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math_formulas

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-18,390
\tfrac{5\cdot m + m^2}{m^2 + m\cdot 11 + 30} = \frac{(5 + m)\cdot m}{(6 + m)\cdot \left(m + 5\right)}
8,650
(1 - x) \cdot (1 + \ldots + x^{m + (-1)}) = 1 + \ldots + x^{m + (-1)} - x + \ldots + x^m = 1 - x^m
7,646
z^4\cdot 2 + z \cdot z\cdot 2 + \left(-1\right) = (z^2\cdot 2 + 1 - \sqrt{3})\cdot (\sqrt{3} + z^2\cdot 2 + 1)/2
9,160
(1 + x^2 - x) (x + 1) (x + (-1)) \left(x^2 + x + 1\right) = (x^3 + (-1)) \left(x \cdot x^2 + 1\right)
37,146
-x \geq 0\Longrightarrow x \leq 0
20,784
1 = -h + g \implies g = 1, h = 0
32,386
\left(7 - 2\cdot \sqrt{3}\right)\cdot (2\cdot \sqrt{3} + 7) = 37
1,611
\frac{1}{10}9*8/9/8 = 1/10
-9,351
-11*11*z*z = -121*z^2
-14,036
\frac{81}{6 + 3} = 81/9 = \tfrac{81}{9} = 9
3,557
(-c + g) \cdot \left(g + c\right) = -c^2 + g^2
46,110
\frac{1}{4\cdot 4} + \frac{2}{4}\cdot 1/4 + 3\cdot \frac14/4 + \frac{1}{4}\cdot 4/4 = \frac58
-4,955
45 \cdot 10^7 = 45 \cdot 10^{1 + 6}
-4,899
0.78\cdot 10^{0 (-1) + 2} = 0.78\cdot 10^2
-3,282
\sqrt{10}*(4(-1) + 5 + 2) = \sqrt{10}*3
9,723
-\frac{1}{(y - i)^2} = d/dy \left(y - i\right)^{-1}
48,596
18 = 5 + 4 + 9
-18,306
\frac{1}{y^2 - y + 30\cdot (-1)}\cdot (y^2 + 5\cdot y) = \tfrac{(5 + y)\cdot y}{(5 + y)\cdot \left(6\cdot (-1) + y\right)}
29,204
2 + b\cdot a - b + a = \left(a + (-1)\right)\cdot (b + (-1)) + 1
-4,490
\frac{y + 17 \cdot (-1)}{3 \cdot (-1) + y^2 + y \cdot 2} = \tfrac{5}{y + 3} - \frac{4}{\left(-1\right) + y}
39,948
3^{\tfrac{1}{m}} = 3^{\frac1m}
5,314
\frac{1}{(-x + 1)^2}*\left(k*x^{1 + k} - x^k*\left(k + 1\right) + 1\right) = 1 + x*2 + x^2*3 + \cdots + x^{k + (-1)}*k
-7,158
4/5 \cdot \frac{3}{4} = \frac{3}{5}
22,200
a*b*e = e*b*a
-22,352
(8 + n)*\left(n + 5*\left(-1\right)\right) = 40*\left(-1\right) + n^2 + n*3
39,705
e\cdot n = e + \left(-1\right)^e\cdot n = n = n + \left(-1\right)^n\cdot e = n\cdot e
13,554
3\cdot \left(144 - 84\right) - 2\cdot 84 = 12
40,938
\dfrac85 = \frac85
27,714
(a + 1)^2 d = (a^2 + 2a + 1) d = a^2 d + 2ad + d = ada + ad + ad + d
13,052
\frac{10*9 + 2*10}{{13 \choose 3}} = \frac{1}{13}*5
24,227
x^{10} + (-1) = (1 + x^8 + x^6 + x^4 + x^2) (x + 1) ((-1) + x)
2,532
3^k + (-1) + 2*3^k = (-1) + 3^{k + 1}
3,530
((-1) + x) * ((-1) + x) = ((-1) + x)*(x + (-1))
9,499
7 \cdot 1/36/\left(\tfrac{1}{4}\right) = 7/9
3,088
3\cdot 5/(\sqrt{5}) = \frac{1}{1/5 \sqrt{5}}3
-20,679
-20/(-6) = -\frac{2}{-2} \cdot 10/3
4,725
1 + y + y \cdot y + \cdots = \dfrac{1}{-y + 1}
30,643
24 \times 6 = 2 \times 6 \times 24/2 = 12 \times 12
-23,086
\frac{1}{16}7 = -\dfrac12 (-\dfrac78)
13,933
\sin(x) = \left(\sqrt{\sin(x)}\right)^2
11,687
\left(-1\right) + y^2 = (1 + y)\cdot \left(y + \left(-1\right)\right)
16,656
\dfrac{9}{32} = \frac{1}{2} \cdot 9 / 16
25,885
r_1/(s_1) \cdot r_2/(s_2) = \frac{r_2 \cdot r_1}{s_2 \cdot s_1}
17,772
2^{l + 1 + 1} + (-1) = 2^{l + 2} = 2\cdot 2^{l + 1}
34,014
\sin{a} = \sin(-a + \pi)
32,109
3\cdot 2 + 4 = 10
-20,314
\frac{5\cdot r + 7}{7 + 5\cdot r}\cdot \frac94 = \frac{63 + r\cdot 45}{r\cdot 20 + 28}
-23,300
1/(3\cdot 7) = 1/21
14,922
f x h = f x h
20,435
4 = \left(-1\right) \cdot (-4) = (-4) \cdot \left(-1\right)
21,662
1 = \frac{ag}{ag} = g*1/a a/g
1,221
|x| = |x - c + c| \leq |x - c| + |c|
17,395
y + 1 = 1 + 0*y^2 + y
2,801
\mathbb{E}[U] \cdot \mathbb{E}[C] = \mathbb{E}[U \cdot C]
26,278
A^{b + h} = A^h\cdot A^b
22,257
\alpha^2 + \alpha + 1 = -\alpha * \alpha + \alpha + (-1) = \alpha
-8,970
67.2\% = \dfrac{67.2}{100}
-1,577
\pi*25/12 - 2*\pi = \pi/12
40,955
766 = 2\cdot 383
6,767
-d\cdot x = x\cdot (-d)
22,938
(B \cdot A/B)^k = \frac{A^k}{B} \cdot B
15,445
(z^2 + 4)^2 = z^4 + z^2*8 + 16
18,745
-l \cdot l + a_n^2 = (-l + a_n)^2 + 2l\cdot (a_n - l)
-18,983
1/6 = \frac{1}{4 \times \pi} \times A_s \times 4 \times \pi = A_s
28,103
\sin{x} = (e^{i\cdot x} - e^{-i\cdot x})/(2\cdot i)\cdot \cos{x} = \frac{1}{2}\cdot (e^{i\cdot x} + e^{-i\cdot x})
6,171
\cos\left(y\right) = \sin\left(y + \frac{\pi}{2}\right)
6,996
2*x = x - -x
18,098
\frac{\partial}{\partial y} y^g = y^{(-1) + g}\cdot g
1,263
\cos(2\cdot X) = 1 - 2\cdot \sin^2(X) = 2\cdot \cos^2\left(X\right) + (-1)
38,953
\dfrac{10!}{10^{10}} = \dfrac{9!}{10^9}
28,725
\left(x + 1\right)^n*(x + 1)^n = (x + 1)^{2*n}
10,354
2z^2 + 8z + 6 = 2(z^2 + 4z + 3) = 2(z + 3) (z + 1)
-30,299
2\cdot \pi - \pi/4 = \frac74\cdot \pi
14,815
0 \lt 9 + 3 \cdot z^2 + z \cdot 12 \Rightarrow z^2 + 4 \cdot z + 3 \gt 0
-1,950
\pi \cdot \frac{1}{12} \cdot 37 = 17/12 \cdot \pi + 5/3 \cdot \pi
15,888
2017 = 44^2 + 9^2 = \left(-44\right)^2 + 9^2 = ...
10,681
x + \frac1x = x + \left(-1\right) + 1 + \frac{1}{x} \geq (x + (-1))/x + \dfrac1x + 1
-20,642
\dfrac{1}{8 + k\cdot 6}\cdot (6\cdot k + 8)\cdot (-4/3) = \frac{1}{18\cdot k + 24}\cdot (-k\cdot 24 + 32\cdot (-1))
25,567
x^2 - 3\cdot x + \frac94 = (x + h)^2 = x^2 + 2\cdot h\cdot x + h^2
7,399
56 = -3\cdot 62 + 242
-9,908
0.01 \cdot \left(-35\right) = -35/100 = -0.35
18,570
y^k \cdot y^h = y^{k + h}
-20,789
\frac{48 (-1) - n\cdot 8}{18 + 3n} = \frac{1}{n + 6}(n + 6) (-8/3)
-20,285
\dfrac{1}{1} \times \dfrac{z - 8}{z - 8} = \dfrac{z - 8}{z - 8}
-2,743
\sqrt{3} \cdot \left(1 + 2 + 4\right) = 7 \cdot \sqrt{3}
-15,793
-\frac{8}{10} + 1 = \dfrac{1}{10} \cdot 2
11,293
-35 yc - c\cdot 2 + 35 b = -35 (cy + b) - 2c
10,047
\tfrac{1}{2^{32}}(2^{32} + (-1)) = 1 - \frac{1}{2^{32}}
28,225
0 \neq c = c^{1 + 0} = c\times c^0
15,901
4 + 6\cdot n = 2\cdot (n\cdot 3 + 2)
18,152
120 - x\cdot 3 \gt 0 \Rightarrow x \lt 40
-1,367
1/\left(9*9/7\right) = \frac19*7/9
26,872
E[Q_{r - j} \cdot Q_{r - j}\cdot Q_r \cdot Q_r] = E[Q_{-j + r} \cdot Q_{-j + r}]\cdot E[Q_r \cdot Q_r]
25,960
\frac{2^\chi}{2^k} = 2^{-k + \chi}
23,383
4/52 = \frac{4}{51}*48/52 + \frac{1}{52}*4*3/51
9,375
\tan\left(\frac{\pi}{12}\right) = -\sqrt{3} + 2
3,729
\frac{B^2}{4} + \left(-1\right) = (2 + B)\cdot (2\cdot (-1) + B)/4
-4,933
3.78 \cdot 10 = \frac{3.78}{10^6} \cdot 10 = \frac{1}{10^5} \cdot 3.78
-10,617
3 = 30 t + 30 (-1) + 15 = 30 t + 15 (-1)
-22,366
18\times (-1) + x^2 - 3\times x = (6\times (-1) + x)\times \left(3 + x\right)