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math_formulas

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-20,365
\frac{1}{t\cdot 30 + 5}\cdot \left(5\cdot (-1) + 5\cdot t\right) = \frac{t + (-1)}{6\cdot t + 1}\cdot \frac55
13,705
\frac{y^l}{2^l}*2^{l + (-1)} = y^l/2
11,086
1/16 = -\frac18 + 3/16
-20,027
\frac44 \dfrac{s + 10}{(-1) + s} = \dfrac{1}{4s + 4(-1)}(4s + 40)
4,875
\sum_{x=1}^l F_x^2\cdot x^2 = \sum_{x=1}^l F_x \cdot F_x\cdot (1 + x)\cdot \left(x + (-1)\right) + \sum_{x=1}^l F_x^2
6,058
Var\left(R\right) + \mathbb{E}\left(R\right)^2 = \mathbb{E}\left(R \cdot R\right)
-4,693
\frac{2*z + 2}{z * z + 2*z + 15*\left(-1\right)} = \frac{1}{z + 3*(-1)} + \frac{1}{z + 5}
39,789
\binom{5}{3} = \frac{5!}{3!(5-3)!} = 10
-22,431
64^{\frac23} = 64^{\frac{1}{3}} \cdot 64^{\frac{1}{3}} = 4^2 = 4\cdot 4 = 16
24,415
\left(1 + n\right)! + (1 + n)!\cdot (n + 1) = (n + 1 + 1)\cdot (1 + n)!
29,427
S \cdot S - B_2^2 - (S - B_1)^2 = 0 = 2\cdot S\cdot B_1 - B_2^2 - B_1^2
5,382
\frac{\sin{1/(s_n)}*r_n/(s_n)}{\frac{1}{s_n}} = \sin{1/\left(s_n\right)}*r_n
13,466
1 = \frac{1}{5!}*(2!*3! + 4!*2! + 3*3!*2! + 2*2!*3!)
-1,845
\pi \frac135 + \frac74 \pi = \frac{1}{12}41 \pi
-27,989
\frac{d}{dx} \sec{x} = \tan{x} \cdot \sec{x}
-26,495
x\cdot 30 = 2\cdot x\cdot 5\cdot 3
23,420
t = 1/3 + \frac23 \cdot (1/3 + \frac13 \cdot t) = 5/9 + \frac29 \cdot t
16,074
(X\cdot Z)^2 = X \cdot X\cdot Z^2
21,590
x + d = (x + d)^2 = x^2 + x\cdot d + d\cdot x + d \cdot d = x + x\cdot d + d\cdot x + d
28,195
\dfrac{1}{Y + u*v^T} = \frac{1}{Y} - \frac{1/Y*\frac1Y*v^T*u}{\frac{u}{Y}*v^T + 1}
12,311
\sin(t + x) = \sin\left(t\right) \cos(x) + \cos(t) \sin(x)
6,367
\dfrac{1}{52} + 1/26 + 1/39 = 1/12
27,159
\left(1 = 1/x + x \Leftrightarrow 1 + x^2 - x = 0\right) \implies x \cdot x^2 + 1 = (x + 1)\cdot (x^2 - x + 1) = 0
14,808
\frac{y + \left(-1\right)}{y + 1} = 1 - \frac{2}{y + 1}
20,087
-24 \cdot 8! + 9! \cdot {4 \choose 2} \cdot 2 = 84 \cdot 8!
34,253
3 \cdot (-1) + 3^4 + 13 \cdot \left(-1\right) = 65
11,396
\frac{10}{2}*1 = 20/4
6,743
\dfrac{1}{2\frac{1}{1 - x^2}(1 + x + 1 - x)} = \frac{1}{2 \cdot (1 - x^2)}2 = \dfrac{1}{1 - x^2}
19,883
\operatorname{E}[X_1] \operatorname{E}[X_2^2] = \operatorname{E}[X_1 X_2^2]
7,580
(-1) + x^m = ((-1) + x) \cdot (x^{(-1) + m} + x^{m + 2 \cdot (-1)} + \ldots + 1)
-24,667
-(i \cdot 4 + 3) - 13 + 16 \cdot i = i \cdot 12 - 16
25,647
-(180 + 90) + 300 \implies 20 = 300 + 280\cdot (-1)
-1,203
\left((-9)*\frac{1}{7}\right)/(8*1/3) = -\frac17*9*3/8
19,895
(1 - \cos{H})\cdot \left(\cos{H} + 1\right) = (1 - \cos{H})\cdot (1 + \cos{H}) = 1 - \cos^2{H} = \sin^2{H}
-24,185
7 + 7 \cdot 7 = 7 + 7\cdot 7 = 7 + 49 = 56
29,282
z^k = zz^{k + (-1)}
14,930
g^b = g^{2 \cdot \frac{b}{2}} = (g^2)^{\frac{b}{2}}
-5,464
\dfrac{m \cdot 3}{(m + 5) \cdot (5 \cdot (-1) + m)} = \frac{m \cdot 3}{m^2 + 25 \cdot (-1)}
7,491
y^0 = \frac{y^4}{y^4} \times 1
55,005
2^7= 128
-11,569
-9i = -i*9 + 0 + 0(-1)
6,368
\dfrac{1}{A + \frac{1}{A}} = 1/(2*A) = \frac{2}{A} = 2*A
40,912
3^7 = 3^3 \times 3^4
8,688
S \cdot Q = S \cdot Q
4,032
8 = \dfrac{1}{1 - \dfrac{a}{2}}\cdot a \implies a = 8 - 4\cdot a
33,036
-1.625=-\frac {13}8
13,880
\dfrac{1}{1 - \frac{1}{e}} = \frac{e}{e + (-1)}
35,284
36 = 2^2\times 3^2 = 6^2
-24,092
\frac{48}{3 + 5} = \frac1848 = \frac{48}{8} = 6
8,069
(b\cdot 2 + (-1))\cdot y_1\cdot y_2 = b\cdot y_1\cdot y_2 + (b + \left(-1\right))\cdot y_2\cdot y_1
5,605
\left(e^1 - 1/e\right)/2 = \sinh\left(1\right)
17,221
\frac12 \cdot (1 - 1/100) = \frac{1}{200} \cdot 99 = 0.495
11,962
0 = \overline{\sum_{l=0}^x g_l\cdot y^l} = \sum_{l=0}^x g_l\cdot \overline{y}^l
-13,184
-\frac{0.01932}{-0.4} = 0.0483
5,738
2^{1/2} = \frac{4\cdot \cos(\pi/12)}{3 - \tan(\pi/12)}\cdot 1
14,084
\sin{z} = \sin((2l + 1) \pi - z) = \sin(z + 2l\pi)
44,469
459818240 = 2^8\times 5\times 7\times 19\times 37\times 73
-20,416
\frac{z\cdot 5 + 2}{2 + 5\cdot z}\cdot \frac27 = \dfrac{10\cdot z + 4}{35\cdot z + 14}
-10,486
-\dfrac{1}{y^2 \cdot 60} \cdot (48 \cdot y + 72) = 12/12 \cdot (-\dfrac{y \cdot 4 + 6}{y \cdot y \cdot 5})
2,730
\lambda dy = \lambda d y
15,850
\binom{2(-1) + r + (-1) + k}{2(-1) + k} = \binom{r + k + 3(-1)}{k + 2(-1)}
12,337
\frac{1}{a\cdot f} = \dfrac{1}{f\cdot a} \neq \frac{1}{a\cdot f}
7,786
2^{55}-2=2\cdot3^4\cdot7\cdot19\cdot73\cdot87211\cdot262657
26,921
25 \times \left(-1\right) + 25 = 25 + 25 \times (-1)
25,468
10118160 = \binom{48}{4}\cdot \binom{4}{3}\cdot 13
19,088
5\cdot 10^{k + 1} + 10^k + 3 = 10^k\cdot 10\cdot 5 + 10^{k + (-1)}\cdot 10 + 30 + 27\cdot (-1)
-520
\pi = -\pi*18 + 19 \pi
3,202
\frac1d \left(-f + b\right) = -\frac1d f + b/d
-23,084
-4/3 = 2 (-2/3)
6,530
c^k \cdot a = a \cdot c^k
21,687
A*9 = 9 rightarrow A = 1
22,894
\int x^3 \cdot e^{-x}\,dx = -x^3 \cdot e^{-x} + \int 3 \cdot x^2 \cdot e^{-x}\,dx = -x^3 \cdot e^{-x} - 3 \cdot x^2 \cdot e^{-x} + 6 \cdot \int x \cdot e^{-x}\,dx
10,732
\dfrac{1}{28} \cdot 3 = -\frac{25}{28} + 1
39,064
\left(12 + 5 + 10\right) \cdot 4 \cdot 0.25 \cdot 0.25 = 6.75
3,668
x^2\cdot 4/5/8 = \frac{1}{10}x^2
15,505
A = Z/2 \implies A \gt Z
5,715
9 \cdot (9^x + (-1)) = 9^{x + 1} + 9(-1)
-4,283
\frac{r^5}{r} \cdot 54/45 = \frac{r^5 \cdot 54}{45 \cdot r}
-3,062
(1 + 2 + 4)\times 5^{1/2} = 7\times 5^{1/2}
25,362
( a, h, e) = ( h, e, a) = \left( e, a, h\right)
35,490
-\sin(D) = \sin(-D)
-510
(e^{3*\pi*i/4})^3 = e^{3*3*i*\pi/4}
-15,964
-62/10 = \frac{10}{10} - 8\cdot \frac{9}{10}
-5,890
\frac{1}{3*(2*(-1) + r)}*3 = \frac{3}{6*(-1) + r*3}
-7,661
\dfrac{1}{26} \cdot (100 + 150 \cdot i - 20 \cdot i + 30) = \dfrac{1}{26} \cdot (130 + 130 \cdot i) = 5 + 5 \cdot i
11,805
\sin{y} = \frac{\tan{y/2}\cdot 2}{1 + \tan^2{\frac{y}{2}}}
29,176
\dfrac{1}{14} = 216/3024
34,521
a^{n + m} = a^m*a^n
14,734
3 \cdot (1 + m) + 1 = 3 \cdot m + 4
30,534
i = 2^{2(x + 1)} + (-1) = 4\cdot 4^x + (-1)
-5,487
\frac{4}{(2 \left(-1\right) + z)*5} = \frac{4}{5 z + 10 (-1)}
14,676
16 + 36 \cdot (-1) = 45 \cdot \left(-1\right) + 25
-20,109
\frac37 \tfrac{1}{6\left(-1\right) + c}(c + 6(-1)) = \frac{c \cdot 3 + 18 (-1)}{42 \left(-1\right) + c \cdot 7}
10,863
\dfrac{1}{1 + y^2}\times 8 = d/dy \tan^{-1}(y)\times 8
-6,259
\dfrac{f\cdot 4}{20 + f^2 - f\cdot 12} = \dfrac{4\cdot f}{(f + 10\cdot \left(-1\right))\cdot (2\cdot \left(-1\right) + f)}
1,715
1 + 10^n = m^2 \Rightarrow 10^n = ((-1) + m)\times (1 + m)
24,536
2*(2*\left((-1) + x*2\right)*(k*2 + \left(-1\right)) + 2*x + 2*k + 2*(-1)) = (4*x*k - k - x)*4
-23,611
5/9\cdot \frac56 = 25/54
-8,040
\frac{1}{-1 + i}\cdot (2\cdot i + 4) = \dfrac{-1 - i}{-1 - i}\cdot \frac{4 + 2\cdot i}{-1 + i}
-25,023
\operatorname{atan}(-x\cdot 4) = -4\cdot x + x^3\cdot 64/3 - 1024/5\cdot x^5 + 16384/7\cdot x^7 - \dots