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math_formulas

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-10,390
\tfrac{1}{12}12 \dfrac{7 + r}{5r + 20 (-1)} = \frac{12 r + 84}{60 r + 240 (-1)}
8,609
\tfrac{1}{k!\cdot (-k + n)!}\cdot n! = \binom{n}{k}
-3,099
\sqrt{13}\cdot 3 = \sqrt{13}\cdot ((-1) + 4)
14,278
{l \choose j} + {l \choose (-1) + j} = {l + 1 \choose j}
30,762
k*3 + 8 (-1) = 3 \left(k + (-1)\right) + 8 (-1) + 3
5,527
\frac{1}{y + 3}(\tfrac{1}{2(-1) + y}40 + 5y + 15) = 5 + \frac{40}{\left(y + 3\right) (2\left(-1\right) + y)}
8,529
\tan\left(\operatorname{arccot}(t)\right) = \frac{1}{\cot(\operatorname{arccot}(t))} = \frac{1}{t}
-20,551
\frac{a \cdot 24}{-8 \cdot a + 16 \cdot (-1)} = 8/8 \cdot \frac{3 \cdot a}{2 \cdot (-1) - a}
-4,927
\frac{7.6}{10^5} = \frac{1}{10^5} 7.6
13,921
x \cdot x = \left(2 \cdot (-1) + x\right) \cdot (2 + x) + 4
28,932
T \cdot (g_2 \cdot x + g_1) = g_1 \cdot T + g_2 \cdot T \cdot x
-17,520
33 = 92 + 59*\left(-1\right)
-21,641
-\frac{7}{8} = -7/8
22
Y \setminus B = Y \setminus B \cap Y = B \cup Y \setminus B
21,587
\arcsin(1)=\pi/2
7,482
(24\cdot e - 41\cdot s)\cdot 5 = 120\cdot e - 205\cdot s
12,900
\dfrac12(\cos(-D + A) - \cos\left(D + A\right)) = \sin{A} \sin{D}
2,146
\sin(\frac{\pi}{12}\times 19) = -\cos(\pi/12)
34,183
\tan^{-1}(1 + \sqrt{2}) = 3/8 \pi
-13,032
5 + 3 + 10 = 18
24,324
3 = \frac{18}{3*(1 + 5 + 4*(-1))}
13,161
1 - 1/2 + 1/3 - \frac{1}{4} = 7/12
8,204
(6 \cdot (-1) + t)^2 - 4 \cdot (t^2 - t \cdot 6 + (-1)) = -t^2 \cdot 3 + t \cdot 12 + 40
27,056
3 \cdot 7 - z = -z + 21
-13,454
(6 + 10 - 9 \cdot 10) \cdot 5 = (6 + 10 + 90 \cdot \left(-1\right)) \cdot 5 = (6 - 80) \cdot 5 = (6 + 80 \cdot (-1)) \cdot 5 = (-74) \cdot 5 = (-74) \cdot 5 = -370
-4,202
a^4/a*110/44 = 110*a^4/(44*a)
25,684
{d \choose b} = {d \choose d - b}
5,465
\frac{(1 + \left(-1\right) + 1 + 1)!}{(1 + \left(-1\right))! \cdot 1! \cdot 1!} = \frac{2!}{0! \cdot 1! \cdot 1!} = 2! = 2
-2,474
-\sqrt{16\times 3} + \sqrt{25\times 3} = \sqrt{75} - \sqrt{48}
-488
-4\cdot π + π\cdot \frac{19}{4} = π\cdot \frac{3}{4}
11,071
4^{578} = 4 \cdot 4\cdot (4^6)^{96}
39,321
{-1 \choose m} = ((-1)\cdot (-1 + (-1))\cdot (-1 + 2\cdot (-1))\cdot \dotsm\cdot (-1 - m + 1))/m! = (-1)^m\cdot m!/m! = (-1)^m
29,899
3 \cdot 7 \cdot 17 \cdot 23 \cdot 31 - 2 \cdot 2 \cdot 5 \cdot 11 \cdot 13 \cdot 89 = 1
5,503
x^3 + 0\cdot x^2 + 0\cdot x + 0 = (x + 0)^3
-1,689
-\frac{11}{6}*\pi + \pi/3 = -\frac{3}{2}*\pi
52,829
\frac{dy}{dx}=\frac{-12x^2y+4y^3+4y}{4x^3-12xy^2-4x}=\frac{-4x^2y+y^3+y}{x^3-3xy^2-x}
-2,614
\sqrt{10}*\left(3 + 5 + (-1)\right) = \sqrt{10}*7
20,176
-g \cdot g = -g\cdot g
33,988
140 - 30 + 50 + 10 \Rightarrow 70 = 60 + 10
-5,856
\frac{4}{(z + 1) \cdot \left(4 + z\right)} = \frac{4}{z^2 + 5 \cdot z + 4}
20,717
q^{k + 1} > q^{k + 1} + (-1) = (q^k + \left(-1\right))^q > q^{(k + \left(-1\right))\cdot q}
-17,517
52 + 22 (-1) = 30
-19,615
\dfrac{5}{6} \cdot 8 = 40/6
29,282
y \cdot y^{k + (-1)} = y^k
-5,021
10^{-5 + 6}\cdot 18.0 = 18\cdot 10^1
8,452
3d_1 d_2 = (d_2 + d_1)^2 - d_2^2 - d_2 d_1 + d_1^2
19,769
123 = 3\cdot 10^0 + 2\cdot 10^1 + 10^2
-30,254
\frac{1}{y + 4}\cdot \left(y^2 + 16\cdot \left(-1\right)\right) = \frac{1}{y + 4}\cdot \left(y + 4\right)\cdot (y + 4\cdot \left(-1\right)) = y + 4\cdot \left(-1\right)
44,758
(500\cdot3)\cdot3=500\cdot3^2
-20,886
\frac{1}{c \cdot (-14)} \cdot \left(c \cdot 7 + 63\right) = \frac17 \cdot 7 \cdot \frac{1}{c \cdot (-2)} \cdot (c + 9)
-22,932
\frac{10*13}{13*9} = \dfrac{130}{117}
22,300
\dfrac{5!}{\left(5 + 2 \cdot (-1)\right)!} \cdot \frac{10!}{(10 + 3 \cdot (-1))!} \cdot 7! \cdot \tfrac{1}{(7 + 2 \cdot (-1))!} \cdot 3! = 720 \cdot 42 \cdot 20 \cdot 6 = 3628800
-19,260
\dfrac{1}{2} = H_s/(81*\pi)*81*\pi = H_s
4,408
\frac{2*x + 3}{x + 2} = \frac{1}{x + 2}*\left(x + 2 + x + 1\right) = 1 + \frac{x + 1}{x + 2}
-9,908
0.01 \left(-35\right) = -35/100 = -0.35
-4,275
\frac{p \cdot 80}{p^3 \cdot 8} = \frac{1}{p^3} \cdot p \cdot \dfrac{80}{8}
30,675
34358689792 = (2^{15} - 1)*2^{20}
5,594
5 = \mathbb{Var}(C) = \mathbb{E}(C^2) - \mathbb{E}(C) * \mathbb{E}(C) = \mathbb{E}(C^2) + 4*(-1)
30,613
2^{m + 1} + 2 \cdot \left(-1\right) = 2^1 \cdot 2^m + 2 \cdot \left(-1\right) = 2 \cdot (2^m + (-1))
20,568
\left(\frac12\cdot (1 + 1) + \frac{1}{1}\cdot 2 + 2/1\right)/3 = \frac{5}{3}
112
\tfrac{3!}{(3 + 2(-1))!\cdot 2!} = 3
770
x + 2*m*(2*m + b) = x + m * m*4 + 2*m*b
-23,120
\frac18\cdot 7 = 7\cdot 1/4/2
17,670
w\cdot (u + x) = w\cdot u + x\cdot w
26,556
z = i\Longrightarrow e^z = e^i
-20,606
\dfrac{y \cdot 9 + 27 \cdot (-1)}{y \cdot 9 + 36 \cdot \left(-1\right)} = \frac{1}{4 \cdot (-1) + y} \cdot \left(y + 3 \cdot (-1)\right) \cdot 9/9
9,356
\cos(\alpha)*\cos\left(\theta\right) - \sin(\alpha)*\sin(\theta) = \cos(\alpha + \theta)
31,730
1 + p + 1 = p + 2
42,730
11 = 55 - (-1) + 45
14,251
144^{\sin^2\left(y\right)} = (12^2)^{\sin^2(y)} = 12^{\sin^2(y)} \cdot 12^{\sin^2(y)}
-29,187
-5 = 5\left(-1\right) + 3*0
635
(-t + r) \cdot (t + r) \cdot (r \cdot r + t \cdot t) = -t^4 + r^4
-9,428
q \cdot 3 \cdot 3 \cdot 11 + 11 = q \cdot 99 + 11
26,869
-\sin^2(y)\cdot 2 + 1 = \cos(y\cdot 2) \Rightarrow -\cos(2y) + 1 = 2\sin^2(y)
19,978
6 = 15 + 3\cdot \left(-1\right) + 6\cdot (-1)
33,248
\left(-1\right)^{\dfrac{6}{2}} = (-1)^2 \cdot (-1)
-7,594
\frac{1}{5 - i*4}\left(-25 + 20 i\right) \frac{5 + 4i}{i*4 + 5} = \frac{1}{-4i + 5}(20 i - 25)
16,901
\cos(x) \times \sin(x) = \frac{1}{2} \times \sin(x \times 2)
340
\frac{X^9 + (-1)}{X + (-1)} = 1 + X + \dotsm + X^8 = \mathbb{P}(X)
3,607
\dfrac{1}{1 + \dfrac{1}{y^m}\cdot 7} = \frac{y^m}{y^m + 7}
3,328
(z \cdot x) \cdot (z \cdot x) = x^2 \cdot z^2
5,792
\Sigma_j\times y^j = y\times y^{(-1) + j}\times \Sigma_j
18,540
3^{2 n} + (-1) = 9^n + (-1) = (8 + 1)^n + (-1)
6,744
9 Z + Z + 5 (-1) = 2 \Rightarrow Z = \frac{7}{10}
38,335
(5 + f)^2 + 25 \left(-1\right) = 25 + 2*5f + f^2 + 25 (-1) = 2*5f + f^2
-29,140
4\cdot \left(-2\right) - 3 = -11
-1,087
\frac{1}{7/6 \cdot 9} = \frac{1}{9} \cdot 6 / 7
-6,055
\frac{c}{(10 \cdot (-1) + c) \cdot \left(c + 10\right)} = \frac{c}{100 \cdot (-1) + c \cdot c}
15,317
1050 = 10!\cdot 5/\left(4!\cdot 6!\right)
17,281
-\frac14\cdot 9 = -\frac{1}{4}\cdot 15 - -3/2
12,418
(n - m) \cdot \alpha = \alpha \cdot n - m \cdot \alpha
-30,376
\frac{1}{10000} 8.235 = 8.235*0.0001
-22,201
72 \cdot (-1) + t^2 - t = (t + 9 \cdot (-1)) \cdot (8 + t)
-4,135
72/108*\dfrac{y^2}{y^5} = 2*36/(3*36)*\tfrac{1}{y^5}*y * y
29,679
\frac{\sqrt{7}}{2} \cdot i + 1/2 = \frac{1}{2} \cdot (1 + \sqrt{-7})
11,368
\sin\left(\beta\right)*\cos(x) + \sin(x)*\cos(\beta) = \sin(x + \beta)
-10,344
-\frac{1}{a \cdot 10 + 10} \cdot \left(15 \cdot a + 50\right) = 5/5 \cdot (-\dfrac{1}{2 + 2 \cdot a} \cdot (3 \cdot a + 10))
13,577
1/7 = \frac{1}{1000} \times (1 - 1/7) + 0.142
15,884
\tan(π/2 - a) = \frac{1}{\tan(a)}
-8,015
\frac{1}{-2}\cdot (-4\cdot i - 4) = -\tfrac{4}{-2} - 4\cdot i/\left(-2\right)