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math_formulas

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-21,594
\sin(\pi*\frac{1}{6}*11) = -0.5
18,339
1/(t\cdot d) = \frac{1}{t\cdot d}
-15,928
-\dfrac{83}{10} = -10 \cdot \frac{9}{10} + \frac{7}{10}
17,835
1 + kx + x = 1 + \left(k + 1\right) x \leq (1 + x)^k + x
50,749
\frac{5^{2013}\cdot 2^{2013}\cdot 3^{2008}}{3^{2010}\cdot 2^{2010}\cdot 5^{2012}} = 40/9
39,123
(h + b)^2 = h^2 + 2hb + b^2 \geq h \cdot h + b \cdot b
12,561
(-a \cdot c + a^2 + b^2 + c^2 - b \cdot a - c \cdot b) \cdot (c + a + b) = -3 \cdot b \cdot c \cdot a + a^3 + b^3 + c^2 \cdot c
17,134
\tfrac{1}{4} = \frac{1}{2*2}
29,264
(1 - \sqrt{y}) \cdot (\sqrt{y} + 1) = 1 - y
17,018
c^2 + \frac{1}{c^2} + 1 = \left(c + 1/c\right)^2 + (-1) = (c + 1/c + 1) (c + 1/c + (-1))
7,846
\sqrt{13}/2 = \sqrt{\frac{1}{1 - 5/13}\cdot 2}
15,072
\dfrac{4}{4!}\times 10\times 8\times 6 = 80
18,100
\frac{1/9 z}{1 - -z^4/9} = \frac{z}{z^4 + 9}
-23,205
-\frac{1}{2}\cdot 3\cdot 8 = -12
23,258
\left(2 \cdot n\right)! = 2 \cdot n \cdot \left(\left(-1\right) + 2 \cdot n\right)!
17,876
\left(2a \cdot a + 1\right)^2 + (-1) = 4a^4 + 4a^2 = (2a^2) \cdot (2a^2) + (2a)^2
-3,072
\sqrt{54} + \sqrt{96} = \sqrt{9 \cdot 6} + \sqrt{16 \cdot 6}
-24,856
\frac{x}{3} - \dfrac12\cdot v = -1/2\cdot (\dfrac{x}{3} + \frac{v}{2}) + 1 = ((-1)\cdot x)/6 - \dfrac14\cdot v + 1
3,673
z + 2*\left(-1\right) - y^2 + 1 = 3*(-1) + z - y * y
37,391
\frac{f \times t^4}{t^3 \times f} = \frac{t^5 \times f}{f \times t^4}
6,197
-4 = b + a \Rightarrow -4 = -b + a
34,179
2^k - 2^{k + (-1)} = 2*2^{k + (-1)} - 2^{k + (-1)} = 2^{k + (-1)} (2 + (-1)) = 2^{k + (-1)}
17,806
\left(-a\right) \times \left(-a\right) = a^2
22,920
G^C \cdot G = G \cdot G^C
-22,375
m^2 + 7 m + 12 = (m + 3) (m + 4)
-9,632
-10\% = -\dfrac{10}{100} = -\dfrac{1}{10}
47,924
2 = (\left(-1\right) + 3)
-22,196
35\cdot (-1) + s^2 - 2\cdot s = (s + 5)\cdot (s + 7\cdot (-1))
2,313
det\left(I + XY a\right) = det\left(I + X^{\frac12} Y X^{\frac{1}{2}} a\right)
36,807
\dfrac{5}{12} = 15/36
22,922
|H_1|*|H_2| = |H_1*H_2|
-15,150
\frac{1}{lg^{20} l^{10}} = \frac{1}{l*(l^2 g^4)^5}
36,890
\sqrt{6 + \sqrt{2}} \times \sqrt{6 - \sqrt{2}} = \sqrt{36 + 2 \times (-1)} = \sqrt{34}
-17,806
73 = 65 + 8
5,912
10 \cdot 10 \cdot 10\cdot 10^3 = 10^6
-10,053
-0.02 = -\frac{1}{50}
38,521
-1/4 + 1 + (-1) + 1/2 - 1/2 + 1/3 - 1/3 + \dfrac14 = 0
43,031
10\cdot 7 + 40 (-1) = 30
11,548
r + r = (r + r)^2 = (r + r)\cdot (r + r) = r^2 + r^2 + r \cdot r + r^2 = r + r + r + r
38,946
3^{10^{20}} = \ldots*8084427865522000000000000000000001
16,820
\frac{1}{6} + \dfrac{1}{3} + \frac{1}{2} = 1
4,808
z^2 - p^2 = (z - p)\cdot (p + z)
15,105
(b + x)\cdot (-x + b) = b^2 - x^2
10,920
972 = 3^5 \times 2^2
-1,203
(\dfrac17*(-9))/(8*1/3) = -\frac17*9*3/8
4,173
-7 \cdot 7 + 8^2 = -1^2 + 4^2
-8,026
\frac{-5 - 5 \cdot i}{-5 - i \cdot 5} \cdot \frac{i \cdot 30 - 10}{-5 + i \cdot 5} = \frac{i \cdot 30 - 10}{i \cdot 5 - 5}
-6,733
6/100 + \frac{1}{10} 0 = \dfrac{6}{100} + \dfrac{0}{100}
2,151
\left[255,391\right] = \left[136,255\right] = \emptyset = 17 \Rightarrow 17
28,686
5^2 + 10^2 = 2^2 + 11^2
22,669
53\cdot 4 = -5\cdot 2\cdot 4 + 7\cdot 9\cdot 4
23,330
\frac{1}{k!\cdot (n - k)!}\cdot n! = {n \choose k}
-25,398
\frac{\text{d}}{\text{d}z} \left(\dfrac{\sin{z}}{z * z}\right) = \frac{1}{z^3}*(\cos{z}*z - 2*\sin{z})
5,520
c = u\cdot a\cdot c + v\cdot b\cdot c = (u\cdot c + v\cdot b\cdot c/a)\cdot a
614
\frac{16}{0 + 1} = 9 + 7^{\frac{1}{2}} \times 7^{\frac{1}{2}}
10,016
0 = \left(3\cdot 6 + 2\cdot (-1)\right)^{1/2} + 2 + 6\cdot (-1)
9,485
\frac{1}{n + 2}*2*4^n = \frac{2^{2*n + 1}}{n + 2}
20,045
-2^{6 + (-1)}\cdot 6 = -192
10,794
1/2 + A_2 = 0 \Rightarrow A_2 = -1/2
4,063
h^{-f} = \dfrac{1}{h^f}
-4,127
\dfrac18*7 = \dfrac78
20,044
3! \cdot (3! + (-1)) \cdot ... \cdot 2 = (3!)!
-17,835
50 = 74 + 24*\left(-1\right)
8,740
b_1*a_1 + a_2*b_2 = a_2*b_2 + b_1*a_1
-18,406
\dfrac{-8\cdot y + y^2}{y^2 - y\cdot 16 + 64} = \frac{1}{(8\cdot (-1) + y)\cdot \left(y + 8\cdot (-1)\right)}\cdot y\cdot (8\cdot (-1) + y)
-10,408
3/3\cdot (-\frac{3}{n + 3}) = -\frac{1}{3\cdot n + 9}\cdot 9
-17,212
4/5 = \dfrac{1}{5}4
4,498
\frac{1}{\cos(x)} + \sin(x) = \frac{1}{\cos(x)}*(\sin\left(x\right)*\cos(x) + 1)
4,314
\frac{1}{\left(2*y + (-1)\right)^2} = \tfrac{1}{(2*(y - 1/2))^2} = \dfrac{\frac14}{(y - 1/2) * (y - 1/2)}
4,450
(2 \cdot n + 1) \cdot (n \cdot 3 + \left(-1\right)) = 6 \cdot n^2 + n + (-1)
-9,057
17.1\% = \tfrac{17.1}{100}
18,542
\sin(F \cdot 2) = \sin(F) \cdot \cos(F) \cdot 2
2,272
x_l - x \lt \nu \implies x_l \lt \nu + x
9,579
6/27*\frac56 = \dfrac{1}{27}5
-20,561
\frac31\cdot \dfrac{1}{4 - z\cdot 9}\cdot (4 - 9\cdot z) = \frac{-27\cdot z + 12}{-9\cdot z + 4}
-11,579
0 + 12 + i\cdot 4 = 12 + i\cdot 4
48,694
6\cdot2^2\cdot6=144
-18,281
\frac{m^2 - m \cdot 3}{12 + m^2 - m \cdot 7} = \frac{\left(3\left(-1\right) + m\right) m}{(3(-1) + m) (m + 4(-1))}
15,481
1 + x^2 = (x^2\cdot 42 + 42)/42
-9,386
-3*x^3 = -x*x*3*x
31,468
e^{-ix} = \cos(-x) + i\sin(-x) = \cos(x) - i\sin(x)
480
\frac{t}{s - t} + 1 = \frac{s}{-t + s}
-27,236
\sum_{k=1}^∞ \frac{(-11 + 5)^k}{k \times 6^k} \times (k + 2) = \sum_{k=1}^∞ \dfrac{1}{k \times 6^k} \times (-6)^k \times (k + 2) = \sum_{k=1}^∞ \dfrac{1}{k \times 6^k} \times (-1)^k \times 6^k \times (k + 2) = \sum_{k=1}^∞ \frac{(-1)^k}{k} \times (k + 2)
-20,151
-\frac{1}{1} 4 \frac{t*\left(-9\right)}{\left(-9\right) t} = 36 t/(t*(-9))
10,539
s_j b_j = s_j b_j
-17,208
\dfrac{1}{\cos^2{\theta}} = \frac{1}{\cos^2{\theta}}*\sin^2{\theta} + \frac{\cos^2{\theta}}{\cos^2{\theta}}
30,061
e^{-2\times \lambda - \lambda} = e^{-3\times \lambda}
8,013
0 = f^k = f^{k + 2\cdot (-1)}\cdot f \cdot f = f^{k + 2\cdot \left(-1\right)}\cdot f = f^{k + \left(-1\right)}
17,640
l^2 = (100 gl) * (100 gl) = 10000 gl^2
21,440
\sin\left(\operatorname{atan}(x)\right) = \dfrac{1}{\left(x^2 + 1\right)^{1/2}} \cdot x
16,689
\frac{x\cdot 6 + 9(-1)}{x + (-1)} = 3\frac{1}{x + (-1)}(3(-1) + x\cdot 2)
-18,992
29/45 = \dfrac{Z_s}{9*\pi}*9*\pi = Z_s
7,084
x^2 + 5x + 6 = (x+2)(x+3)
-19,536
\frac{1}{2*1/9}\frac{9}{2} = \dfrac129*9/2
-6,264
\frac{\dfrac{1}{5\cdot (-1) + t}}{(9 + t)\cdot 2}\cdot (5\cdot (-1) + t) = \frac{5\cdot (-1) + t}{(t + 5\cdot \left(-1\right))\cdot (t + 9)\cdot 2}
8,188
3\times (-1) + C^2 - 2\times C = (C + 1)\times \left(C + 3\times (-1)\right)
19,405
4*\left(-1\right) + l^2 = (2 + l)*(l + 2*(-1))
-23,214
1 = \frac13*3
7,553
16 (-1) + x^8 = (x \cdot x + 2(-1)) (4 + x^4) (x^2 + 2)
-13,594
(8 + 2 - 7*6)*10 = (8 + 2 + 42*(-1))*10 = (8 - 40)*10 = \left(8 + 40*(-1)\right)*10 = (-32)*10 = (-32)*10 = -320