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math_formulas

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\tfrac{1/(1/b)*f}{\frac{1}{c}} = f/(1/(\frac{1}{1/c}*b))
-4,390
36/9 \cdot \frac{q^5}{q^2} = \frac{q^5 \cdot 36}{q \cdot q \cdot 9} \cdot 1
-7,111
5/8 \cdot 4/7 = \frac{1}{14} \cdot 5
-22,715
\dfrac{6}{3*6}*5 = \frac{30}{18}
20,846
\mathbb{E}[X] = \mathbb{E}[\sum_{i=1}^n X_i] = \sum_{i=1}^n \mathbb{E}[X_i]
-1,325
((-5) \cdot 1/7)/\left(1/2 (-9)\right) = -5/7 (-2/9)
18,489
\|V_2 - V_1\| = \|V_2 - Z + Z - V_1\| \leq \|V_2 - Z\| + \|Z - V_1\|
-23,299
-\frac{1}{7} + 1 = 6/7
27,366
\sqrt{a} \sqrt{a} = a
227
\sin(x + \tfrac{\pi}{2}) = \cos{x}
19,525
\frac{\partial}{\partial z} z^m = m \cdot z^{(-1) + m}
40,145
180 = \alpha + 18\Longrightarrow 162 = \alpha
36,186
e^{\log_e\left(2\right)/2} = e^{\log_e\left(\sqrt{2}\right)} = \sqrt{2}
-546
(e^{\dfrac{11}{12}\times \pi\times i})^{12} = e^{i\times \pi\times 11/12\times 12}
31,313
\cos\left(\pi \cdot 2 + x\right) = \cos{x}
-26,429
10/3*\frac{3}{2} = 5
225
(1991 + x) \cdot (x + a) + 1 = x^2 + (1991 + a) \cdot x + a \cdot 1991 + 1
3,949
\dfrac{1}{-x + \sqrt{x^2 + 1}} = \sqrt{1 + x^2} + x
22,365
\frac12 + \frac{1}{3} = \dfrac{5}{6}
-16
6 + 1 = 7
30,282
270000 = 2^4 \cdot 3^3 \cdot 5^4
16,512
y + 4 \times (-1) + 4 = y
36,424
\frac{1}{216}*6 = 1/36
15,519
2^{15} + (-1) = (2^3)^5 + \left(-1\right) = (2^3 + (-1)) \cdot \left((2 \cdot 2^2)^4 + 2^3 \cdot 2^3 + 2 \cdot 2^2 + 1\right)
13,715
( G\cdot G^t\cdot u, w) = \left( G^t\cdot u, G^t\cdot w\right) = \left( u, G\cdot G^t\cdot w\right)
10,788
BA = (\left(A + B\right)^2 - A^2 - B^2)/2
12,974
E(Z_2^x*Z_1^n) = E(Z_2^x)*E(Z_1^n)
3,870
\dfrac{bh}{dg} = \dfrac{hb}{gd}
34,579
(b*x)^i = (b*x)^i
20,998
b^2 - x^2 = (b - x) (b + x)
7,453
\left(x + y\right)^3 = x\times y \times y\times 3 + x^3 + y^3 + 3\times x^2\times y
5,381
\frac{1}{18} = \frac{1}{3\cdot 9} + \frac{\dfrac{2}{3}}{36}\cdot 1
8,288
G \cdot G^2 \cdot G \cdot G^2 = G^6
-7,326
\dfrac45 \cdot 0 = 0
7,595
q\cdot x\cdot d = b\cdot q^n \Rightarrow x\cdot d = q^{(-1) + n}\cdot b
41,200
i = 2^{2 x + 1} + \left(-1\right) = 2*4^x + (-1)
18,766
-c_2 \cdot c_2^2 + c_1^3 = (c_1 - c_2)\cdot (c_2^2 + c_1^2 + c_1\cdot c_2)
-22,932
\dfrac{130}{13 \cdot 9}1 = \frac{1}{117}130
-20,240
\frac{1}{7 - z \cdot 5} \cdot (35 \cdot z + 49 \cdot \left(-1\right)) = \dfrac{7 - z \cdot 5}{-5 \cdot z + 7} \cdot (-7/1)
-20,616
\frac{1}{-18}\cdot 30 = -\frac{1}{-6}\cdot 6\cdot (-5/3)
942
(\eta - z)^2 = (\eta - m + m - z) * (\eta - m + m - z) = (\eta - m)^2 + 2*(\eta - m)*(m - z) + (m - z)^2
42,217
R\Rightarrow R
26,800
14 = \binom{7}{2} + 7\times \left(-1\right)
3,043
\cos(-a + x) = \sin(a)\cdot \sin(x) + \cos(x)\cdot \cos(a)
14,797
x^2 - 2 \cdot x + 5 = x^2 - 2 \cdot x + 1 + 4 = (x + (-1))^2 + 4
-9,783
-\frac{37}{50} = -0.74
-15,102
\dfrac{1}{q^2 \cdot \frac{x^2}{q^2}} = \frac{1}{(\dfrac{x}{q})^2 \cdot q^2}
19,114
\dfrac{65}{42} = \frac{45}{42}\cdot 49/42\cdot \frac{52}{42}
13,771
2 = 2^{\frac{1}{2}}*2^{1/2}
-10,777
-\dfrac{4}{20 + r*5}*\dfrac{3}{3} = -\frac{1}{60 + 15*r}*12
25,246
\frac{1}{8}(1 - \cos(4z)) = (1 - \cos^{22}(z) - \sin^{22}\left(z\right))/8 = \frac18(1 - 1 - 2\sin^{22}(z))
25,847
5 * 5 * 5/3*5 = 625/3
47,463
0 = \left(-1\right) + 1^3
26,013
(1^2 + 7^2)/2 = 5 * 5
22,106
\left(x^4 + x^3 + x^2 + x + 1\right) \cdot (x + (-1)) = x^5 + (-1)
-7,906
\frac{1}{10} \cdot (6 - 12 \cdot i + 2 \cdot i + 4) = \dfrac{1}{10} \cdot (10 - 10 \cdot i) = 1 - i
20,571
e\cdot x = 159\cdot 267\cdot 348 = x\cdot e
47,957
1/2\cdot 0\cdot x^0/0! + 2^0\cdot \frac{x^1}{1!} + 2^1\cdot 2\cdot \frac{1}{2!}\cdot x \cdot x = \frac{1}{2}\cdot (x^2/2!\cdot 2 \cdot 2\cdot 2 + 2^0\cdot 0\cdot \frac{1}{0!}\cdot x^0 + 2^1\cdot x^1/1!)
13,061
\frac12 \cdot \left(b^2 + a^2\right) = \tfrac{a^2}{2} + \dfrac{b^2}{2}
21,426
\tfrac{95}{100} = \frac{1}{20}\cdot 19
34,922
\cos(\pi) \cos(0)*2 = -2
29,879
\tfrac{1}{25} \cdot 2 = \frac{1}{1300} \cdot 104
9,601
b \cdot \frac{x^i}{b} = \left(b \cdot x/b\right)^i
6,524
e = e\dfrac{1}{e}e
-15,319
\frac{1}{\frac{k^2}{p^4} p \cdot p} = \dfrac{1}{p^2\cdot \tfrac{1}{p^4 \frac{1}{k^2}}}
5,563
6\cdot (-1) + 3\cdot k = k + (k + 3\cdot (-1))\cdot 2
25,720
1000x+y=9y\implies1000x=8y\implies125x=y
-15,845
-74/10 = \tfrac{7}{10} - 9*\frac{9}{10}
-6,562
\dfrac{4}{4 \cdot k + 28 \cdot (-1)} = \dfrac{4}{4 \cdot (k + 7 \cdot (-1))}
8,839
(1 + k)^2 = 1 + k^2 + 2 \cdot k
-3,063
3*\sqrt{2} = (5 + 2*(-1))*\sqrt{2}
23,910
z = b*z = z*b
33,508
12 = 10 \cdot \left(-1\right) + 22
4,531
\frac{1}{a\cdot \phi + \phi^2} = (\frac{1}{\phi} - \frac{1}{a + \phi})\cdot 1/a
-10,483
\dfrac{1/4*4}{y + 4} = \dfrac{4}{16 + y*4}
10,112
b*2^m + a*2^m = 2^m*(a + b)
7,349
det\left(j*G\right) = j^{29}*det\left(G\right) = j*det\left(G\right)
24,079
(X + (-1)) \cdot (X + 1) = (-1) + X \cdot X
13,208
x + \frac{1}{3}*w = 0\Longrightarrow -w/3 = x
12,089
0 = y^2 - y + 380 \cdot \left(-1\right) = (y + 19) \cdot \left(y + 20 \cdot \left(-1\right)\right)
17,755
1 = 2*c rightarrow c = 1/2
-4,648
\frac{1}{15*(-1) + y * y + y*2}*(y*4 + 20*\left(-1\right)) = \dfrac{5}{y + 5} - \frac{1}{3*(-1) + y}
28,442
h\cdot x\cdot g = x\cdot g\cdot h
6,535
\frac{4968}{105}\cdot \pi = \frac{54\cdot \pi}{1}\cdot \frac{1}{105}\cdot 92
-24,985
2 \cdot 2 \cdot \pi = 4 \cdot \pi
735
\tfrac{5}{2}\cdot \sqrt{l} = \sqrt{l}\cdot 2 + \dfrac{l}{2\cdot \sqrt{l}}
-18,156
14 = 53 + 39 \cdot \left(-1\right)
3,824
\mathbb{E}\left(\bar{C}^2\right) = \mathbb{Var}\left(\bar{C}^2\right) + \mathbb{E}\left(\bar{C}\right)^2
31,388
e^{-1/2} = e^{-\tfrac12}
42,140
6 = 3 \left(-1\right) + 3*3
27,655
2 \times 2\times 3\times 5\times 7 = 420
11,053
585 = (8 + 1)*(4 + 1)*(12 + 1)
28,124
2\cdot \cos{B}\cdot \sin{B} = \sin{2\cdot B}
19,404
\frac{\tan(E)\cdot 2}{\tan^2(E) + 1} = \sin(2\cdot E)
34,506
6! {16 \choose 6} = 6!*8008 = 5765760
9,154
\sqrt{\left(-1\right)^6} = ((-1)^6)^{1/2} = 1
41,618
11^2 = 2^7 + 7(-1)
28,870
F \cdot E = x \cdot E\Longrightarrow F \cdot E \cdot 2 = F \cdot x
-28,869
\tfrac{20\cdot 0.01}{0.01\cdot 60} = 1/3
-23,051
-7/8 = \frac{1}{2} \cdot (1/4 \cdot (-7))