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ddrg
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math_formulas

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-10,529
\dfrac{1}{60\cdot z + 180}\cdot 60 = \frac{20}{20}\cdot \frac{3}{3\cdot z + 9}
33,521
1331 \Rightarrow 132 = 133 + (-1)
17,314
\frac{x + c}{1 + c} = c \Rightarrow c^2 = x
50,401
\frac{1}{y^2 + 3} = ((y - i \cdot \sqrt{3}) \cdot \left(y + i \cdot \sqrt{3}\right))^{-1} = \dfrac{1}{2 \cdot i \cdot \sqrt{3}} \cdot \left((y - i \cdot \sqrt{3})^{-1} - (y + i \cdot \sqrt{3})^{-1}\right)
-11,523
25 \cdot i - 20 + 5 = -15 + i \cdot 25
12,072
-u\cdot 6 = e^{-u} \implies -u\cdot 6 = \tfrac{1}{e^u}
5,693
x^{x^{x^{\cdots}}} = k\Longrightarrow k^{1/k} = x
38,021
0 = -(0 + 0*\left(-1\right))
10,727
\frac{n!^2}{2 \cdot n} = \frac{2}{2 \cdot 2 \cdot n} \cdot n!^2
36,137
{k + 1 \choose k} = k + 1
31,350
-\sin^2(z)*2 + 1 = \cos(2*z)
12,670
2\cdot (-1)^k + (-1)^{k + 1}\cdot 3 = (-1)^{1 + k}
-22,373
(n + 6*(-1))*(2 + n) = n^2 - n*4 + 12*(-1)
15,552
x\cdot 4 + x + 3 (-1) = 13 \left(-1\right) + 5 (x + 2)
-23,070
-7 \cdot (-\frac{3}{2}) = \frac{1}{2} \cdot 21
820
\tan{\dfrac{\pi}{8}} = (-1) + \sqrt{2}
31,119
\mathbb{E}(X) = \mathbb{E}(p_A X_1 + p_B X_2) = p_A \mathbb{E}(X_1) + p_B \mathbb{E}(X_2)
6,539
(-1) + x = 2\left(-1\right) + x + 1
26,507
3 = 155\cdot (-1) + 158
12,406
\sqrt{49 + 48*(-1)} = 1
16,930
2 \cdot (1 + 1/17) = 35/17 < \frac{1}{15} \cdot 32
-14,267
3 \times 5 + 9 \times \dfrac{ 6 }{ 3 } = 3 \times 5 + 9 \times 2 = 15 + 9 \times 2 = 15 + 18 = 33
8,519
\sqrt{m*4} = 2*\sqrt{m}
29,647
h_1 \cdot z^4 \cdot 4 + 4 \cdot z \cdot h_2 = 0 \Rightarrow h_1 \cdot z^4 = -z \cdot h_2
24,017
19/27 = 12/27 + \dfrac{1}{27}\cdot 6 + 1/27
19,704
0 \lt g,x,l \in \mathbb{Z} \Rightarrow g^l\cdot g^x = g^{x + l}
19,600
(-Z + H)\cdot t\cdot U = -U\cdot Z\cdot t + t\cdot H\cdot U
44,851
8-24=-16
-4,157
63/35\cdot \frac{x^3}{x^5} = \dfrac{63}{35\cdot x^5}\cdot x^3
25,113
(-\cos{A} + 1)\cdot \cos{A}/\sin{A}\cdot (1 + \frac{1}{\cos{A}}) = \sin{A}
4,777
z^{1 / 2}/z = \frac{1}{z^{\frac{1}{2}}}
-15,969
-5/10 \cdot 9 + \frac{1}{10}5 \cdot 9 = 0
-2,236
-3/12 + \frac{1}{12}\cdot 5 = 2/12
10,171
\cos\left(-\operatorname{acos}(q)\right) = \cos(\operatorname{acos}(q)) = q
25,363
\sqrt{X} = \frac{1}{2}\sqrt{X\cdot 4}
17,394
-91 = 6 + 3 + 100 \times (-1)
-11,081
(y + 10\cdot (-1))^2 + f = (y + 10\cdot (-1))\cdot (y + 10\cdot (-1)) + f = y^2 - 20\cdot y + 100 + f
-19,702
\dfrac57\cdot 3 = 15/7
31,451
k + |1|\cdot x = 0 rightarrow -x = k
11,862
6n + 3 = (2n + 1)*3
5,472
((f + x)^2 - (-x + f)^2)/4 = xf
-4,162
\dfrac{1}{i^5}\times i^2\times \frac{45}{2\times 45} = 45/90\times \dfrac{1}{i^5}\times i \times i
29,380
a\cdot b\cdot a = b\cdot a^2
27,021
\dfrac12\pi^{1/2} = \int_0^\infty e^{\beta \cdot \beta}\,\mathrm{d}\beta > \int_0^1 e^{\beta^2}\,\mathrm{d}\beta
21,473
\frac{1 + x + (-1)}{(-1) + x} = \frac{x}{x + (-1)}
6,329
(1 + z^2 + z^4) \cdot (-z \cdot z + 1) = 1 - z^6
35,306
1^3 + 2 \cdot 2 \cdot 2 = 3^2
3,214
(2 \cdot \left(-1\right) + 51) \cdot 2 + 2 = 100
15,181
x^3 + 27 \cdot \left(-1\right) = (x + 3 \cdot (-1)) \cdot (x^2 + 3 \cdot x + 9)
17,345
2 + 2/3 = \frac13\times 8
-20,454
-\frac{2}{-10*k + 4} = \frac22*\left(-\frac{1}{2 - k*5}\right)
8,251
\left(\frac{1}{7\cdot z - y}\cdot (z\cdot 3 - y) = \frac25 \Rightarrow 15\cdot z - 5\cdot y = -2\cdot y + 14\cdot z\right) \Rightarrow z/3 = y
22,684
0 = 2 + 3 + 5\cdot \left(-1\right)
30,921
R \cap T = T \cap (A \cap R) = R \cap (A \cap T)
17,608
{3 + 0(-1) + 3 + 2(-1) \choose 3 + 2(-1)} = {4 \choose 1} = 4
3,758
\cos^2{w \cdot t} = (1 + \cos{2 \cdot w \cdot t})/2 = \frac12 + \cos{2 \cdot w \cdot t}/2
4,597
( Xf, z) = z^X Xf = (z^X Xf)^X = f^X X^X z
5,588
b^2 + 10*P * P - 7*P*b = (-P*2 + b)*\left(-5*P + b\right)
3,640
\frac{1/7}{1/14} \cdot 2 = 4
-10,360
\frac{6}{10 + 5T} \frac{3}{3} = \dfrac{18}{15 T + 30}
-4,233
7/6 x * x = x^2*7/6
24,058
0 = \frac{1}{4} \left(x\cdot 2 + 5\right) \Rightarrow -\frac{1}{2} 5 = x
-13,629
\dfrac{20}{2 + 8} = 20/10 = \frac{20}{10} = 2
23,091
(1 + n^3 - n)*(n^2 + n + 1) = (n^2 + n + 1)*(n^3 - n^2 + n^2 - n + 1)
36,707
\left(\left(3 \gt x_n rightarrow 27 > 9*x_n\right) rightarrow 12 + 12*x_n \lt 3*x_n + 39\right) rightarrow 12*\left(1 + x_n\right) < (x_n + 13)*3
36,293
4 \cdot (1 + t^2) = (1 + t^2 - t \cdot z)^2 + z \cdot z = \left(1 + t^2\right) \cdot (1 + (z - t)^2)
-26,210
5 \cdot 7 - 3 \cdot 8 + 11 = 35 + 24 \cdot (-1) + 11 = 22
-19,267
9 \cdot 1/2/5 = \frac{9}{5 \cdot 2} \cdot 1 = \tfrac{9}{10}
32,240
\frac{dx}{dx} = \frac{x}{1 - x} - x = \frac{x^2}{1 - x}
24,350
z/y = z/y
38,181
J \cap x = \left\{\left( 0, 0\right)\right\} = x*J
9,424
l^{-(q + (-1))} = \dfrac{1}{l^q} \cdot l
14,755
\left|{x + Z A}\right| = \left|{A Z + x}\right|
-3,212
12 \cdot 2^{1/2} = (3 + 4 + 5) \cdot 2^{1/2}
16,312
x^2*2^{x^{1/2}} = \dfrac{1}{2^{-x^{1/2}}}*x * x
4,439
(-1) + y^2 = \left((-1) + y\right)\cdot (y + 1)
23,491
(i + (-1))\cdot (1 + i) = i^2 + (-1)
929
y \cdot b + y^2 \implies (y + \tfrac12 \cdot b)^2 - (\frac12 \cdot b)^2
4,957
\frac{1}{(-1)\cdot k}\cdot (k\cdot 2 - w^2\cdot m) = m\cdot w^2/k + 2\cdot (-1)
12,511
(3 - \sqrt{5})/2 \left(3 + \sqrt{5}\right)/2 = 1
4,637
\mathbb{E}[XQ * Q] = \mathbb{E}[X] \mathbb{E}[Q^2]
32,344
{23 \choose 3} = {(-1) + 20 + 4 \choose (-1) + 4}
25,996
\frac{1}{0.0679 + 0.0294} 0.0294 = \frac{0.0294}{0.0973} = 0.302158273381295
32,421
(r \cdot e^{\dfrac{i}{4} \cdot \pi})^4 = r^4 \cdot (\cos(4 \cdot \pi/4) + i \cdot \sin(4 \cdot \pi/4)) = -r^4
-20,945
\frac{1}{9} \cdot (-\frac{1}{a \cdot 7} \cdot a \cdot (-7)) = \frac{1}{a \cdot (-63)} \cdot \left(a \cdot \left(-7\right)\right)
-26,448
20 \cdot \left(-\frac{40}{20} + 60 \cdot m/20\right) = 20 \cdot \left(3 \cdot m + 2 \cdot (-1)\right)
12,228
z^2 + 2\cdot y^2 + \alpha^2 + y^2\cdot 2 = \alpha \cdot \alpha + 4\cdot y^2 + z \cdot z
-19,460
7\cdot 1/5/(1/9\cdot 8) = 9/8\cdot 7/5
-23,063
40/27 = \dfrac{1}{9} \times 20 \times \dfrac{2}{3}
24,257
15/256 = \frac{15}{16} \cdot 1/16
3,378
-h_1 \cdot (-h_2) = h_1 \cdot h_2
11,779
\pi \cdot R \cdot 2 \cdot 2 \cdot r \cdot \pi = 4 \cdot r \cdot R \cdot \pi^2
52,064
3 \cdot 50 + 6 \cdot 60 = 510
3,814
\left\{( 1, 2), ( 1, 1), ( 3, 1), ( 3, 2)\right\} = \left\{( 1, 1), \left( 1, 2\right), \left( 3, 1\right), \left( 3, 2\right)\right\}
-19,540
\frac{1}{9\cdot 3/7} = \tfrac13\cdot 7/9
13,181
\frac1z z^{\frac12} = z^{\frac{1}{2} + \left(-1\right)} = z^{-1/2} = \frac{1}{z^{\frac{1}{2}}}
9,702
(x + 4)*\left((-1) + 3*x\right) = 4*(-1) + x^2*3 + x*11
-18,288
\frac{x^2 + 16\cdot (-1)}{x^2 - x\cdot 4} = \frac{(x + 4)\cdot (4\cdot (-1) + x)}{x\cdot (x + 4\cdot \left(-1\right))}
31,301
\frac12\cdot 756 = 378
35,138
\frac{1}{(1 + x^2)^{\frac52}} \cdot x \cdot x \cdot x = -\tfrac{1}{(1 + x^2)^{5/2}} \cdot x + \frac{1}{(x^2 + 1)^{\dfrac32}} \cdot x