot \left(-100\right) = -\frac{100}{100} = -1^{-1}
18,207
\frac{1}{x \times G} = \dfrac{1}{G \times x}
-14,116
\frac{18}{6 + 4 \cdot (-1)} = 18/2 = 18/2 = 9
35,014
I + r\cdot r' = (r' + I)\cdot \left(I + r\right)
-12,848
18 - 6 = 12
3,038
(-x)^2 \cdot \left(-x\right) = -x\cdot (-x)^2 = -x\cdot x^2 = -x^3
35,711
-\dfrac{1}{z \cdot z} + 1 = \dfrac{-1/z + 1}{z \cdot \frac{1}{z + 1}}
-20,095
\frac{5 \cdot (-1) + r}{r + 5 \cdot (-1)} \cdot 9/4 = \tfrac{r \cdot 9 + 45 \cdot (-1)}{4 \cdot r + 20 \cdot \left(-1\right)}
3,600
(z + y)^3 \geq z^3 + y^3 = 2 rightarrow z + y \geq 2^{\frac13}
19,395
\frac{6}{6^2 * 6} = 6/216 = 1/36
21,491
7^2 - 2^2 = -6 * 6 + 9 * 9
27,218
z^R \times x = \left(x^R \times z\right)^R = x^R \times z
28,851
x*3 + \frac{\mathrm{d}}{\mathrm{d}x} \tan^3{x} - \tan{x}*3 = 3*\tan^4{x}
26,887
\left|{H_2\cdot H_1}\right| = \left|{H_1\cdot H_2}\right| = \left|{H_2}\right|\cdot \left|{H_1}\right|
-11,409
(z + f) \cdot (z + f) = (z + f)\cdot \left(z + f\right) = z^2 + 2\cdot f\cdot z + f^2
8,416
1 = \frac{1}{1 - \tfrac16 \cdot 5} \cdot f = f/\left(\frac16\right)
16,212
991 + 109 \left(-1\right) + 840\cdot 883 = 840\cdot 883 + 882
27,988
-(n + (-1))^3 + n n n = 3 n n - 3 n + 1
13,478
x^2 + z^2 + (x + z)^2 = 2\cdot (z \cdot z + x^2 + z\cdot x)
-30,283
\frac{1}{(-1) + z} \cdot \left(z \cdot z + 2\right) = z + 1 + \frac{3}{z + \left(-1\right)}
4,763
1 - 2^{\dfrac12} \cdot (2^{-1/2} + \tfrac{1}{2^{\frac{1}{2}}} \cdot k) = 1 - 1 + k = -k = e^{\dfrac12 \cdot (\left(-1\right) \cdot k \cdot \pi)}
38,423
\left(z + 1\right) \cdot (z + 3) = (z + 1) \cdot z + (z + 3) \cdot 3 = z^2 + z + 3 \cdot z + 9 = z \cdot z + 4 \cdot z + 9
14,692
\|u\|^2 = ((u_1^2 + u_2 \cdot u_2 + u_3^2)^{1/2})^2 = u_1^2 + u_2^2 + u_3 \cdot u_3